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Pearson's chi-squared test

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8541: 7366: 8536:{\displaystyle {\begin{aligned}P(\chi _{P}^{2}(\{p_{i}\})>T)&\sim {\sqrt {\frac {2\pi n}{\prod _{i=1}^{m}2\pi k_{i}}}}\int _{\chi _{P}^{2}(\{{\sqrt {n}}x_{i}+np_{i}\},\{p_{i}\})>T}\left\{\prod _{i=1}^{m-1}{{\sqrt {n}}dx_{i}}\right\}\left\{\prod _{i=1}^{m-1}\left(1+{\frac {x_{i}}{{\sqrt {n}}p_{i}}}\right)^{-(np_{i}+{\sqrt {n}}x_{i})}\left(1-{\frac {\sum _{i=1}^{m-1}{x_{i}}}{{\sqrt {n}}p_{m}}}\right)^{-\left(np_{m}-{\sqrt {n}}\sum _{i=1}^{m-1}x_{i}\right)}\right\}\\&={\sqrt {\frac {2\pi n}{\prod _{i=1}^{m}\left(2\pi np_{i}+2\pi {\sqrt {n}}x_{i}\right)}}}\int _{\chi _{P}^{2}(\{{\sqrt {n}}x_{i}+np_{i}\},\{p_{i}\})>T}\left\{\prod _{i=1}^{m-1}{{\sqrt {n}}dx_{i}}\right\}\times \\&\qquad \qquad \times \left\{\prod _{i=1}^{m-1}\exp \left\exp \left\right\}\end{aligned}}} 13939: 1691: 13925: 13963: 13951: 9043: 4381:
check-ups. Specifically, individuals who have graduated from college or university attend routine check-ups at a higher proportion (31.52%) compared to those who have not graduated high school (8.44%). This finding may suggest that higher educational attainment is associated with a greater likelihood of engaging in health-promoting behaviors such as routine check-ups.
7075: 6651: 5297:; if its assumption of fixed marginal distributions is met it is substantially more accurate in obtaining a significance level, especially with few observations. In the vast majority of applications this assumption will not be met, and Fisher's exact test will be over conservative and not have correct coverage. 8576: 10094: 950:
A test of homogeneity compares the distribution of counts for two or more groups using the same categorical variable (e.g. choice of activity—college, military, employment, travel—of graduates of a high school reported a year after graduation, sorted by graduation year, to see if number of graduates
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For example, to test the hypothesis that a random sample of 100 people has been drawn from a population in which men and women are equal in frequency, the observed number of men and women would be compared to the theoretical frequencies of 50 men and 50 women. If there were 44 men in the sample and
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The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability of selection. Variants of the test have been developed for complex samples, such as where the data is weighted. Other
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For the test of independence, also known as the test of homogeneity, a chi-squared probability of less than or equal to 0.05 (or the chi-squared statistic being at or larger than the 0.05 critical point) is commonly interpreted by applied workers as justification for rejecting the null hypothesis
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The chi-squared test indicates a statistically significant association between the level of education completed and routine check-up attendance (chi2(3) = 14.6090, p = 0.002). The proportions suggest that as the level of education increases, so does the proportion of individuals attending routine
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The approximation to the chi-squared distribution breaks down if expected frequencies are too low. It will normally be acceptable so long as no more than 20% of the events have expected frequencies below 5. Where there is only 1 degree of freedom, the approximation is not reliable if expected
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The result about the numbers of degrees of freedom is valid when the original data are multinomial and hence the estimated parameters are efficient for minimizing the chi-squared statistic. More generally however, when maximum likelihood estimation does not coincide with minimum chi-squared
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When testing whether observations are random variables whose distribution belongs to a given family of distributions, the "theoretical frequencies" are calculated using a distribution from that family fitted in some standard way. The reduction in the degrees of freedom is calculated as
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In cases where the expected value, E, is found to be small (indicating a small underlying population probability, and/or a small number of observations), the normal approximation of the multinomial distribution can fail, and in such cases it is found to be more appropriate to use the
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Broadly similar arguments as above lead to the desired result, though the details are more involved. One may apply an orthogonal change of variables to turn the limiting summands in the test statistic into one fewer squares of i.i.d. standard normal random variables.
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A sample with a sufficiently large size is assumed. If a chi squared test is conducted on a sample with a smaller size, then the chi squared test will yield an inaccurate inference. The researcher, by using chi squared test on small samples, might end up committing a
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Adequate expected cell counts. Some require 5 or more, and others require 10 or more. A common rule is 5 or more in all cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero expected count. When this assumption is not met,
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By the normal approximation to a binomial this is the squared of one standard normal variate, and hence is distributed as chi-squared with 1 degree of freedom. Note that the denominator is one standard deviation of the Gaussian approximation, so can be written
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A 6-sided die is thrown 60 times. The number of times it lands with 1, 2, 3, 4, 5 and 6 face up is 5, 8, 9, 8, 10 and 20, respectively. Is the die biased, according to the Pearson's chi-squared test at a significance level of 95% and/or 99%?
9038:{\displaystyle P(\chi _{P}^{2}(\{p_{i}\})>T)\sim {\frac {1}{\sqrt {(2\pi )^{m-1}\prod _{i=1}^{m}p_{i}}}}\int _{\chi _{P}^{2}(\{{\sqrt {n}}x_{i}+np_{i}\},\{p_{i}\})>T}\left\{\prod _{i=1}^{m-1}dx_{i}\right\}\prod _{i=1}^{m-1}\exp \left} 6404: 5854:
So as consistent with the meaning of the chi-squared distribution, we are measuring how probable the observed number of standard deviations away from the mean is under the Gaussian approximation (which is a good approximation for large
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degrees of freedom and the selected confidence level (one-sided, since the test is only in one direction, i.e. is the test value greater than the critical value?), which in many cases gives a good approximation of the distribution of
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cells. A simple application is to test the hypothesis that, in the general population, values would occur in each cell with equal frequency. The "theoretical frequency" for any cell (under the null hypothesis of a
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frequencies are below 10. In this case, a better approximation can be obtained by reducing the absolute value of each difference between observed and expected frequencies by 0.5 before squaring; this is called
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of observing this difference (or a more extreme difference than this) if men and women are equally numerous in the population is approximately 0.23. This probability is higher than conventional criteria for
7355: 365: 5849: 465: 11123:"On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling" 751: 7371: 1682:, there would be five degrees of freedom because there are six categories or parameters (each number); the number of times the die is rolled does not influence the number of degrees of freedom. 6258: 4508: 577:
If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.
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Sustain or reject the null hypothesis that the observed frequency distribution is the same as the theoretical distribution based on whether the test statistic exceeds the critical value of
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is sufficiently large, the above binomial distribution may be approximated by a Gaussian (normal) distribution and thus the Pearson test statistic approximates a chi-squared distribution,
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The observations are always assumed to be independent of each other. This means chi-squared cannot be used to test correlated data (like matched pairs or panel data). In those cases,
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is the number of parameters in the model adjusted to make the model best fit the observations: The number of categories reduced by the number of fitted parameters in the distribution.
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A simple example is testing the hypothesis that an ordinary six-sided dice is "fair" (i. e., all six outcomes are equally likely to occur). In this case, the observed data is
256: 9051: 10211: 6394: 6021: 4099: 10403: 6646:{\displaystyle P(\chi _{P}^{2}(\{p_{i}\})>T)=\sum _{\{k_{i}\}|\chi _{P}^{2}(\{k_{i}\},\{p_{i}\})>T}{\frac {n!}{k_{1}!\cdots k_{m}!}}\prod _{i=1}^{m}{p_{i}}^{k_{i}}} 11568: 11013: 10153: 9662: 9603: 6339: 6054: 5919: 5122: 3997: 3969: 1291: 1202: 1175: 1145: 1109: 995: 917: 58: 6782: 11033: 10362: 10334: 7259: 7232: 6685: 6081: 5989: 4349: 4134: 4028: 1517: 1453: 1260: 1229: 4769: 368: 10920:
If the null hypothesis is true (i.e., men and women are chosen with equal probability), the test statistic will be drawn from a chi-squared distribution with one
10237: 10179: 10126: 9629: 6365: 4375: 1645: 1619: 1593: 1567: 1426: 6752: 10803: 10306: 10089:{\displaystyle P(\chi _{P}^{2}(\{p_{i}\})>T)\sim C\int _{\sum _{i=1}^{m-1}y_{i}^{2}>T}\left\{\prod _{i=1}^{m-1}dy_{i}\right\}\prod _{i=1}^{m-1}\exp \left} 9516: 8568: 7205: 6725: 6705: 5962: 5942: 4531: 4215: 4195: 4155: 4054: 1665: 1537: 1473: 1345: 1325: 135: 4539: 4652: 1293:
value, then no clear conclusion can be reached, and the null hypothesis is sustained (we fail to reject the null hypothesis), though not necessarily accepted.
6089: 9489:{\displaystyle -{\frac {1}{2}}\sum _{i,j=1}^{m-1}x_{i}A_{ij}x_{j},\qquad i,j=1,\cdots ,m-1,\quad A_{ij}={\tfrac {\delta _{ij}}{p_{i}}}+{\tfrac {1}{p_{m}}}.} 5548: 958:, are independent of each other (e.g. polling responses from people of different nationalities to see if one's nationality is related to the response). 13989: 9670: 7086: 1266:
a difference between the distributions) can be accepted, both with the selected level of confidence. If the test statistic falls below the threshold
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table, the tabular value refers to the sum of the squared variables each divided by the expected outcomes. For the present example, this means
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The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions:
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David E. Bock, Paul F. Velleman, Richard D. De Veaux (2007). "Stats, Modeling the World," pp. 606-627, Pearson Addison Wesley, Boston,
4390: 4226: 5699: 3931:{\displaystyle \chi ^{2}=\sum _{i=1}^{n}{\frac {(O_{i}-E_{i})^{2}}{E_{i}}}=N\sum _{i=1}^{n}{\frac {\left(O_{i}/N-p_{i}\right)^{2}}{p_{i}}}} 4423:
In this case, an "observation" consists of the values of two outcomes and the null hypothesis is that the occurrence of these outcomes is
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In the above example the hypothesised probability of a male observation is 0.5, with 100 samples. Thus we expect to observe 50 males.
7267: 10965:-based test statistic. When the total sample size is small, it is necessary to use an appropriate exact test, typically either the 13113: 9203:, is precisely the argument of the exponent (except for the -1/2; note that the final term in the exponent's argument is equal to 4166: 13552: 10265:
The null hypothesis is that the die is unbiased, hence each number is expected to occur the same number of times, in this case,
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to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many
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corresponds to the variables having an association or relationship where the structure of this relationship is not specified.
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of both theoretical and empirical distributions are unnormalised counts, and for a chi-squared test the total sample sizes
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be the number of observations from the sample that are in the first cell. The Pearson test statistic can be expressed as
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This approximation arises as the true distribution, under the null hypothesis, if the expected value is given by a
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independent normally distributed variables of zero mean and unit variance will be greater than T, namely that
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A test of independence assesses whether observations consisting of measures on two variables, expressed in a
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is the number of parameters used in fitting the distribution. For instance, when checking a three-parameter
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test. The above reasons for the above issues become apparent when the higher order terms are investigated.
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The experimental sum of 13.4 is between the critical values of 97.5% and 99% significance or confidence (
4408: 863: 13672: 13644: 13639: 13387: 13146: 13052: 13032: 12940: 12651: 12469: 11952: 11824: 10409: 9521: 9196:{\displaystyle \chi _{P}^{2}(\{k_{i}\},\{p_{i}\})=\chi _{P}^{2}(\{{\sqrt {n}}x_{i}+np_{i}\},\{p_{i}\})} 4439:
columns in the table, the "theoretical frequency" for a cell, given the hypothesis of independence, is
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corresponds to the number of independent groups (i.e. columns in the associated contingency table).
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Loukas, Orestis; Chung, Ho Ryun (2022). "Entropy-based Characterization of Modeling Constraints".
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The chi-squared distribution is then integrated on the right of the statistic value to obtain the
4061: 1569:, and when checking a normal distribution (where the parameters are mean and standard deviation), 574:. The p-value of the test statistic is computed either numerically or by looking it up in a table. 13796: 13409: 13349: 13286: 12924: 12908: 12646: 12508: 12498: 12348: 12262: 11083: 10982: 10368: 11044: 13834: 13764: 13557: 13494: 13249: 13136: 12133: 12030: 11937: 11816: 11715: 11546: 11066: 10991: 10974: 10782: 10131: 9634: 9575: 6317: 6314:
be the distribution of this statistic. We will show that the latter probability approaches the
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In the special case where there are only two cells in the table, the expected values follow a
13859: 13801: 13744: 13570: 13463: 13372: 13098: 12982: 12841: 12833: 12723: 12715: 12530: 12426: 12404: 12363: 12328: 12295: 12241: 12216: 12171: 12110: 12070: 11872: 11695: 11498: 11471: 11060: 10962: 6728: 5356: 5340: 4901:{\displaystyle \chi ^{2}=\sum _{i=1}^{r}\sum _{j=1}^{c}{(O_{i,j}-E_{i,j})^{2} \over E_{i,j}}} 1042:
corresponds to the number of categories (i.e. rows in the associated contingency table), and
79: 11430:"Seven Proofs of the Pearson Chi-Squared Independence Test and its Graphical Interpretation" 6757: 13782: 13357: 13306: 13282: 13244: 13162: 13141: 13093: 12972: 12950: 12919: 12828: 12705: 12656: 12574: 12547: 12503: 12459: 12221: 11997: 11877: 11333: 11018: 10703:
This is the experimental result whose unlikeliness (with a fair die) we wish to estimate.
10340: 10312: 7237: 7210: 6663: 6059: 5967: 5243: 4322: 4112: 4006: 1490: 1431: 1238: 1207: 4427:. Each observation is allocated to one cell of a two-dimensional array of cells (called a 8: 13929: 13854: 13777: 13458: 13222: 13215: 13177: 13085: 13065: 13037: 12770: 12636: 12631: 12621: 12613: 12431: 12392: 12282: 12272: 12181: 11960: 11916: 11834: 11759: 11661: 10216: 10158: 10105: 9608: 6344: 4632:{\displaystyle p_{i\cdot }={\frac {O_{i\cdot }}{N}}=\sum _{j=1}^{c}{\frac {O_{i,j}}{N}},} 4396: 4354: 1624: 1598: 1572: 1546: 1405: 11337: 6734: 4742:{\displaystyle p_{\cdot j}={\frac {O_{\cdot j}}{N}}=\sum _{i=1}^{r}{\frac {O_{i,j}}{N}}} 4319:
estimation, the distribution will lie somewhere between a chi-squared distribution with
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difference between the distributions) can be rejected, and the alternative hypothesis (
1067: 120: 652:, the number of times that the dice has fallen on each number. The null hypothesis is 13938: 13849: 13819: 13811: 13631: 13622: 13547: 13478: 13334: 13319: 13294: 13182: 13123: 12989: 12977: 12603: 12520: 12464: 12387: 12231: 12153: 11932: 11806: 11639: 11508: 11459: 11351: 11285: 11199: 5875: 5286: 4428: 1690: 955: 951:
choosing a given activity has changed from class to class, or from decade to decade).
11455: 5683:{\displaystyle {\frac {(O_{1}-np)^{2}}{np}}+{\frac {(n-O_{1}-n(1-p))^{2}}{n(1-p)}},} 5188:, i.e. only if the expected and true number of observations are equal in all cells. 1478:
One specific example of its application would be its application for log-rank test.
13874: 13829: 13593: 13580: 13473: 13448: 13382: 13314: 13192: 12800: 12693: 12626: 12539: 12486: 12305: 12176: 11970: 11854: 11769: 11736: 11611: 11581: 11443: 11341: 11275: 11267: 11134: 10924:(because if the male frequency is known, then the female frequency is determined). 8547: 83: 71: 67: 63: 20: 11395:"A Bayesian Formulation for Exploratory Data Analysis and Goodness-of-Fit Testing" 11049: 4411:
for the population probability is the observed probability, and one may compute a
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Loukas, Orestis; Chung, Ho Ryun (2023). "Total Empiricism: Learning from Data".
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Fitting the model of "independence" reduces the number of degrees of freedom by
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in 1900. In contexts where it is important to improve a distinction between the
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Evaluates how likely it is that any difference between data sets arose by chance
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For all three tests, the computational procedure includes the following steps:
99: 11586: 11542: 11138: 13983: 13897: 13864: 13727: 13688: 13499: 13468: 12932: 12886: 12491: 12193: 12020: 11784: 11779: 11355: 10966: 10910:{\displaystyle \chi ^{2}={(44-50)^{2} \over 50}+{(56-50)^{2} \over 50}=1.44.} 9801:
This linear change of variables merely multiplies the integral by a constant
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The degrees of freedom are not based on the number of observations as with a
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Let us now prove that the distribution indeed approaches asymptotically the
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be Pearson's cumulative test statistic for such a configuration, and let
3971:= Pearson's cumulative test statistic, which asymptotically approaches a 1078: 4391:
Categorical distribution § Bayesian inference using conjugate prior
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Pearson's chi-squared test is used to assess three types of comparison:
853:{\displaystyle \chi ^{2}:=\sum _{i=1}^{6}{\frac {(O_{i}-N/6)^{2}}{N/6}}} 567:{\displaystyle \chi ^{2}:=\sum _{i}{\frac {(O_{i}-Np_{i})^{2}}{Np_{i}}}} 12728: 12208: 11908: 11839: 11789: 11764: 11684: 11623: 10213:
the distribution of Pearson's chi approaches the chi distribution with
87: 4305:{\displaystyle \chi ^{2}=\sum _{i=1}^{n}{\frac {O_{i}^{2}}{E_{i}}}-N.} 12881: 12733: 12353: 12148: 12060: 12045: 12040: 12005: 5772:{\displaystyle \left({\frac {O_{1}-np}{\sqrt {np(1-p)}}}\right)^{2}.} 1027:
is the number of observation categories recognized by the model, and
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of both these distributions (sums of all cells of the corresponding
4760:" refers to absolute numbers rather than already normalized values. 12397: 12015: 11892: 11887: 11882: 11438: 11346: 11321: 11179: 11158: 9572:. It is therefore possible to make a linear change of variables in 4756:
ignoring the row attribute (fraction of column totals). The term "
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is the total sample size (the sum of all cells in the table), and
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degrees of freedom (See for instance Chernoff and Lehmann, 1954).
13902: 13603: 10764: 10694:{\displaystyle {\chi ^{2}}=25/10+4/10+1/10+4/10+0/10+100/10=13.4} 5878:
containing two rows and two columns, the test is equivalent to a
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that the row variable is independent of the column variable. The
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the probability of an observation to fall in the i-th cell, for
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distribution as the number of observations approaches infinity.
13824: 12805: 12779: 12759: 12010: 11801: 11071: 10958: 7350:{\displaystyle k_{m}=np_{m}-{\sqrt {n}}\sum _{i=1}^{m-1}x_{i},} 5879: 1061:
corresponds to the number of categories in the second variable.
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Before the experiment, the experimenter fixes a certain number
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corresponds to the number of categories in one variable, and
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ignoring the column attribute (fraction of row totals), and
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sum of squared deviations between observed and theoretical
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procedures whose results are evaluated by reference to the
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The chi-squared statistic can then be used to calculate a
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A test of goodness of fit establishes whether an observed
360:{\displaystyle \mathrm {Multinomial} (N;p_{1},...,p_{n})} 6656:
We will use a procedure similar to the approximation in
5844:{\displaystyle {\frac {(O_{1}-\mu )^{2}}{\sigma ^{2}}}.} 4315:
This result is the consequence of the Binomial theorem.
4418: 460:{\displaystyle \mathrm {Categorical} (p_{1},...,p_{n})} 9465: 9433: 5382: 1708:
Upper-tail critical values of chi-square distribution
1177:. If the test statistic exceeds the critical value of 11549: 11021: 10994: 10822: 10791: 10588: 10577:
Upper-tail critical values of chi-square distribution
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Autoregressive conditional heteroskedasticity (ARCH)
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The null distribution of the Pearson statistic with
4220:
The chi-squared statistic can be also calculated as
11052:– a measure of correlation for the chi-squared test 10770: 13028: 11562: 11027: 11007: 10909: 10797: 10693: 10451: 10397: 10356: 10328: 10300: 10231: 10205: 10173: 10147: 10120: 10088: 9790: 9656: 9623: 9597: 9560: 9510: 9488: 9275: 9195: 9037: 8562: 8535: 7349: 7253: 7226: 7199: 7176: 7069: 6776: 6746: 6719: 6699: 6679: 6645: 6388: 6359: 6333: 6306: 6253:{\displaystyle \chi _{P}^{2}(\{k_{i}\},\{p_{i}\})} 6252: 6176: 6075: 6048: 6015: 5983: 5956: 5936: 5913: 5843: 5771: 5682: 5524: 5409: 5180: 5116: 5086: 4900: 4741: 4631: 4525: 4502: 4369: 4343: 4304: 4209: 4189: 4149: 4128: 4093: 4048: 4022: 3991: 3963: 3930: 1659: 1639: 1613: 1587: 1561: 1531: 1511: 1467: 1447: 1420: 1391: 1339: 1319: 1285: 1254: 1223: 1196: 1169: 1139: 1103: 989: 911: 885: 852: 745: 644: 566: 459: 359: 250: 207: 129: 52: 11598:(1983). "Karl Pearson and the Chi-Squared Test". 11243:. National Institute of Standards and Technology. 11237:"Critical Values of the Chi-Squared Distribution" 1685: 1297: 13981: 11630: 11400:. International Statistical Review. p. 375. 10283:= 10. The outcomes can be tabulated as follows: 5869: 4503:{\displaystyle E_{i,j}=Np_{i\cdot }p_{\cdot j},} 1678:. For example, if testing for a fair, six-sided 1302: 13114:Multivariate adaptive regression splines (MARS) 11537: 11241:NIST/SEMATECH e-Handbook of Statistical Methods 5293:A test that relies on different assumptions is 1402:and the reduction in the degrees of freedom is 11521:Link is to a fragmentary edition of March 1996 11418:. Pearson's Theorem. Retrieved 21 March 2007. 8550:the logarithm and taking the leading terms in 5410:{\displaystyle O\ \sim \ {\mbox{Bin}}(n,p),\,} 5343:says this distribution tends toward a certain 1428:, notionally because the observed frequencies 11669: 11427: 6056:the configuration where for each i there are 5211:, minus the reduction in degrees of freedom, 4197:, minus the reduction in degrees of freedom, 265:is that the count numbers are sampled from a 11543:"The Use of Maximum Likelihood Estimates in 11080:, earlier statistic, replaced by chi-squared 10102:This is the probability that squared sum of 9852: 9839: 9651: 9638: 9592: 9579: 9187: 9174: 9168: 9132: 9105: 9092: 9086: 9073: 8778: 8765: 8759: 8723: 8617: 8604: 8112: 8099: 8093: 8057: 7567: 7554: 7548: 7512: 7411: 7398: 6925: 6912: 6906: 6893: 6867: 6854: 6831: 6818: 6539: 6526: 6520: 6507: 6481: 6468: 6445: 6432: 6298: 6285: 6244: 6231: 6225: 6212: 6043: 6030: 94:. Its properties were first investigated by 11172: 11151: 10184:We have thus shown that at the limit where 9276:{\displaystyle (k_{m}-np_{m})^{2}/(np_{m})} 4101:= the expected (theoretical) count of type 11714: 11676: 11662: 5181:{\displaystyle O_{i,j}=E_{i,j}\forall i,j} 367:. That is, the underlying data is sampled 12327: 11585: 11437: 11345: 11279: 11178: 11157: 11015:test is a low order approximation of the 10716:Probability less than the critical value 6083:observations in the i-th cell. Note that 5521: 5427:= probability, under the null hypothesis, 5406: 1720:Probability less than the critical value 1385: 13990:Statistical tests for contingency tables 11594: 11504:Probability Theory: The Logic of Science 11428:Benhamou, Eric; Melot, Valentin (2018). 11370:"The Cash Statistic and Forward Fitting" 6307:{\displaystyle \chi _{P}^{2}(\{p_{i}\})} 4752:is the fraction of observations of type 4642:is the fraction of observations of type 4407:. If one took a uniform prior, then the 1701:on the x-axis and P-value on the y-axis. 1689: 947:differs from a theoretical distribution. 19:For broader coverage of this topic, see 11117: 11063:, another measure of the quality of fit 10931:for 1 degree of freedom shows that the 5433:= number of observations in the sample. 1392:{\displaystyle E_{i}={\frac {N}{n}}\,,} 645:{\displaystyle (O_{1},O_{2},...,O_{6})} 208:{\displaystyle (O_{1},O_{2},...,O_{n})} 102:and its distribution, names similar to 13982: 13640:Kaplan–Meier estimator (product limit) 11497: 11253: 11194: 11192: 11190: 10981:which do not make this assumption are 5307:Derivation using Central Limit Theorem 1481: 1066:Select a desired level of confidence ( 1051:df = (Rows − 1)×(Cols − 1) 1036:df = (Rows − 1)×(Cols − 1) 13713: 13280: 13027: 12326: 12096: 11713: 11657: 11574:The Annals of Mathematical Statistics 11256:"The chi-square test of independence" 10181:degrees of freedom is larger than T. 4030:= the number of observations of type 13950: 13650:Accelerated failure time (AFT) model 11507:. C. University Press. p. 298. 11319: 10244:An alternative derivation is on the 5332: âˆ’ 1) degrees of freedom. 4419:Testing for statistical independence 4167:comparing the value of the statistic 13962: 13245:Analysis of variance (ANOVA, anova) 12097: 11608:International Statistical Institute 11404: 11187: 10256: 4763:The value of the test-statistic is 4157:= the number of cells in the table. 3743:The value of the test-statistic is 13: 13340:Cochran–Mantel–Haenszel statistics 11966:Pearson product-moment correlation 11022: 10197: 6380: 5693:which can in turn be expressed as 5166: 4384: 886:{\displaystyle \chi ^{2}>11.07} 690: 687: 684: 681: 678: 675: 672: 669: 666: 663: 660: 412: 409: 406: 403: 400: 397: 394: 391: 388: 385: 382: 306: 303: 300: 297: 294: 291: 288: 285: 282: 279: 276: 14: 14011: 11306:Discovering Statistics Using SPSS 11303: 10951:Yates's correction for continuity 10452:{\displaystyle (O_{i}-E_{i})^{2}} 9561:{\displaystyle (m-1)\times (m-1)} 9286:This argument can be written as: 4415:around this or another estimate. 13961: 13949: 13937: 13924: 13923: 13714: 11600:International Statistical Review 10771:Chi-squared goodness of fit test 5345:multivariate normal distribution 5207:is equal to the number of cells 4177:is equal to the number of cells 251:{\displaystyle \sum _{i}O_{i}=N} 13599:Least-squares spectral analysis 11491: 11421: 11387: 11362: 11056:Degrees of freedom (statistics) 9415: 9378: 8196: 8195: 7143: 6136: 6130: 5944:be the number of observations, 5320:columns is approximated by the 5203: âˆ’ 1. The number of 1327:observations are divided among 1111:to the critical value from the 1019:For a test of goodness-of-fit, 966:Calculate the chi-squared test 113:test. The setup is as follows: 84:portmanteau test in time series 12580:Mean-unbiased minimum-variance 11683: 11636:A guide to chi-squared testing 11313: 11310:for assumptions on Chi Square. 11296: 11247: 11229: 11208: 11166: 11145: 11111: 10886: 10873: 10852: 10839: 10440: 10413: 10194: 9864: 9855: 9836: 9818: 9555: 9543: 9537: 9525: 9270: 9254: 9240: 9210: 9190: 9129: 9108: 9070: 8781: 8720: 8651: 8641: 8629: 8620: 8601: 8583: 8115: 8054: 7762: 7726: 7570: 7509: 7423: 7414: 7395: 7377: 6928: 6890: 6871: 6843: 6834: 6815: 6797: 6542: 6504: 6485: 6457: 6448: 6429: 6411: 6377: 6301: 6282: 6247: 6209: 5874:When the test is applied to a 5816: 5796: 5750: 5738: 5671: 5659: 5645: 5641: 5629: 5604: 5578: 5555: 5515: 5512: 5500: 5482: 5471: 5459: 5400: 5388: 5339:. For large sample sizes, the 5234: 5011: 4984: 4870: 4831: 4056:= total number of observations 3817: 3790: 1686:Calculating the test-statistic 1541:Generalized gamma distribution 1298:Test for fit of a distribution 825: 797: 740: 694: 639: 588: 537: 507: 454: 416: 354: 310: 202: 151: 1: 13893:Geographic information system 13109:Simultaneous equations models 11530: 11410:Statistics for Applications. 11254:McHugh, Mary (15 June 2013). 11099:Reduced chi-squared statistic 11094:Minimum chi-square estimation 10246:multinomial distribution page 10206:{\displaystyle n\to \infty ,} 7187:we may approximate for large 6389:{\displaystyle n\to \infty .} 6016:{\displaystyle 1\leq i\leq m} 5885: 5870:Two-by-two contingency tables 5300: 5264:. For small sample sizes the 1667:is the number of categories. 1350:discrete uniform distribution 1303:Discrete uniform distribution 1081:) for the result of the test. 13076:Coefficient of determination 12687:Uniformly most powerful test 6660:. Contributions from small 5350: 4094:{\displaystyle E_{i}=Np_{i}} 1049:For a test of independence, 106:test or statistic are used. 7: 13645:Proportional hazards models 13589:Spectral density estimation 13571:Vector autoregression (VAR) 13005:Maximum posterior estimator 12237:Randomized controlled trial 11038: 10943: 10398:{\displaystyle O_{i}-E_{i}} 10251: 6687:are of subleading order in 6398:For any arbitrary value T: 4409:maximum likelihood estimate 1034:For a test of homogeneity, 10: 14016: 14000:Statistical approximations 13405:Multivariate distributions 11825:Average absolute deviation 11570:Tests for Goodness of Fit" 10774: 5249:forms can be used such as 4399:, one would instead use a 4388: 1647:degrees of freedom, where 1455:are constrained to sum to 470:The Pearson's chi-squared 467:over the given categories. 29:Pearson's chi-squared test 18: 13919: 13873: 13810: 13763: 13726: 13722: 13709: 13681: 13663: 13630: 13621: 13579: 13526: 13487: 13436: 13427: 13393:Structural equation model 13348: 13305: 13301: 13276: 13235: 13201: 13155: 13122: 13084: 13051: 13047: 13023: 12963: 12872: 12791: 12755: 12746: 12729:Score/Lagrange multiplier 12714: 12667: 12612: 12538: 12529: 12339: 12335: 12322: 12281: 12255: 12207: 12162: 12144:Sample size determination 12109: 12105: 12092: 11996: 11951: 11925: 11907: 11863: 11815: 11735: 11726: 11722: 11709: 11691: 11563:{\displaystyle \chi ^{2}} 11541:; Lehmann, E. L. (1954). 11326:The Astrophysical Journal 11139:10.1080/14786440009463897 11008:{\displaystyle \chi ^{2}} 10988:It can be shown that the 10715: 10708: 10564: 10148:{\displaystyle \chi ^{2}} 9657:{\displaystyle \{y_{i}\}} 9598:{\displaystyle \{x_{i}\}} 6658:de Moivre–Laplace theorem 6334:{\displaystyle \chi ^{2}} 6049:{\displaystyle \{k_{i}\}} 5914:{\displaystyle \chi ^{2}} 5256:Sample size (whole table) 5215:, which reduces to ( 5117:{\displaystyle \chi ^{2}} 4425:statistically independent 3992:{\displaystyle \chi ^{2}} 3964:{\displaystyle \chi ^{2}} 1719: 1712: 1707: 1286:{\displaystyle \chi ^{2}} 1197:{\displaystyle \chi ^{2}} 1170:{\displaystyle \chi ^{2}} 1140:{\displaystyle \chi ^{2}} 1104:{\displaystyle \chi ^{2}} 990:{\displaystyle \chi ^{2}} 912:{\displaystyle p<0.05} 53:{\displaystyle \chi ^{2}} 13888:Environmental statistics 13410:Elliptical distributions 13203:Generalized linear model 13132:Simple linear regression 12902:Hodges–Lehmann estimator 12359:Probability distribution 12268:Stochastic approximation 11830:Coefficient of variation 11634:; Nikulin, M.S. (1996). 11432:. SSRN (preprint): 5-6. 11104: 10938:statistical significance 10929:chi-squared distribution 7234:by an integral over the 5964:the number of cells and 5337:multinomial distribution 5322:chi-squared distribution 5289:may be more appropriate. 4171:chi-squared distribution 1695:Chi-squared distribution 1352:) is thus calculated as 1113:chi-squared distribution 1021:df = Cats − Params 922: 860:. As detailed below, if 373:categorical distribution 267:multinomial distribution 92:chi-squared distribution 13548:Cross-correlation (XCF) 13156:Non-standard predictors 12590:Lehmann–ScheffĂ© theorem 12263:Adaptive clinical trial 11587:10.1214/aoms/1177728726 10983:uniformly more powerful 10809:) have to be the same. 10099:Where C is a constant. 9518:is a regular symmetric 6367:degrees of freedom, as 1204:, the null hypothesis ( 1077:, or the corresponding 13944:Mathematics portal 13765:Engineering statistics 13673:Nelson–Aalen estimator 13250:Analysis of covariance 13137:Ordinary least squares 13061:Pearson product-moment 12465:Statistical functional 12376:Empirical distribution 12209:Controlled experiments 11938:Frequency distribution 11716:Descriptive statistics 11564: 11479:Cite journal requires 11374:hesperia.gsfc.nasa.gov 11127:Philosophical Magazine 11029: 11009: 10911: 10799: 10695: 10453: 10399: 10358: 10330: 10302: 10233: 10207: 10175: 10149: 10122: 10090: 10060: 10004: 9959: 9904: 9792: 9769: 9706: 9658: 9625: 9599: 9562: 9512: 9490: 9341: 9277: 9197: 9039: 9006: 8919: 8868: 8823: 8686: 8564: 8537: 8479: 8417: 8231: 8157: 7974: 7906: 7808: 7671: 7612: 7468: 7351: 7333: 7255: 7228: 7201: 7178: 7071: 7046: 6959: 6784:to get the following: 6778: 6777:{\displaystyle k_{i}!} 6748: 6721: 6701: 6681: 6647: 6616: 6390: 6361: 6335: 6308: 6254: 6178: 6157: 6113: 6077: 6050: 6017: 5985: 5958: 5938: 5915: 5845: 5773: 5684: 5526: 5411: 5229:alternative hypothesis 5182: 5118: 5088: 4902: 4827: 4806: 4743: 4715: 4633: 4602: 4527: 4504: 4401:Dirichlet distribution 4371: 4345: 4306: 4263: 4211: 4191: 4151: 4130: 4095: 4050: 4024: 3993: 3965: 3932: 3865: 3786: 1702: 1661: 1641: 1621:. Thus, there will be 1615: 1589: 1563: 1533: 1513: 1469: 1449: 1422: 1393: 1341: 1321: 1287: 1256: 1225: 1198: 1171: 1141: 1105: 1053:, where in this case, 991: 945:frequency distribution 913: 887: 854: 793: 747: 646: 568: 461: 361: 252: 209: 131: 54: 13860:Population statistics 13802:System identification 13536:Autocorrelation (ACF) 13464:Exponential smoothing 13378:Discriminant analysis 13373:Canonical correlation 13237:Partition of variance 13099:Regression validation 12943:(Jonckheere–Terpstra) 12842:Likelihood-ratio test 12531:Frequentist inference 12443:Location–scale family 12364:Sampling distribution 12329:Statistical inference 12296:Cross-sectional study 12283:Observational studies 12242:Randomized experiment 12071:Stem-and-leaf display 11873:Central limit theorem 11565: 11061:Deviance (statistics) 11030: 11028:{\displaystyle \Psi } 11010: 10912: 10800: 10781:In this context, the 10696: 10454: 10400: 10359: 10357:{\displaystyle E_{i}} 10331: 10329:{\displaystyle O_{i}} 10303: 10234: 10208: 10176: 10150: 10123: 10091: 10034: 9978: 9933: 9878: 9793: 9743: 9674: 9659: 9626: 9600: 9563: 9513: 9491: 9309: 9278: 9198: 9040: 8980: 8893: 8842: 8797: 8666: 8565: 8538: 8453: 8391: 8205: 8131: 7954: 7880: 7782: 7645: 7586: 7448: 7352: 7307: 7256: 7254:{\displaystyle x_{i}} 7229: 7227:{\displaystyle k_{i}} 7202: 7179: 7072: 7026: 6939: 6779: 6749: 6722: 6702: 6682: 6680:{\displaystyle k_{i}} 6648: 6596: 6391: 6362: 6336: 6309: 6255: 6179: 6137: 6093: 6078: 6076:{\displaystyle k_{i}} 6051: 6018: 5986: 5984:{\displaystyle p_{i}} 5959: 5939: 5916: 5846: 5774: 5685: 5527: 5412: 5357:binomial distribution 5341:central limit theorem 5183: 5119: 5089: 4903: 4807: 4786: 4744: 4695: 4634: 4582: 4528: 4505: 4389:Further information: 4372: 4346: 4344:{\displaystyle n-1-p} 4307: 4243: 4212: 4192: 4152: 4131: 4129:{\displaystyle p_{i}} 4109:in the population is 4096: 4051: 4025: 4023:{\displaystyle O_{i}} 3994: 3966: 3933: 3845: 3766: 1693: 1662: 1642: 1616: 1590: 1564: 1534: 1514: 1512:{\displaystyle p=s+1} 1470: 1450: 1448:{\displaystyle O_{i}} 1423: 1394: 1342: 1322: 1288: 1257: 1255:{\displaystyle H_{1}} 1226: 1224:{\displaystyle H_{0}} 1199: 1172: 1142: 1106: 1016:, of that statistic. 992: 914: 888: 855: 773: 748: 647: 569: 462: 362: 253: 210: 132: 55: 13783:Probabilistic design 13368:Principal components 13211:Exponential families 13163:Nonlinear regression 13142:General linear model 13104:Mixed effects models 13094:Errors and residuals 13071:Confounding variable 12973:Bayesian probability 12951:Van der Waerden test 12941:Ordered alternative 12706:Multiple comparisons 12585:Rao–Blackwellization 12548:Estimating equations 12504:Statistical distance 12222:Factorial experiment 11755:Arithmetic-Geometric 11547: 11448:10.2139/ssrn.3239829 11272:10.11613/BM.2013.018 11045:Chi-squared nomogram 11019: 10992: 10927:Consultation of the 10820: 10789: 10586: 10410: 10369: 10341: 10313: 10292: 10239:degrees of freedom. 10217: 10188: 10159: 10132: 10106: 9812: 9671: 9635: 9609: 9576: 9522: 9502: 9293: 9207: 9052: 8577: 8554: 7367: 7268: 7238: 7211: 7191: 7087: 7080:By substituting for 6791: 6758: 6735: 6711: 6691: 6664: 6405: 6371: 6345: 6318: 6264: 6191: 6090: 6060: 6027: 5995: 5968: 5948: 5928: 5898: 5790: 5700: 5549: 5451: 5366: 5244:Simple random sample 5128: 5124:is 0 if and only if 5101: 4913: 4770: 4653: 4540: 4517: 4446: 4355: 4323: 4227: 4201: 4181: 4141: 4113: 4062: 4040: 4007: 3976: 3948: 3750: 1651: 1625: 1599: 1573: 1547: 1523: 1491: 1459: 1432: 1406: 1359: 1331: 1311: 1270: 1239: 1208: 1181: 1154: 1124: 1088: 997:, which resembles a 974: 897: 864: 757: 656: 585: 478: 378: 272: 219: 148: 121: 37: 13855:Official statistics 13778:Methods engineering 13459:Seasonal adjustment 13227:Poisson regressions 13147:Bayesian regression 13086:Regression analysis 13066:Partial correlation 13038:Regression analysis 12637:Prediction interval 12632:Likelihood interval 12622:Confidence interval 12614:Interval estimation 12575:Unbiased estimators 12393:Model specification 12273:Up-and-down designs 11961:Partial correlation 11917:Index of dispersion 11835:Interquartile range 11638:. New York: Wiley. 11338:1979ApJ...228..939C 11084:Mann–Whitney U test 11067:Fisher's exact test 10975:Fisher's exact test 10574:We then consult an 10232:{\displaystyle m-1} 10174:{\displaystyle m-1} 10121:{\displaystyle m-1} 10075: 9919: 9835: 9784: 9624:{\displaystyle m-1} 9128: 9069: 8936: 8719: 8600: 8053: 7508: 7394: 6889: 6814: 6707:and thus for large 6503: 6428: 6360:{\displaystyle m-1} 6281: 6208: 5295:Fisher's exact test 5271:Expected cell count 4397:Bayesian statistics 4370:{\displaystyle n-1} 4280: 1640:{\displaystyle n-p} 1614:{\displaystyle p=2} 1588:{\displaystyle p=3} 1562:{\displaystyle p=4} 1482:Other distributions 1421:{\displaystyle p=1} 137:of samples to take. 66:applied to sets of 13875:Spatial statistics 13755:Medical statistics 13655:First hitting time 13609:Whittle likelihood 13260:Degrees of freedom 13255:Multivariate ANOVA 13188:Heteroscedasticity 13000:Bayesian estimator 12965:Bayesian inference 12814:Kolmogorov–Smirnov 12699:Randomization test 12669:Testing hypotheses 12642:Tolerance interval 12553:Maximum likelihood 12448:Exponential family 12381:Density estimation 12341:Statistical theory 12301:Natural experiment 12247:Scientific control 12164:Survey methodology 11850:Standard deviation 11560: 11412:MIT OpenCourseWare 11025: 11005: 10971:contingency tables 10907: 10807:contingency tables 10795: 10691: 10449: 10395: 10354: 10326: 10298: 10229: 10203: 10171: 10145: 10118: 10086: 10061: 9905: 9821: 9788: 9770: 9654: 9621: 9595: 9568:matrix, and hence 9558: 9508: 9486: 9481: 9459: 9273: 9193: 9114: 9055: 9035: 8922: 8705: 8586: 8560: 8533: 8531: 8039: 7494: 7380: 7347: 7251: 7224: 7197: 7174: 7067: 6938: 6875: 6800: 6774: 6747:{\displaystyle n!} 6744: 6729:Stirling's formula 6717: 6697: 6677: 6643: 6552: 6489: 6414: 6386: 6357: 6341:distribution with 6331: 6304: 6267: 6250: 6194: 6174: 6073: 6046: 6013: 5981: 5954: 5934: 5911: 5841: 5769: 5680: 5522: 5407: 5386: 5277:Yates's correction 5251:purposive sampling 5205:degrees of freedom 5178: 5114: 5084: 4949: 4898: 4739: 4629: 4523: 4500: 4367: 4341: 4302: 4266: 4207: 4187: 4175:degrees of freedom 4147: 4126: 4091: 4046: 4020: 3989: 3961: 3928: 1703: 1657: 1637: 1611: 1585: 1559: 1529: 1509: 1465: 1445: 1418: 1389: 1337: 1317: 1283: 1252: 1221: 1194: 1167: 1137: 1101: 1068:significance level 1010:degrees of freedom 987: 909: 883: 850: 743: 642: 564: 503: 457: 357: 248: 231: 205: 127: 50: 13977: 13976: 13915: 13914: 13911: 13910: 13850:National accounts 13820:Actuarial science 13812:Social statistics 13705: 13704: 13701: 13700: 13697: 13696: 13632:Survival function 13617: 13616: 13479:Granger causality 13320:Contingency table 13295:Survival analysis 13272: 13271: 13268: 13267: 13124:Linear regression 13019: 13018: 13015: 13014: 12990:Credible interval 12959: 12958: 12742: 12741: 12558:Method of moments 12427:Parametric family 12388:Statistical model 12318: 12317: 12314: 12313: 12232:Random assignment 12154:Statistical power 12088: 12087: 12084: 12083: 11933:Contingency table 11903: 11902: 11770:Generalized/power 11514:978-0-521-59271-0 11320:Cash, W. (1979). 10922:degree of freedom 10899: 10865: 10798:{\displaystyle N} 10761: 10760: 10572: 10571: 10301:{\displaystyle i} 10027: 9511:{\displaystyle A} 9480: 9458: 9307: 9140: 8972: 8947: 8891: 8731: 8698: 8697: 8563:{\displaystyle n} 8512: 8499: 8389: 8337: 8324: 8272: 8164: 8065: 8032: 8031: 8013: 7878: 7841: 7828: 7750: 7715: 7702: 7619: 7520: 7487: 7486: 7305: 7207:the sum over the 7200:{\displaystyle n} 7138: 7137: 7065: 7064: 6992: 6849: 6720:{\displaystyle n} 6700:{\displaystyle n} 6594: 6463: 6134: 5957:{\displaystyle m} 5937:{\displaystyle n} 5876:contingency table 5836: 5754: 5753: 5675: 5596: 5480: 5457: 5385: 5380: 5374: 5223: âˆ’ 1). 5072: 4934: 4927: 4924: 4921: 4918: 4896: 4737: 4690: 4624: 4577: 4526:{\displaystyle N} 4429:contingency table 4291: 4210:{\displaystyle p} 4190:{\displaystyle n} 4150:{\displaystyle n} 4049:{\displaystyle N} 3926: 3837: 3741: 3740: 1660:{\displaystyle n} 1532:{\displaystyle s} 1468:{\displaystyle N} 1383: 1340:{\displaystyle n} 1320:{\displaystyle N} 956:contingency table 848: 562: 494: 222: 130:{\displaystyle N} 104:Pearson χ-squared 72:chi-squared tests 14007: 13965: 13964: 13953: 13952: 13942: 13941: 13927: 13926: 13830:Crime statistics 13724: 13723: 13711: 13710: 13628: 13627: 13594:Fourier analysis 13581:Frequency domain 13561: 13508: 13474:Structural break 13434: 13433: 13383:Cluster analysis 13330:Log-linear model 13303: 13302: 13278: 13277: 13219: 13193:Homoscedasticity 13049: 13048: 13025: 13024: 12944: 12936: 12928: 12927:(Kruskal–Wallis) 12912: 12897: 12852:Cross validation 12837: 12819:Anderson–Darling 12766: 12753: 12752: 12724:Likelihood-ratio 12716:Parametric tests 12694:Permutation test 12677:1- & 2-tails 12568:Minimum distance 12540:Point estimation 12536: 12535: 12487:Optimal decision 12438: 12337: 12336: 12324: 12323: 12306:Quasi-experiment 12256:Adaptive designs 12107: 12106: 12094: 12093: 11971:Rank correlation 11733: 11732: 11724: 11723: 11711: 11710: 11678: 11671: 11664: 11655: 11654: 11649: 11627: 11591: 11589: 11569: 11567: 11566: 11561: 11559: 11558: 11524: 11518: 11495: 11489: 11488: 11482: 11477: 11475: 11467: 11441: 11425: 11419: 11408: 11402: 11401: 11399: 11391: 11385: 11384: 11382: 11380: 11366: 11360: 11359: 11349: 11317: 11311: 11309: 11300: 11294: 11293: 11283: 11260:Biochemia Medica 11251: 11245: 11244: 11233: 11227: 11226: 11224: 11222: 11212: 11206: 11196: 11185: 11184: 11182: 11170: 11164: 11163: 11161: 11149: 11143: 11142: 11133:(302): 157–175. 11115: 11034: 11032: 11031: 11026: 11014: 11012: 11011: 11006: 11004: 11003: 10963:likelihood ratio 10916: 10914: 10913: 10908: 10900: 10895: 10894: 10893: 10871: 10866: 10861: 10860: 10859: 10837: 10832: 10831: 10804: 10802: 10801: 10796: 10706: 10705: 10700: 10698: 10697: 10692: 10681: 10667: 10653: 10639: 10625: 10611: 10600: 10599: 10598: 10458: 10456: 10455: 10450: 10448: 10447: 10438: 10437: 10425: 10424: 10404: 10402: 10401: 10396: 10394: 10393: 10381: 10380: 10363: 10361: 10360: 10355: 10353: 10352: 10335: 10333: 10332: 10327: 10325: 10324: 10307: 10305: 10304: 10299: 10286: 10285: 10282: 10280: 10279: 10274: 10271: 10257:Fairness of dice 10238: 10236: 10235: 10230: 10212: 10210: 10209: 10204: 10180: 10178: 10177: 10172: 10154: 10152: 10151: 10146: 10144: 10143: 10127: 10125: 10124: 10119: 10095: 10093: 10092: 10087: 10085: 10081: 10080: 10076: 10074: 10069: 10059: 10048: 10028: 10020: 10003: 9992: 9977: 9973: 9972: 9971: 9958: 9947: 9927: 9926: 9918: 9913: 9903: 9892: 9851: 9850: 9834: 9829: 9797: 9795: 9794: 9789: 9783: 9778: 9768: 9757: 9739: 9738: 9729: 9728: 9716: 9715: 9705: 9694: 9663: 9661: 9660: 9655: 9650: 9649: 9630: 9628: 9627: 9622: 9604: 9602: 9601: 9596: 9591: 9590: 9567: 9565: 9564: 9559: 9517: 9515: 9514: 9509: 9495: 9493: 9492: 9487: 9482: 9479: 9478: 9466: 9460: 9457: 9456: 9447: 9446: 9434: 9428: 9427: 9374: 9373: 9364: 9363: 9351: 9350: 9340: 9329: 9308: 9300: 9282: 9280: 9279: 9274: 9269: 9268: 9253: 9248: 9247: 9238: 9237: 9222: 9221: 9202: 9200: 9199: 9194: 9186: 9185: 9167: 9166: 9151: 9150: 9141: 9136: 9127: 9122: 9104: 9103: 9085: 9084: 9068: 9063: 9044: 9042: 9041: 9036: 9034: 9030: 9029: 9028: 9023: 9019: 9018: 9017: 9016: 9005: 8994: 8973: 8971: 8970: 8969: 8953: 8948: 8946: 8945: 8935: 8930: 8921: 8918: 8907: 8892: 8884: 8867: 8856: 8841: 8837: 8836: 8835: 8822: 8811: 8791: 8790: 8777: 8776: 8758: 8757: 8742: 8741: 8732: 8727: 8718: 8713: 8699: 8696: 8695: 8685: 8680: 8665: 8664: 8640: 8636: 8616: 8615: 8599: 8594: 8569: 8567: 8566: 8561: 8542: 8540: 8539: 8534: 8532: 8528: 8524: 8523: 8519: 8518: 8514: 8513: 8511: 8510: 8509: 8500: 8495: 8492: 8491: 8490: 8489: 8478: 8467: 8451: 8432: 8428: 8427: 8426: 8416: 8405: 8390: 8385: 8380: 8379: 8348: 8344: 8343: 8339: 8338: 8336: 8335: 8334: 8325: 8320: 8317: 8316: 8307: 8288: 8284: 8283: 8282: 8273: 8268: 8263: 8262: 8230: 8219: 8191: 8184: 8180: 8179: 8178: 8177: 8165: 8160: 8156: 8145: 8125: 8124: 8111: 8110: 8092: 8091: 8076: 8075: 8066: 8061: 8052: 8047: 8033: 8030: 8029: 8025: 8024: 8023: 8014: 8009: 7998: 7997: 7973: 7968: 7952: 7941: 7940: 7932: 7928: 7924: 7923: 7922: 7921: 7917: 7916: 7915: 7905: 7894: 7879: 7874: 7869: 7868: 7847: 7843: 7842: 7840: 7839: 7838: 7829: 7824: 7821: 7820: 7819: 7818: 7807: 7796: 7780: 7766: 7765: 7761: 7760: 7751: 7746: 7741: 7740: 7721: 7717: 7716: 7714: 7713: 7712: 7703: 7698: 7695: 7694: 7685: 7670: 7659: 7639: 7635: 7634: 7633: 7632: 7620: 7615: 7611: 7600: 7580: 7579: 7566: 7565: 7547: 7546: 7531: 7530: 7521: 7516: 7507: 7502: 7488: 7485: 7484: 7483: 7467: 7462: 7446: 7435: 7434: 7410: 7409: 7393: 7388: 7356: 7354: 7353: 7348: 7343: 7342: 7332: 7321: 7306: 7301: 7296: 7295: 7280: 7279: 7260: 7258: 7257: 7252: 7250: 7249: 7233: 7231: 7230: 7225: 7223: 7222: 7206: 7204: 7203: 7198: 7183: 7181: 7180: 7175: 7139: 7133: 7132: 7131: 7130: 7115: 7114: 7104: 7099: 7098: 7076: 7074: 7073: 7068: 7066: 7063: 7062: 7061: 7045: 7040: 7024: 7013: 7012: 7010: 7009: 7008: 7007: 6997: 6993: 6991: 6990: 6981: 6980: 6979: 6966: 6958: 6953: 6937: 6924: 6923: 6905: 6904: 6888: 6883: 6874: 6866: 6865: 6830: 6829: 6813: 6808: 6783: 6781: 6780: 6775: 6770: 6769: 6753: 6751: 6750: 6745: 6726: 6724: 6723: 6718: 6706: 6704: 6703: 6698: 6686: 6684: 6683: 6678: 6676: 6675: 6652: 6650: 6649: 6644: 6642: 6641: 6640: 6639: 6629: 6628: 6627: 6615: 6610: 6595: 6593: 6589: 6588: 6573: 6572: 6562: 6554: 6551: 6538: 6537: 6519: 6518: 6502: 6497: 6488: 6480: 6479: 6444: 6443: 6427: 6422: 6395: 6393: 6392: 6387: 6366: 6364: 6363: 6358: 6340: 6338: 6337: 6332: 6330: 6329: 6313: 6311: 6310: 6305: 6297: 6296: 6280: 6275: 6259: 6257: 6256: 6251: 6243: 6242: 6224: 6223: 6207: 6202: 6183: 6181: 6180: 6175: 6167: 6166: 6156: 6151: 6135: 6132: 6123: 6122: 6112: 6107: 6082: 6080: 6079: 6074: 6072: 6071: 6055: 6053: 6052: 6047: 6042: 6041: 6022: 6020: 6019: 6014: 5990: 5988: 5987: 5982: 5980: 5979: 5963: 5961: 5960: 5955: 5943: 5941: 5940: 5935: 5920: 5918: 5917: 5912: 5910: 5909: 5882:of proportions. 5850: 5848: 5847: 5842: 5837: 5835: 5834: 5825: 5824: 5823: 5808: 5807: 5794: 5778: 5776: 5775: 5770: 5765: 5764: 5759: 5755: 5731: 5730: 5720: 5719: 5709: 5689: 5687: 5686: 5681: 5676: 5674: 5654: 5653: 5652: 5622: 5621: 5602: 5597: 5595: 5587: 5586: 5585: 5567: 5566: 5553: 5531: 5529: 5528: 5523: 5481: 5478: 5458: 5455: 5416: 5414: 5413: 5408: 5387: 5383: 5378: 5372: 5328: âˆ’ 1)( 5219: âˆ’ 1)( 5187: 5185: 5184: 5179: 5165: 5164: 5146: 5145: 5123: 5121: 5120: 5115: 5113: 5112: 5093: 5091: 5090: 5085: 5083: 5082: 5077: 5073: 5071: 5070: 5069: 5057: 5056: 5043: 5042: 5041: 5029: 5028: 5007: 5002: 5001: 4982: 4975: 4974: 4962: 4961: 4948: 4925: 4922: 4919: 4916: 4907: 4905: 4904: 4899: 4897: 4895: 4894: 4879: 4878: 4877: 4868: 4867: 4849: 4848: 4829: 4826: 4821: 4805: 4800: 4782: 4781: 4748: 4746: 4745: 4740: 4738: 4733: 4732: 4717: 4714: 4709: 4691: 4686: 4685: 4673: 4668: 4667: 4638: 4636: 4635: 4630: 4625: 4620: 4619: 4604: 4601: 4596: 4578: 4573: 4572: 4560: 4555: 4554: 4532: 4530: 4529: 4524: 4509: 4507: 4506: 4501: 4496: 4495: 4483: 4482: 4464: 4463: 4376: 4374: 4373: 4368: 4350: 4348: 4347: 4342: 4311: 4309: 4308: 4303: 4292: 4290: 4289: 4279: 4274: 4265: 4262: 4257: 4239: 4238: 4216: 4214: 4213: 4208: 4196: 4194: 4193: 4188: 4173:. The number of 4156: 4154: 4153: 4148: 4135: 4133: 4132: 4127: 4125: 4124: 4100: 4098: 4097: 4092: 4090: 4089: 4074: 4073: 4055: 4053: 4052: 4047: 4029: 4027: 4026: 4021: 4019: 4018: 3998: 3996: 3995: 3990: 3988: 3987: 3970: 3968: 3967: 3962: 3960: 3959: 3937: 3935: 3934: 3929: 3927: 3925: 3924: 3915: 3914: 3909: 3905: 3904: 3903: 3888: 3883: 3882: 3867: 3864: 3859: 3838: 3836: 3835: 3826: 3825: 3824: 3815: 3814: 3802: 3801: 3788: 3785: 3780: 3762: 3761: 1705: 1704: 1666: 1664: 1663: 1658: 1646: 1644: 1643: 1638: 1620: 1618: 1617: 1612: 1594: 1592: 1591: 1586: 1568: 1566: 1565: 1560: 1538: 1536: 1535: 1530: 1518: 1516: 1515: 1510: 1474: 1472: 1471: 1466: 1454: 1452: 1451: 1446: 1444: 1443: 1427: 1425: 1424: 1419: 1398: 1396: 1395: 1390: 1384: 1376: 1371: 1370: 1346: 1344: 1343: 1338: 1326: 1324: 1323: 1318: 1292: 1290: 1289: 1284: 1282: 1281: 1261: 1259: 1258: 1253: 1251: 1250: 1230: 1228: 1227: 1222: 1220: 1219: 1203: 1201: 1200: 1195: 1193: 1192: 1176: 1174: 1173: 1168: 1166: 1165: 1146: 1144: 1143: 1138: 1136: 1135: 1110: 1108: 1107: 1102: 1100: 1099: 1052: 1037: 1022: 996: 994: 993: 988: 986: 985: 918: 916: 915: 910: 892: 890: 889: 884: 876: 875: 859: 857: 856: 851: 849: 847: 843: 834: 833: 832: 820: 809: 808: 795: 792: 787: 769: 768: 752: 750: 749: 744: 736: 710: 693: 651: 649: 648: 643: 638: 637: 613: 612: 600: 599: 573: 571: 570: 565: 563: 561: 560: 559: 546: 545: 544: 535: 534: 519: 518: 505: 502: 490: 489: 466: 464: 463: 458: 453: 452: 428: 427: 415: 366: 364: 363: 358: 353: 352: 328: 327: 309: 257: 255: 254: 249: 241: 240: 230: 214: 212: 211: 206: 201: 200: 176: 175: 163: 162: 136: 134: 133: 128: 80:likelihood ratio 68:categorical data 64:statistical test 59: 57: 56: 51: 49: 48: 21:Chi-squared test 14015: 14014: 14010: 14009: 14008: 14006: 14005: 14004: 13995:Normality tests 13980: 13979: 13978: 13973: 13936: 13907: 13869: 13806: 13792:quality control 13759: 13741:Clinical trials 13718: 13693: 13677: 13665:Hazard function 13659: 13613: 13575: 13559: 13522: 13518:Breusch–Godfrey 13506: 13483: 13423: 13398:Factor analysis 13344: 13325:Graphical model 13297: 13264: 13231: 13217: 13197: 13151: 13118: 13080: 13043: 13042: 13011: 12955: 12942: 12934: 12926: 12910: 12895: 12874:Rank statistics 12868: 12847:Model selection 12835: 12793:Goodness of fit 12787: 12764: 12738: 12710: 12663: 12608: 12597:Median unbiased 12525: 12436: 12369:Order statistic 12331: 12310: 12277: 12251: 12203: 12158: 12101: 12099:Data collection 12080: 11992: 11947: 11921: 11899: 11859: 11811: 11728:Continuous data 11718: 11705: 11687: 11682: 11652: 11646: 11632:Greenwood, P.E. 11616:10.2307/1402731 11596:Plackett, R. L. 11554: 11550: 11548: 11545: 11544: 11533: 11528: 11527: 11515: 11496: 11492: 11480: 11478: 11469: 11468: 11426: 11422: 11409: 11405: 11397: 11393: 11392: 11388: 11378: 11376: 11368: 11367: 11363: 11318: 11314: 11301: 11297: 11252: 11248: 11235: 11234: 11230: 11220: 11218: 11214: 11213: 11209: 11197: 11188: 11171: 11167: 11150: 11146: 11116: 11112: 11107: 11041: 11020: 11017: 11016: 10999: 10995: 10993: 10990: 10989: 10979:Boschloo's test 10946: 10889: 10885: 10872: 10870: 10855: 10851: 10838: 10836: 10827: 10823: 10821: 10818: 10817: 10813:56 women, then 10790: 10787: 10786: 10779: 10777:Goodness of fit 10773: 10712: 10710: 10677: 10663: 10649: 10635: 10621: 10607: 10594: 10590: 10589: 10587: 10584: 10583: 10443: 10439: 10433: 10429: 10420: 10416: 10411: 10408: 10407: 10389: 10385: 10376: 10372: 10370: 10367: 10366: 10348: 10344: 10342: 10339: 10338: 10320: 10316: 10314: 10311: 10310: 10293: 10290: 10289: 10275: 10272: 10269: 10268: 10266: 10259: 10254: 10242: 10241: 10218: 10215: 10214: 10189: 10186: 10185: 10160: 10157: 10156: 10139: 10135: 10133: 10130: 10129: 10107: 10104: 10103: 10070: 10065: 10049: 10038: 10033: 10029: 10019: 10015: 10011: 9993: 9982: 9967: 9963: 9948: 9937: 9932: 9928: 9914: 9909: 9893: 9882: 9877: 9873: 9846: 9842: 9830: 9825: 9813: 9810: 9809: 9779: 9774: 9758: 9747: 9734: 9730: 9721: 9717: 9711: 9707: 9695: 9678: 9672: 9669: 9668: 9645: 9641: 9636: 9633: 9632: 9610: 9607: 9606: 9586: 9582: 9577: 9574: 9573: 9523: 9520: 9519: 9503: 9500: 9499: 9474: 9470: 9464: 9452: 9448: 9439: 9435: 9432: 9420: 9416: 9369: 9365: 9356: 9352: 9346: 9342: 9330: 9313: 9299: 9294: 9291: 9290: 9264: 9260: 9249: 9243: 9239: 9233: 9229: 9217: 9213: 9208: 9205: 9204: 9181: 9177: 9162: 9158: 9146: 9142: 9135: 9123: 9118: 9099: 9095: 9080: 9076: 9064: 9059: 9053: 9050: 9049: 9048:Pearson's chi, 9024: 9012: 9008: 9007: 8995: 8984: 8979: 8975: 8974: 8965: 8961: 8957: 8952: 8941: 8937: 8931: 8926: 8920: 8908: 8897: 8883: 8879: 8875: 8857: 8846: 8831: 8827: 8812: 8801: 8796: 8792: 8772: 8768: 8753: 8749: 8737: 8733: 8726: 8714: 8709: 8704: 8700: 8691: 8687: 8681: 8670: 8654: 8650: 8635: 8611: 8607: 8595: 8590: 8578: 8575: 8574: 8555: 8552: 8551: 8530: 8529: 8505: 8501: 8494: 8493: 8485: 8481: 8480: 8468: 8457: 8452: 8450: 8443: 8439: 8422: 8418: 8406: 8395: 8384: 8375: 8371: 8367: 8363: 8359: 8355: 8330: 8326: 8319: 8318: 8312: 8308: 8306: 8299: 8295: 8278: 8274: 8267: 8258: 8254: 8250: 8246: 8242: 8238: 8220: 8209: 8204: 8200: 8189: 8188: 8173: 8169: 8159: 8158: 8146: 8135: 8130: 8126: 8106: 8102: 8087: 8083: 8071: 8067: 8060: 8048: 8043: 8038: 8034: 8019: 8015: 8008: 7993: 7989: 7979: 7975: 7969: 7958: 7953: 7942: 7939: 7930: 7929: 7911: 7907: 7895: 7884: 7873: 7864: 7860: 7856: 7852: 7848: 7834: 7830: 7823: 7822: 7814: 7810: 7809: 7797: 7786: 7781: 7779: 7772: 7768: 7767: 7756: 7752: 7745: 7736: 7732: 7722: 7708: 7704: 7697: 7696: 7690: 7686: 7684: 7677: 7673: 7672: 7660: 7649: 7644: 7640: 7628: 7624: 7614: 7613: 7601: 7590: 7585: 7581: 7561: 7557: 7542: 7538: 7526: 7522: 7515: 7503: 7498: 7493: 7489: 7479: 7475: 7463: 7452: 7447: 7436: 7433: 7426: 7405: 7401: 7389: 7384: 7370: 7368: 7365: 7364: 7338: 7334: 7322: 7311: 7300: 7291: 7287: 7275: 7271: 7269: 7266: 7265: 7261:. Noting that: 7245: 7241: 7239: 7236: 7235: 7218: 7214: 7212: 7209: 7208: 7192: 7189: 7188: 7126: 7122: 7110: 7106: 7105: 7103: 7094: 7090: 7088: 7085: 7084: 7057: 7053: 7041: 7030: 7025: 7014: 7011: 7003: 6999: 6998: 6986: 6982: 6975: 6971: 6967: 6965: 6961: 6960: 6954: 6943: 6919: 6915: 6900: 6896: 6884: 6879: 6870: 6861: 6857: 6853: 6825: 6821: 6809: 6804: 6792: 6789: 6788: 6765: 6761: 6759: 6756: 6755: 6736: 6733: 6732: 6712: 6709: 6708: 6692: 6689: 6688: 6671: 6667: 6665: 6662: 6661: 6635: 6631: 6630: 6623: 6619: 6618: 6617: 6611: 6600: 6584: 6580: 6568: 6564: 6563: 6555: 6553: 6533: 6529: 6514: 6510: 6498: 6493: 6484: 6475: 6471: 6467: 6439: 6435: 6423: 6418: 6406: 6403: 6402: 6372: 6369: 6368: 6346: 6343: 6342: 6325: 6321: 6319: 6316: 6315: 6292: 6288: 6276: 6271: 6265: 6262: 6261: 6238: 6234: 6219: 6215: 6203: 6198: 6192: 6189: 6188: 6162: 6158: 6152: 6141: 6131: 6118: 6114: 6108: 6097: 6091: 6088: 6087: 6067: 6063: 6061: 6058: 6057: 6037: 6033: 6028: 6025: 6024: 6023:. We denote by 5996: 5993: 5992: 5975: 5971: 5969: 5966: 5965: 5949: 5946: 5945: 5929: 5926: 5925: 5905: 5901: 5899: 5896: 5895: 5888: 5872: 5830: 5826: 5819: 5815: 5803: 5799: 5795: 5793: 5791: 5788: 5787: 5760: 5715: 5711: 5710: 5708: 5704: 5703: 5701: 5698: 5697: 5655: 5648: 5644: 5617: 5613: 5603: 5601: 5588: 5581: 5577: 5562: 5558: 5554: 5552: 5550: 5547: 5546: 5541: 5477: 5454: 5452: 5449: 5448: 5381: 5367: 5364: 5363: 5353: 5309: 5308: 5303: 5237: 5154: 5150: 5135: 5131: 5129: 5126: 5125: 5108: 5104: 5102: 5099: 5098: 5078: 5062: 5058: 5049: 5045: 5044: 5034: 5030: 5021: 5017: 5003: 4991: 4987: 4983: 4981: 4977: 4976: 4967: 4963: 4954: 4950: 4938: 4914: 4911: 4910: 4884: 4880: 4873: 4869: 4857: 4853: 4838: 4834: 4830: 4828: 4822: 4811: 4801: 4790: 4777: 4773: 4771: 4768: 4767: 4722: 4718: 4716: 4710: 4699: 4678: 4674: 4672: 4660: 4656: 4654: 4651: 4650: 4609: 4605: 4603: 4597: 4586: 4565: 4561: 4559: 4547: 4543: 4541: 4538: 4537: 4518: 4515: 4514: 4488: 4484: 4475: 4471: 4453: 4449: 4447: 4444: 4443: 4421: 4413:credible region 4405:conjugate prior 4393: 4387: 4385:Bayesian method 4356: 4353: 4352: 4324: 4321: 4320: 4285: 4281: 4275: 4270: 4264: 4258: 4247: 4234: 4230: 4228: 4225: 4224: 4202: 4199: 4198: 4182: 4179: 4178: 4142: 4139: 4138: 4120: 4116: 4114: 4111: 4110: 4085: 4081: 4069: 4065: 4063: 4060: 4059: 4041: 4038: 4037: 4014: 4010: 4008: 4005: 4004: 3983: 3979: 3977: 3974: 3973: 3955: 3951: 3949: 3946: 3945: 3920: 3916: 3910: 3899: 3895: 3884: 3878: 3874: 3873: 3869: 3868: 3866: 3860: 3849: 3831: 3827: 3820: 3816: 3810: 3806: 3797: 3793: 3789: 3787: 3781: 3770: 3757: 3753: 3751: 3748: 3747: 1716: 1714: 1688: 1652: 1649: 1648: 1626: 1623: 1622: 1600: 1597: 1596: 1574: 1571: 1570: 1548: 1545: 1544: 1524: 1521: 1520: 1492: 1489: 1488: 1484: 1460: 1457: 1456: 1439: 1435: 1433: 1430: 1429: 1407: 1404: 1403: 1375: 1366: 1362: 1360: 1357: 1356: 1332: 1329: 1328: 1312: 1309: 1308: 1305: 1300: 1277: 1273: 1271: 1268: 1267: 1246: 1242: 1240: 1237: 1236: 1215: 1211: 1209: 1206: 1205: 1188: 1184: 1182: 1179: 1178: 1161: 1157: 1155: 1152: 1151: 1131: 1127: 1125: 1122: 1121: 1095: 1091: 1089: 1086: 1085: 1050: 1035: 1020: 981: 977: 975: 972: 971: 929:goodness of fit 925: 898: 895: 894: 871: 867: 865: 862: 861: 839: 835: 828: 824: 816: 804: 800: 796: 794: 788: 777: 764: 760: 758: 755: 754: 732: 706: 659: 657: 654: 653: 633: 629: 608: 604: 595: 591: 586: 583: 582: 555: 551: 547: 540: 536: 530: 526: 514: 510: 506: 504: 498: 485: 481: 479: 476: 475: 448: 444: 423: 419: 381: 379: 376: 375: 348: 344: 323: 319: 275: 273: 270: 269: 263:null hypothesis 236: 232: 226: 220: 217: 216: 196: 192: 171: 167: 158: 154: 149: 146: 145: 122: 119: 118: 44: 40: 38: 35: 34: 24: 17: 12: 11: 5: 14013: 14003: 14002: 13997: 13992: 13975: 13974: 13972: 13971: 13959: 13947: 13933: 13920: 13917: 13916: 13913: 13912: 13909: 13908: 13906: 13905: 13900: 13895: 13890: 13885: 13879: 13877: 13871: 13870: 13868: 13867: 13862: 13857: 13852: 13847: 13842: 13837: 13832: 13827: 13822: 13816: 13814: 13808: 13807: 13805: 13804: 13799: 13794: 13785: 13780: 13775: 13769: 13767: 13761: 13760: 13758: 13757: 13752: 13747: 13738: 13736:Bioinformatics 13732: 13730: 13720: 13719: 13707: 13706: 13703: 13702: 13699: 13698: 13695: 13694: 13692: 13691: 13685: 13683: 13679: 13678: 13676: 13675: 13669: 13667: 13661: 13660: 13658: 13657: 13652: 13647: 13642: 13636: 13634: 13625: 13619: 13618: 13615: 13614: 13612: 13611: 13606: 13601: 13596: 13591: 13585: 13583: 13577: 13576: 13574: 13573: 13568: 13563: 13555: 13550: 13545: 13544: 13543: 13541:partial (PACF) 13532: 13530: 13524: 13523: 13521: 13520: 13515: 13510: 13502: 13497: 13491: 13489: 13488:Specific tests 13485: 13484: 13482: 13481: 13476: 13471: 13466: 13461: 13456: 13451: 13446: 13440: 13438: 13431: 13425: 13424: 13422: 13421: 13420: 13419: 13418: 13417: 13402: 13401: 13400: 13390: 13388:Classification 13385: 13380: 13375: 13370: 13365: 13360: 13354: 13352: 13346: 13345: 13343: 13342: 13337: 13335:McNemar's test 13332: 13327: 13322: 13317: 13311: 13309: 13299: 13298: 13274: 13273: 13270: 13269: 13266: 13265: 13263: 13262: 13257: 13252: 13247: 13241: 13239: 13233: 13232: 13230: 13229: 13213: 13207: 13205: 13199: 13198: 13196: 13195: 13190: 13185: 13180: 13175: 13173:Semiparametric 13170: 13165: 13159: 13157: 13153: 13152: 13150: 13149: 13144: 13139: 13134: 13128: 13126: 13120: 13119: 13117: 13116: 13111: 13106: 13101: 13096: 13090: 13088: 13082: 13081: 13079: 13078: 13073: 13068: 13063: 13057: 13055: 13045: 13044: 13041: 13040: 13035: 13029: 13021: 13020: 13017: 13016: 13013: 13012: 13010: 13009: 13008: 13007: 12997: 12992: 12987: 12986: 12985: 12980: 12969: 12967: 12961: 12960: 12957: 12956: 12954: 12953: 12948: 12947: 12946: 12938: 12930: 12914: 12911:(Mann–Whitney) 12906: 12905: 12904: 12891: 12890: 12889: 12878: 12876: 12870: 12869: 12867: 12866: 12865: 12864: 12859: 12854: 12844: 12839: 12836:(Shapiro–Wilk) 12831: 12826: 12821: 12816: 12811: 12803: 12797: 12795: 12789: 12788: 12786: 12785: 12777: 12768: 12756: 12750: 12748:Specific tests 12744: 12743: 12740: 12739: 12737: 12736: 12731: 12726: 12720: 12718: 12712: 12711: 12709: 12708: 12703: 12702: 12701: 12691: 12690: 12689: 12679: 12673: 12671: 12665: 12664: 12662: 12661: 12660: 12659: 12654: 12644: 12639: 12634: 12629: 12624: 12618: 12616: 12610: 12609: 12607: 12606: 12601: 12600: 12599: 12594: 12593: 12592: 12587: 12572: 12571: 12570: 12565: 12560: 12555: 12544: 12542: 12533: 12527: 12526: 12524: 12523: 12518: 12513: 12512: 12511: 12501: 12496: 12495: 12494: 12484: 12483: 12482: 12477: 12472: 12462: 12457: 12452: 12451: 12450: 12445: 12440: 12424: 12423: 12422: 12417: 12412: 12402: 12401: 12400: 12395: 12385: 12384: 12383: 12373: 12372: 12371: 12361: 12356: 12351: 12345: 12343: 12333: 12332: 12320: 12319: 12316: 12315: 12312: 12311: 12309: 12308: 12303: 12298: 12293: 12287: 12285: 12279: 12278: 12276: 12275: 12270: 12265: 12259: 12257: 12253: 12252: 12250: 12249: 12244: 12239: 12234: 12229: 12224: 12219: 12213: 12211: 12205: 12204: 12202: 12201: 12199:Standard error 12196: 12191: 12186: 12185: 12184: 12179: 12168: 12166: 12160: 12159: 12157: 12156: 12151: 12146: 12141: 12136: 12131: 12129:Optimal design 12126: 12121: 12115: 12113: 12103: 12102: 12090: 12089: 12086: 12085: 12082: 12081: 12079: 12078: 12073: 12068: 12063: 12058: 12053: 12048: 12043: 12038: 12033: 12028: 12023: 12018: 12013: 12008: 12002: 12000: 11994: 11993: 11991: 11990: 11985: 11984: 11983: 11978: 11968: 11963: 11957: 11955: 11949: 11948: 11946: 11945: 11940: 11935: 11929: 11927: 11926:Summary tables 11923: 11922: 11920: 11919: 11913: 11911: 11905: 11904: 11901: 11900: 11898: 11897: 11896: 11895: 11890: 11885: 11875: 11869: 11867: 11861: 11860: 11858: 11857: 11852: 11847: 11842: 11837: 11832: 11827: 11821: 11819: 11813: 11812: 11810: 11809: 11804: 11799: 11798: 11797: 11792: 11787: 11782: 11777: 11772: 11767: 11762: 11760:Contraharmonic 11757: 11752: 11741: 11739: 11730: 11720: 11719: 11707: 11706: 11704: 11703: 11698: 11692: 11689: 11688: 11681: 11680: 11673: 11666: 11658: 11651: 11650: 11644: 11628: 11610:(ISI): 59–72. 11592: 11580:(3): 579–586. 11557: 11553: 11534: 11532: 11529: 11526: 11525: 11513: 11490: 11481:|journal= 11420: 11403: 11386: 11361: 11347:10.1086/156922 11312: 11295: 11266:(2): 143–149. 11246: 11228: 11207: 11186: 11165: 11144: 11109: 11108: 11106: 11103: 11102: 11101: 11096: 11091: 11086: 11081: 11075: 11069: 11064: 11058: 11053: 11047: 11040: 11037: 11024: 11002: 10998: 10945: 10942: 10918: 10917: 10906: 10903: 10898: 10892: 10888: 10884: 10881: 10878: 10875: 10869: 10864: 10858: 10854: 10850: 10847: 10844: 10841: 10835: 10830: 10826: 10794: 10775:Main article: 10772: 10769: 10759: 10758: 10755: 10752: 10749: 10746: 10743: 10739: 10738: 10735: 10730: 10727: 10722: 10718: 10717: 10714: 10690: 10687: 10684: 10680: 10676: 10673: 10670: 10666: 10662: 10659: 10656: 10652: 10648: 10645: 10642: 10638: 10634: 10631: 10628: 10624: 10620: 10617: 10614: 10610: 10606: 10603: 10597: 10593: 10570: 10569: 10566: 10562: 10561: 10558: 10555: 10552: 10549: 10545: 10544: 10541: 10538: 10535: 10532: 10528: 10527: 10524: 10521: 10518: 10515: 10511: 10510: 10507: 10504: 10501: 10498: 10494: 10493: 10490: 10487: 10484: 10481: 10477: 10476: 10473: 10470: 10467: 10464: 10460: 10459: 10446: 10442: 10436: 10432: 10428: 10423: 10419: 10415: 10405: 10392: 10388: 10384: 10379: 10375: 10364: 10351: 10347: 10336: 10323: 10319: 10308: 10297: 10258: 10255: 10253: 10250: 10228: 10225: 10222: 10202: 10199: 10196: 10193: 10170: 10167: 10164: 10142: 10138: 10117: 10114: 10111: 10097: 10096: 10084: 10079: 10073: 10068: 10064: 10058: 10055: 10052: 10047: 10044: 10041: 10037: 10032: 10026: 10023: 10018: 10014: 10010: 10007: 10002: 9999: 9996: 9991: 9988: 9985: 9981: 9976: 9970: 9966: 9962: 9957: 9954: 9951: 9946: 9943: 9940: 9936: 9931: 9925: 9922: 9917: 9912: 9908: 9902: 9899: 9896: 9891: 9888: 9885: 9881: 9876: 9872: 9869: 9866: 9863: 9860: 9857: 9854: 9849: 9845: 9841: 9838: 9833: 9828: 9824: 9820: 9817: 9799: 9798: 9787: 9782: 9777: 9773: 9767: 9764: 9761: 9756: 9753: 9750: 9746: 9742: 9737: 9733: 9727: 9724: 9720: 9714: 9710: 9704: 9701: 9698: 9693: 9690: 9687: 9684: 9681: 9677: 9653: 9648: 9644: 9640: 9631:new variables 9620: 9617: 9614: 9594: 9589: 9585: 9581: 9570:diagonalizable 9557: 9554: 9551: 9548: 9545: 9542: 9539: 9536: 9533: 9530: 9527: 9507: 9497: 9496: 9485: 9477: 9473: 9469: 9463: 9455: 9451: 9445: 9442: 9438: 9431: 9426: 9423: 9419: 9414: 9411: 9408: 9405: 9402: 9399: 9396: 9393: 9390: 9387: 9384: 9381: 9377: 9372: 9368: 9362: 9359: 9355: 9349: 9345: 9339: 9336: 9333: 9328: 9325: 9322: 9319: 9316: 9312: 9306: 9303: 9298: 9272: 9267: 9263: 9259: 9256: 9252: 9246: 9242: 9236: 9232: 9228: 9225: 9220: 9216: 9212: 9192: 9189: 9184: 9180: 9176: 9173: 9170: 9165: 9161: 9157: 9154: 9149: 9145: 9139: 9134: 9131: 9126: 9121: 9117: 9113: 9110: 9107: 9102: 9098: 9094: 9091: 9088: 9083: 9079: 9075: 9072: 9067: 9062: 9058: 9046: 9045: 9033: 9027: 9022: 9015: 9011: 9004: 9001: 8998: 8993: 8990: 8987: 8983: 8978: 8968: 8964: 8960: 8956: 8951: 8944: 8940: 8934: 8929: 8925: 8917: 8914: 8911: 8906: 8903: 8900: 8896: 8890: 8887: 8882: 8878: 8874: 8871: 8866: 8863: 8860: 8855: 8852: 8849: 8845: 8840: 8834: 8830: 8826: 8821: 8818: 8815: 8810: 8807: 8804: 8800: 8795: 8789: 8786: 8783: 8780: 8775: 8771: 8767: 8764: 8761: 8756: 8752: 8748: 8745: 8740: 8736: 8730: 8725: 8722: 8717: 8712: 8708: 8703: 8694: 8690: 8684: 8679: 8676: 8673: 8669: 8663: 8660: 8657: 8653: 8649: 8646: 8643: 8639: 8634: 8631: 8628: 8625: 8622: 8619: 8614: 8610: 8606: 8603: 8598: 8593: 8589: 8585: 8582: 8559: 8544: 8543: 8527: 8522: 8517: 8508: 8504: 8498: 8488: 8484: 8477: 8474: 8471: 8466: 8463: 8460: 8456: 8449: 8446: 8442: 8438: 8435: 8431: 8425: 8421: 8415: 8412: 8409: 8404: 8401: 8398: 8394: 8388: 8383: 8378: 8374: 8370: 8366: 8362: 8358: 8354: 8351: 8347: 8342: 8333: 8329: 8323: 8315: 8311: 8305: 8302: 8298: 8294: 8291: 8287: 8281: 8277: 8271: 8266: 8261: 8257: 8253: 8249: 8245: 8241: 8237: 8234: 8229: 8226: 8223: 8218: 8215: 8212: 8208: 8203: 8199: 8194: 8192: 8190: 8187: 8183: 8176: 8172: 8168: 8163: 8155: 8152: 8149: 8144: 8141: 8138: 8134: 8129: 8123: 8120: 8117: 8114: 8109: 8105: 8101: 8098: 8095: 8090: 8086: 8082: 8079: 8074: 8070: 8064: 8059: 8056: 8051: 8046: 8042: 8037: 8028: 8022: 8018: 8012: 8007: 8004: 8001: 7996: 7992: 7988: 7985: 7982: 7978: 7972: 7967: 7964: 7961: 7957: 7951: 7948: 7945: 7938: 7935: 7933: 7931: 7927: 7920: 7914: 7910: 7904: 7901: 7898: 7893: 7890: 7887: 7883: 7877: 7872: 7867: 7863: 7859: 7855: 7851: 7846: 7837: 7833: 7827: 7817: 7813: 7806: 7803: 7800: 7795: 7792: 7789: 7785: 7778: 7775: 7771: 7764: 7759: 7755: 7749: 7744: 7739: 7735: 7731: 7728: 7725: 7720: 7711: 7707: 7701: 7693: 7689: 7683: 7680: 7676: 7669: 7666: 7663: 7658: 7655: 7652: 7648: 7643: 7638: 7631: 7627: 7623: 7618: 7610: 7607: 7604: 7599: 7596: 7593: 7589: 7584: 7578: 7575: 7572: 7569: 7564: 7560: 7556: 7553: 7550: 7545: 7541: 7537: 7534: 7529: 7525: 7519: 7514: 7511: 7506: 7501: 7497: 7492: 7482: 7478: 7474: 7471: 7466: 7461: 7458: 7455: 7451: 7445: 7442: 7439: 7432: 7429: 7427: 7425: 7422: 7419: 7416: 7413: 7408: 7404: 7400: 7397: 7392: 7387: 7383: 7379: 7376: 7373: 7372: 7358: 7357: 7346: 7341: 7337: 7331: 7328: 7325: 7320: 7317: 7314: 7310: 7304: 7299: 7294: 7290: 7286: 7283: 7278: 7274: 7248: 7244: 7221: 7217: 7196: 7185: 7184: 7173: 7170: 7167: 7164: 7161: 7158: 7155: 7152: 7149: 7146: 7142: 7136: 7129: 7125: 7121: 7118: 7113: 7109: 7102: 7097: 7093: 7078: 7077: 7060: 7056: 7052: 7049: 7044: 7039: 7036: 7033: 7029: 7023: 7020: 7017: 7006: 7002: 6996: 6989: 6985: 6978: 6974: 6970: 6964: 6957: 6952: 6949: 6946: 6942: 6936: 6933: 6930: 6927: 6922: 6918: 6914: 6911: 6908: 6903: 6899: 6895: 6892: 6887: 6882: 6878: 6873: 6869: 6864: 6860: 6856: 6852: 6848: 6845: 6842: 6839: 6836: 6833: 6828: 6824: 6820: 6817: 6812: 6807: 6803: 6799: 6796: 6773: 6768: 6764: 6743: 6740: 6716: 6696: 6674: 6670: 6654: 6653: 6638: 6634: 6626: 6622: 6614: 6609: 6606: 6603: 6599: 6592: 6587: 6583: 6579: 6576: 6571: 6567: 6561: 6558: 6550: 6547: 6544: 6541: 6536: 6532: 6528: 6525: 6522: 6517: 6513: 6509: 6506: 6501: 6496: 6492: 6487: 6483: 6478: 6474: 6470: 6466: 6462: 6459: 6456: 6453: 6450: 6447: 6442: 6438: 6434: 6431: 6426: 6421: 6417: 6413: 6410: 6385: 6382: 6379: 6376: 6356: 6353: 6350: 6328: 6324: 6303: 6300: 6295: 6291: 6287: 6284: 6279: 6274: 6270: 6249: 6246: 6241: 6237: 6233: 6230: 6227: 6222: 6218: 6214: 6211: 6206: 6201: 6197: 6185: 6184: 6173: 6170: 6165: 6161: 6155: 6150: 6147: 6144: 6140: 6129: 6126: 6121: 6117: 6111: 6106: 6103: 6100: 6096: 6070: 6066: 6045: 6040: 6036: 6032: 6012: 6009: 6006: 6003: 6000: 5978: 5974: 5953: 5933: 5908: 5904: 5887: 5884: 5871: 5868: 5852: 5851: 5840: 5833: 5829: 5822: 5818: 5814: 5811: 5806: 5802: 5798: 5780: 5779: 5768: 5763: 5758: 5752: 5749: 5746: 5743: 5740: 5737: 5734: 5729: 5726: 5723: 5718: 5714: 5707: 5691: 5690: 5679: 5673: 5670: 5667: 5664: 5661: 5658: 5651: 5647: 5643: 5640: 5637: 5634: 5631: 5628: 5625: 5620: 5616: 5612: 5609: 5606: 5600: 5594: 5591: 5584: 5580: 5576: 5573: 5570: 5565: 5561: 5557: 5539: 5533: 5532: 5520: 5517: 5514: 5511: 5508: 5505: 5502: 5499: 5496: 5493: 5490: 5487: 5484: 5476: 5473: 5470: 5467: 5464: 5461: 5435: 5434: 5428: 5418: 5417: 5405: 5402: 5399: 5396: 5393: 5390: 5377: 5371: 5352: 5349: 5310: 5306: 5305: 5304: 5302: 5299: 5291: 5290: 5287:McNemar's test 5283: 5280: 5272: 5269: 5257: 5254: 5246: 5236: 5233: 5177: 5174: 5171: 5168: 5163: 5160: 5157: 5153: 5149: 5144: 5141: 5138: 5134: 5111: 5107: 5095: 5094: 5081: 5076: 5068: 5065: 5061: 5055: 5052: 5048: 5040: 5037: 5033: 5027: 5024: 5020: 5016: 5013: 5010: 5006: 5000: 4997: 4994: 4990: 4986: 4980: 4973: 4970: 4966: 4960: 4957: 4953: 4947: 4944: 4941: 4937: 4933: 4930: 4908: 4893: 4890: 4887: 4883: 4876: 4872: 4866: 4863: 4860: 4856: 4852: 4847: 4844: 4841: 4837: 4833: 4825: 4820: 4817: 4814: 4810: 4804: 4799: 4796: 4793: 4789: 4785: 4780: 4776: 4750: 4749: 4736: 4731: 4728: 4725: 4721: 4713: 4708: 4705: 4702: 4698: 4694: 4689: 4684: 4681: 4677: 4671: 4666: 4663: 4659: 4640: 4639: 4628: 4623: 4618: 4615: 4612: 4608: 4600: 4595: 4592: 4589: 4585: 4581: 4576: 4571: 4568: 4564: 4558: 4553: 4550: 4546: 4522: 4511: 4510: 4499: 4494: 4491: 4487: 4481: 4478: 4474: 4470: 4467: 4462: 4459: 4456: 4452: 4420: 4417: 4386: 4383: 4366: 4363: 4360: 4340: 4337: 4334: 4331: 4328: 4313: 4312: 4301: 4298: 4295: 4288: 4284: 4278: 4273: 4269: 4261: 4256: 4253: 4250: 4246: 4242: 4237: 4233: 4206: 4186: 4159: 4158: 4146: 4136: 4123: 4119: 4088: 4084: 4080: 4077: 4072: 4068: 4057: 4045: 4035: 4017: 4013: 4002: 3986: 3982: 3958: 3954: 3939: 3938: 3923: 3919: 3913: 3908: 3902: 3898: 3894: 3891: 3887: 3881: 3877: 3872: 3863: 3858: 3855: 3852: 3848: 3844: 3841: 3834: 3830: 3823: 3819: 3813: 3809: 3805: 3800: 3796: 3792: 3784: 3779: 3776: 3773: 3769: 3765: 3760: 3756: 3739: 3738: 3735: 3732: 3729: 3726: 3723: 3719: 3718: 3715: 3712: 3709: 3706: 3703: 3699: 3698: 3695: 3692: 3689: 3686: 3683: 3679: 3678: 3675: 3672: 3669: 3666: 3663: 3659: 3658: 3655: 3652: 3649: 3646: 3643: 3639: 3638: 3635: 3632: 3629: 3626: 3623: 3619: 3618: 3615: 3612: 3609: 3606: 3603: 3599: 3598: 3595: 3592: 3589: 3586: 3583: 3579: 3578: 3575: 3572: 3569: 3566: 3563: 3559: 3558: 3555: 3552: 3549: 3546: 3543: 3539: 3538: 3535: 3532: 3529: 3526: 3523: 3519: 3518: 3515: 3512: 3509: 3506: 3503: 3499: 3498: 3495: 3492: 3489: 3486: 3483: 3479: 3478: 3475: 3472: 3469: 3466: 3463: 3459: 3458: 3455: 3452: 3449: 3446: 3443: 3439: 3438: 3435: 3432: 3429: 3426: 3423: 3419: 3418: 3415: 3412: 3409: 3406: 3403: 3399: 3398: 3395: 3392: 3389: 3386: 3383: 3379: 3378: 3375: 3372: 3369: 3366: 3363: 3359: 3358: 3355: 3352: 3349: 3346: 3343: 3339: 3338: 3335: 3332: 3329: 3326: 3323: 3319: 3318: 3315: 3312: 3309: 3306: 3303: 3299: 3298: 3295: 3292: 3289: 3286: 3283: 3279: 3278: 3275: 3272: 3269: 3266: 3263: 3259: 3258: 3255: 3252: 3249: 3246: 3243: 3239: 3238: 3235: 3232: 3229: 3226: 3223: 3219: 3218: 3215: 3212: 3209: 3206: 3203: 3199: 3198: 3195: 3192: 3189: 3186: 3183: 3179: 3178: 3175: 3172: 3169: 3166: 3163: 3159: 3158: 3155: 3152: 3149: 3146: 3143: 3139: 3138: 3135: 3132: 3129: 3126: 3123: 3119: 3118: 3115: 3112: 3109: 3106: 3103: 3099: 3098: 3095: 3092: 3089: 3086: 3083: 3079: 3078: 3075: 3072: 3069: 3066: 3063: 3059: 3058: 3055: 3052: 3049: 3046: 3043: 3039: 3038: 3035: 3032: 3029: 3026: 3023: 3019: 3018: 3015: 3012: 3009: 3006: 3003: 2999: 2998: 2995: 2992: 2989: 2986: 2983: 2979: 2978: 2975: 2972: 2969: 2966: 2963: 2959: 2958: 2955: 2952: 2949: 2946: 2943: 2939: 2938: 2935: 2932: 2929: 2926: 2923: 2919: 2918: 2915: 2912: 2909: 2906: 2903: 2899: 2898: 2895: 2892: 2889: 2886: 2883: 2879: 2878: 2875: 2872: 2869: 2866: 2863: 2859: 2858: 2855: 2852: 2849: 2846: 2843: 2839: 2838: 2835: 2832: 2829: 2826: 2823: 2819: 2818: 2815: 2812: 2809: 2806: 2803: 2799: 2798: 2795: 2792: 2789: 2786: 2783: 2779: 2778: 2775: 2772: 2769: 2766: 2763: 2759: 2758: 2755: 2752: 2749: 2746: 2743: 2739: 2738: 2735: 2732: 2729: 2726: 2723: 2719: 2718: 2715: 2712: 2709: 2706: 2703: 2699: 2698: 2695: 2692: 2689: 2686: 2683: 2679: 2678: 2675: 2672: 2669: 2666: 2663: 2659: 2658: 2655: 2652: 2649: 2646: 2643: 2639: 2638: 2635: 2632: 2629: 2626: 2623: 2619: 2618: 2615: 2612: 2609: 2606: 2603: 2599: 2598: 2595: 2592: 2589: 2586: 2583: 2579: 2578: 2575: 2572: 2569: 2566: 2563: 2559: 2558: 2555: 2552: 2549: 2546: 2543: 2539: 2538: 2535: 2532: 2529: 2526: 2523: 2519: 2518: 2515: 2512: 2509: 2506: 2503: 2499: 2498: 2495: 2492: 2489: 2486: 2483: 2479: 2478: 2475: 2472: 2469: 2466: 2463: 2459: 2458: 2455: 2452: 2449: 2446: 2443: 2439: 2438: 2435: 2432: 2429: 2426: 2423: 2419: 2418: 2415: 2412: 2409: 2406: 2403: 2399: 2398: 2395: 2392: 2389: 2386: 2383: 2379: 2378: 2375: 2372: 2369: 2366: 2363: 2359: 2358: 2355: 2352: 2349: 2346: 2343: 2339: 2338: 2335: 2332: 2329: 2326: 2323: 2319: 2318: 2315: 2312: 2309: 2306: 2303: 2299: 2298: 2295: 2292: 2289: 2286: 2283: 2279: 2278: 2275: 2272: 2269: 2266: 2263: 2259: 2258: 2255: 2252: 2249: 2246: 2243: 2239: 2238: 2235: 2232: 2229: 2226: 2223: 2219: 2218: 2215: 2212: 2209: 2206: 2203: 2199: 2198: 2195: 2192: 2189: 2186: 2183: 2179: 2178: 2175: 2172: 2169: 2166: 2163: 2159: 2158: 2155: 2152: 2149: 2146: 2143: 2139: 2138: 2135: 2132: 2129: 2126: 2123: 2119: 2118: 2115: 2112: 2109: 2106: 2103: 2099: 2098: 2095: 2092: 2089: 2086: 2083: 2079: 2078: 2075: 2072: 2069: 2066: 2063: 2059: 2058: 2055: 2052: 2049: 2046: 2043: 2039: 2038: 2035: 2032: 2029: 2026: 2023: 2019: 2018: 2015: 2012: 2009: 2006: 2003: 1999: 1998: 1995: 1992: 1989: 1986: 1983: 1979: 1978: 1975: 1972: 1969: 1966: 1963: 1959: 1958: 1955: 1952: 1949: 1946: 1943: 1939: 1938: 1935: 1932: 1929: 1926: 1923: 1919: 1918: 1915: 1912: 1909: 1906: 1903: 1899: 1898: 1895: 1892: 1889: 1886: 1883: 1879: 1878: 1875: 1872: 1869: 1866: 1863: 1859: 1858: 1855: 1852: 1849: 1846: 1843: 1839: 1838: 1835: 1832: 1829: 1826: 1823: 1819: 1818: 1815: 1812: 1809: 1806: 1803: 1799: 1798: 1795: 1792: 1789: 1786: 1783: 1779: 1778: 1775: 1772: 1769: 1766: 1763: 1759: 1758: 1755: 1752: 1749: 1746: 1743: 1739: 1738: 1735: 1732: 1729: 1726: 1722: 1721: 1718: 1710: 1709: 1687: 1684: 1676:F-distribution 1656: 1636: 1633: 1630: 1610: 1607: 1604: 1584: 1581: 1578: 1558: 1555: 1552: 1528: 1508: 1505: 1502: 1499: 1496: 1483: 1480: 1464: 1442: 1438: 1417: 1414: 1411: 1400: 1399: 1388: 1382: 1379: 1374: 1369: 1365: 1336: 1316: 1304: 1301: 1299: 1296: 1295: 1294: 1280: 1276: 1249: 1245: 1218: 1214: 1191: 1187: 1164: 1160: 1148: 1134: 1130: 1098: 1094: 1082: 1064: 1063: 1062: 1047: 1032: 1008:Determine the 1006: 984: 980: 960: 959: 952: 948: 924: 921: 908: 905: 902: 882: 879: 874: 870: 846: 842: 838: 831: 827: 823: 819: 815: 812: 807: 803: 799: 791: 786: 783: 780: 776: 772: 767: 763: 742: 739: 735: 731: 728: 725: 722: 719: 716: 713: 709: 705: 702: 699: 696: 692: 689: 686: 683: 680: 677: 674: 671: 668: 665: 662: 641: 636: 632: 628: 625: 622: 619: 616: 611: 607: 603: 598: 594: 590: 579: 578: 575: 558: 554: 550: 543: 539: 533: 529: 525: 522: 517: 513: 509: 501: 497: 493: 488: 484: 474:is defined as 472:test statistic 468: 456: 451: 447: 443: 440: 437: 434: 431: 426: 422: 418: 414: 411: 408: 405: 402: 399: 396: 393: 390: 387: 384: 356: 351: 347: 343: 340: 337: 334: 331: 326: 322: 318: 315: 312: 308: 305: 302: 299: 296: 293: 290: 287: 284: 281: 278: 259: 247: 244: 239: 235: 229: 225: 204: 199: 195: 191: 188: 185: 182: 179: 174: 170: 166: 161: 157: 153: 138: 126: 100:test statistic 47: 43: 15: 9: 6: 4: 3: 2: 14012: 14001: 13998: 13996: 13993: 13991: 13988: 13987: 13985: 13970: 13969: 13960: 13958: 13957: 13948: 13946: 13945: 13940: 13934: 13932: 13931: 13922: 13921: 13918: 13904: 13901: 13899: 13898:Geostatistics 13896: 13894: 13891: 13889: 13886: 13884: 13881: 13880: 13878: 13876: 13872: 13866: 13865:Psychometrics 13863: 13861: 13858: 13856: 13853: 13851: 13848: 13846: 13843: 13841: 13838: 13836: 13833: 13831: 13828: 13826: 13823: 13821: 13818: 13817: 13815: 13813: 13809: 13803: 13800: 13798: 13795: 13793: 13789: 13786: 13784: 13781: 13779: 13776: 13774: 13771: 13770: 13768: 13766: 13762: 13756: 13753: 13751: 13748: 13746: 13742: 13739: 13737: 13734: 13733: 13731: 13729: 13728:Biostatistics 13725: 13721: 13717: 13712: 13708: 13690: 13689:Log-rank test 13687: 13686: 13684: 13680: 13674: 13671: 13670: 13668: 13666: 13662: 13656: 13653: 13651: 13648: 13646: 13643: 13641: 13638: 13637: 13635: 13633: 13629: 13626: 13624: 13620: 13610: 13607: 13605: 13602: 13600: 13597: 13595: 13592: 13590: 13587: 13586: 13584: 13582: 13578: 13572: 13569: 13567: 13564: 13562: 13560:(Box–Jenkins) 13556: 13554: 13551: 13549: 13546: 13542: 13539: 13538: 13537: 13534: 13533: 13531: 13529: 13525: 13519: 13516: 13514: 13513:Durbin–Watson 13511: 13509: 13503: 13501: 13498: 13496: 13495:Dickey–Fuller 13493: 13492: 13490: 13486: 13480: 13477: 13475: 13472: 13470: 13469:Cointegration 13467: 13465: 13462: 13460: 13457: 13455: 13452: 13450: 13447: 13445: 13444:Decomposition 13442: 13441: 13439: 13435: 13432: 13430: 13426: 13416: 13413: 13412: 13411: 13408: 13407: 13406: 13403: 13399: 13396: 13395: 13394: 13391: 13389: 13386: 13384: 13381: 13379: 13376: 13374: 13371: 13369: 13366: 13364: 13361: 13359: 13356: 13355: 13353: 13351: 13347: 13341: 13338: 13336: 13333: 13331: 13328: 13326: 13323: 13321: 13318: 13316: 13315:Cohen's kappa 13313: 13312: 13310: 13308: 13304: 13300: 13296: 13292: 13288: 13284: 13279: 13275: 13261: 13258: 13256: 13253: 13251: 13248: 13246: 13243: 13242: 13240: 13238: 13234: 13228: 13224: 13220: 13214: 13212: 13209: 13208: 13206: 13204: 13200: 13194: 13191: 13189: 13186: 13184: 13181: 13179: 13176: 13174: 13171: 13169: 13168:Nonparametric 13166: 13164: 13161: 13160: 13158: 13154: 13148: 13145: 13143: 13140: 13138: 13135: 13133: 13130: 13129: 13127: 13125: 13121: 13115: 13112: 13110: 13107: 13105: 13102: 13100: 13097: 13095: 13092: 13091: 13089: 13087: 13083: 13077: 13074: 13072: 13069: 13067: 13064: 13062: 13059: 13058: 13056: 13054: 13050: 13046: 13039: 13036: 13034: 13031: 13030: 13026: 13022: 13006: 13003: 13002: 13001: 12998: 12996: 12993: 12991: 12988: 12984: 12981: 12979: 12976: 12975: 12974: 12971: 12970: 12968: 12966: 12962: 12952: 12949: 12945: 12939: 12937: 12931: 12929: 12923: 12922: 12921: 12918: 12917:Nonparametric 12915: 12913: 12907: 12903: 12900: 12899: 12898: 12892: 12888: 12887:Sample median 12885: 12884: 12883: 12880: 12879: 12877: 12875: 12871: 12863: 12860: 12858: 12855: 12853: 12850: 12849: 12848: 12845: 12843: 12840: 12838: 12832: 12830: 12827: 12825: 12822: 12820: 12817: 12815: 12812: 12810: 12808: 12804: 12802: 12799: 12798: 12796: 12794: 12790: 12784: 12782: 12778: 12776: 12774: 12769: 12767: 12762: 12758: 12757: 12754: 12751: 12749: 12745: 12735: 12732: 12730: 12727: 12725: 12722: 12721: 12719: 12717: 12713: 12707: 12704: 12700: 12697: 12696: 12695: 12692: 12688: 12685: 12684: 12683: 12680: 12678: 12675: 12674: 12672: 12670: 12666: 12658: 12655: 12653: 12650: 12649: 12648: 12645: 12643: 12640: 12638: 12635: 12633: 12630: 12628: 12625: 12623: 12620: 12619: 12617: 12615: 12611: 12605: 12602: 12598: 12595: 12591: 12588: 12586: 12583: 12582: 12581: 12578: 12577: 12576: 12573: 12569: 12566: 12564: 12561: 12559: 12556: 12554: 12551: 12550: 12549: 12546: 12545: 12543: 12541: 12537: 12534: 12532: 12528: 12522: 12519: 12517: 12514: 12510: 12507: 12506: 12505: 12502: 12500: 12497: 12493: 12492:loss function 12490: 12489: 12488: 12485: 12481: 12478: 12476: 12473: 12471: 12468: 12467: 12466: 12463: 12461: 12458: 12456: 12453: 12449: 12446: 12444: 12441: 12439: 12433: 12430: 12429: 12428: 12425: 12421: 12418: 12416: 12413: 12411: 12408: 12407: 12406: 12403: 12399: 12396: 12394: 12391: 12390: 12389: 12386: 12382: 12379: 12378: 12377: 12374: 12370: 12367: 12366: 12365: 12362: 12360: 12357: 12355: 12352: 12350: 12347: 12346: 12344: 12342: 12338: 12334: 12330: 12325: 12321: 12307: 12304: 12302: 12299: 12297: 12294: 12292: 12289: 12288: 12286: 12284: 12280: 12274: 12271: 12269: 12266: 12264: 12261: 12260: 12258: 12254: 12248: 12245: 12243: 12240: 12238: 12235: 12233: 12230: 12228: 12225: 12223: 12220: 12218: 12215: 12214: 12212: 12210: 12206: 12200: 12197: 12195: 12194:Questionnaire 12192: 12190: 12187: 12183: 12180: 12178: 12175: 12174: 12173: 12170: 12169: 12167: 12165: 12161: 12155: 12152: 12150: 12147: 12145: 12142: 12140: 12137: 12135: 12132: 12130: 12127: 12125: 12122: 12120: 12117: 12116: 12114: 12112: 12108: 12104: 12100: 12095: 12091: 12077: 12074: 12072: 12069: 12067: 12064: 12062: 12059: 12057: 12054: 12052: 12049: 12047: 12044: 12042: 12039: 12037: 12034: 12032: 12029: 12027: 12024: 12022: 12021:Control chart 12019: 12017: 12014: 12012: 12009: 12007: 12004: 12003: 12001: 11999: 11995: 11989: 11986: 11982: 11979: 11977: 11974: 11973: 11972: 11969: 11967: 11964: 11962: 11959: 11958: 11956: 11954: 11950: 11944: 11941: 11939: 11936: 11934: 11931: 11930: 11928: 11924: 11918: 11915: 11914: 11912: 11910: 11906: 11894: 11891: 11889: 11886: 11884: 11881: 11880: 11879: 11876: 11874: 11871: 11870: 11868: 11866: 11862: 11856: 11853: 11851: 11848: 11846: 11843: 11841: 11838: 11836: 11833: 11831: 11828: 11826: 11823: 11822: 11820: 11818: 11814: 11808: 11805: 11803: 11800: 11796: 11793: 11791: 11788: 11786: 11783: 11781: 11778: 11776: 11773: 11771: 11768: 11766: 11763: 11761: 11758: 11756: 11753: 11751: 11748: 11747: 11746: 11743: 11742: 11740: 11738: 11734: 11731: 11729: 11725: 11721: 11717: 11712: 11708: 11702: 11699: 11697: 11694: 11693: 11690: 11686: 11679: 11674: 11672: 11667: 11665: 11660: 11659: 11656: 11647: 11645:0-471-55779-X 11641: 11637: 11633: 11629: 11625: 11621: 11617: 11613: 11609: 11605: 11601: 11597: 11593: 11588: 11583: 11579: 11575: 11571: 11555: 11551: 11540: 11536: 11535: 11522: 11516: 11510: 11506: 11505: 11500: 11494: 11486: 11473: 11465: 11461: 11457: 11453: 11449: 11445: 11440: 11435: 11431: 11424: 11417: 11413: 11407: 11396: 11390: 11375: 11371: 11365: 11357: 11353: 11348: 11343: 11339: 11335: 11331: 11327: 11323: 11316: 11307: 11304:Field, Andy. 11299: 11291: 11287: 11282: 11277: 11273: 11269: 11265: 11261: 11257: 11250: 11242: 11238: 11232: 11217: 11211: 11205: 11204:0-13-187621-X 11201: 11195: 11193: 11191: 11181: 11176: 11169: 11160: 11155: 11148: 11140: 11136: 11132: 11128: 11124: 11120: 11119:Pearson, Karl 11114: 11110: 11100: 11097: 11095: 11092: 11090: 11087: 11085: 11082: 11079: 11076: 11073: 11070: 11068: 11065: 11062: 11059: 11057: 11054: 11051: 11048: 11046: 11043: 11042: 11036: 11000: 10996: 10986: 10984: 10980: 10976: 10972: 10968: 10967:binomial test 10964: 10960: 10954: 10952: 10941: 10939: 10934: 10930: 10925: 10923: 10904: 10901: 10896: 10890: 10882: 10879: 10876: 10867: 10862: 10856: 10848: 10845: 10842: 10833: 10828: 10824: 10816: 10815: 10814: 10810: 10808: 10792: 10784: 10778: 10768: 10766: 10756: 10753: 10750: 10747: 10744: 10741: 10740: 10736: 10734: 10731: 10728: 10726: 10723: 10720: 10719: 10707: 10704: 10701: 10688: 10685: 10682: 10678: 10674: 10671: 10668: 10664: 10660: 10657: 10654: 10650: 10646: 10643: 10640: 10636: 10632: 10629: 10626: 10622: 10618: 10615: 10612: 10608: 10604: 10601: 10595: 10591: 10581: 10579: 10578: 10567: 10563: 10559: 10556: 10553: 10550: 10547: 10546: 10542: 10539: 10536: 10533: 10530: 10529: 10525: 10522: 10519: 10516: 10513: 10512: 10508: 10505: 10502: 10499: 10496: 10495: 10491: 10488: 10485: 10482: 10479: 10478: 10474: 10471: 10468: 10465: 10462: 10461: 10444: 10434: 10430: 10426: 10421: 10417: 10406: 10390: 10386: 10382: 10377: 10373: 10365: 10349: 10345: 10337: 10321: 10317: 10309: 10295: 10288: 10287: 10284: 10278: 10263: 10249: 10247: 10240: 10226: 10223: 10220: 10200: 10191: 10182: 10168: 10165: 10162: 10140: 10136: 10115: 10112: 10109: 10100: 10082: 10077: 10071: 10066: 10062: 10056: 10053: 10050: 10045: 10042: 10039: 10035: 10030: 10024: 10021: 10016: 10012: 10008: 10005: 10000: 9997: 9994: 9989: 9986: 9983: 9979: 9974: 9968: 9964: 9960: 9955: 9952: 9949: 9944: 9941: 9938: 9934: 9929: 9923: 9920: 9915: 9910: 9906: 9900: 9897: 9894: 9889: 9886: 9883: 9879: 9874: 9870: 9867: 9861: 9858: 9847: 9843: 9831: 9826: 9822: 9815: 9808: 9807: 9806: 9805:, so we get: 9804: 9785: 9780: 9775: 9771: 9765: 9762: 9759: 9754: 9751: 9748: 9744: 9740: 9735: 9731: 9725: 9722: 9718: 9712: 9708: 9702: 9699: 9696: 9691: 9688: 9685: 9682: 9679: 9675: 9667: 9666: 9665: 9646: 9642: 9618: 9615: 9612: 9605:so as to get 9587: 9583: 9571: 9552: 9549: 9546: 9540: 9534: 9531: 9528: 9505: 9483: 9475: 9471: 9467: 9461: 9453: 9449: 9443: 9440: 9436: 9429: 9424: 9421: 9417: 9412: 9409: 9406: 9403: 9400: 9397: 9394: 9391: 9388: 9385: 9382: 9379: 9375: 9370: 9366: 9360: 9357: 9353: 9347: 9343: 9337: 9334: 9331: 9326: 9323: 9320: 9317: 9314: 9310: 9304: 9301: 9296: 9289: 9288: 9287: 9284: 9265: 9261: 9257: 9250: 9244: 9234: 9230: 9226: 9223: 9218: 9214: 9182: 9178: 9171: 9163: 9159: 9155: 9152: 9147: 9143: 9137: 9124: 9119: 9115: 9111: 9100: 9096: 9089: 9081: 9077: 9065: 9060: 9056: 9031: 9025: 9020: 9013: 9009: 9002: 8999: 8996: 8991: 8988: 8985: 8981: 8976: 8966: 8962: 8958: 8954: 8949: 8942: 8938: 8932: 8927: 8923: 8915: 8912: 8909: 8904: 8901: 8898: 8894: 8888: 8885: 8880: 8876: 8872: 8869: 8864: 8861: 8858: 8853: 8850: 8847: 8843: 8838: 8832: 8828: 8824: 8819: 8816: 8813: 8808: 8805: 8802: 8798: 8793: 8787: 8784: 8773: 8769: 8762: 8754: 8750: 8746: 8743: 8738: 8734: 8728: 8715: 8710: 8706: 8701: 8692: 8688: 8682: 8677: 8674: 8671: 8667: 8661: 8658: 8655: 8647: 8644: 8637: 8632: 8626: 8623: 8612: 8608: 8596: 8591: 8587: 8580: 8573: 8572: 8571: 8557: 8549: 8525: 8520: 8515: 8506: 8502: 8496: 8486: 8482: 8475: 8472: 8469: 8464: 8461: 8458: 8454: 8447: 8444: 8440: 8436: 8433: 8429: 8423: 8419: 8413: 8410: 8407: 8402: 8399: 8396: 8392: 8386: 8381: 8376: 8372: 8368: 8364: 8360: 8356: 8352: 8349: 8345: 8340: 8331: 8327: 8321: 8313: 8309: 8303: 8300: 8296: 8292: 8289: 8285: 8279: 8275: 8269: 8264: 8259: 8255: 8251: 8247: 8243: 8239: 8235: 8232: 8227: 8224: 8221: 8216: 8213: 8210: 8206: 8201: 8197: 8193: 8185: 8181: 8174: 8170: 8166: 8161: 8153: 8150: 8147: 8142: 8139: 8136: 8132: 8127: 8121: 8118: 8107: 8103: 8096: 8088: 8084: 8080: 8077: 8072: 8068: 8062: 8049: 8044: 8040: 8035: 8026: 8020: 8016: 8010: 8005: 8002: 7999: 7994: 7990: 7986: 7983: 7980: 7976: 7970: 7965: 7962: 7959: 7955: 7949: 7946: 7943: 7936: 7934: 7925: 7918: 7912: 7908: 7902: 7899: 7896: 7891: 7888: 7885: 7881: 7875: 7870: 7865: 7861: 7857: 7853: 7849: 7844: 7835: 7831: 7825: 7815: 7811: 7804: 7801: 7798: 7793: 7790: 7787: 7783: 7776: 7773: 7769: 7757: 7753: 7747: 7742: 7737: 7733: 7729: 7723: 7718: 7709: 7705: 7699: 7691: 7687: 7681: 7678: 7674: 7667: 7664: 7661: 7656: 7653: 7650: 7646: 7641: 7636: 7629: 7625: 7621: 7616: 7608: 7605: 7602: 7597: 7594: 7591: 7587: 7582: 7576: 7573: 7562: 7558: 7551: 7543: 7539: 7535: 7532: 7527: 7523: 7517: 7504: 7499: 7495: 7490: 7480: 7476: 7472: 7469: 7464: 7459: 7456: 7453: 7449: 7443: 7440: 7437: 7430: 7428: 7420: 7417: 7406: 7402: 7390: 7385: 7381: 7374: 7363: 7362: 7361: 7360:we arrive at 7344: 7339: 7335: 7329: 7326: 7323: 7318: 7315: 7312: 7308: 7302: 7297: 7292: 7288: 7284: 7281: 7276: 7272: 7264: 7263: 7262: 7246: 7242: 7219: 7215: 7194: 7171: 7168: 7165: 7162: 7159: 7156: 7153: 7150: 7147: 7144: 7140: 7134: 7127: 7123: 7119: 7116: 7111: 7107: 7100: 7095: 7091: 7083: 7082: 7081: 7058: 7054: 7050: 7047: 7042: 7037: 7034: 7031: 7027: 7021: 7018: 7015: 7004: 7000: 6994: 6987: 6983: 6976: 6972: 6968: 6962: 6955: 6950: 6947: 6944: 6940: 6934: 6931: 6920: 6916: 6909: 6901: 6897: 6885: 6880: 6876: 6862: 6858: 6850: 6846: 6840: 6837: 6826: 6822: 6810: 6805: 6801: 6794: 6787: 6786: 6785: 6771: 6766: 6762: 6741: 6738: 6730: 6714: 6694: 6672: 6668: 6659: 6636: 6632: 6624: 6620: 6612: 6607: 6604: 6601: 6597: 6590: 6585: 6581: 6577: 6574: 6569: 6565: 6559: 6556: 6548: 6545: 6534: 6530: 6523: 6515: 6511: 6499: 6494: 6490: 6476: 6472: 6464: 6460: 6454: 6451: 6440: 6436: 6424: 6419: 6415: 6408: 6401: 6400: 6399: 6396: 6383: 6374: 6354: 6351: 6348: 6326: 6322: 6293: 6289: 6277: 6272: 6268: 6239: 6235: 6228: 6220: 6216: 6204: 6199: 6195: 6171: 6168: 6163: 6159: 6153: 6148: 6145: 6142: 6138: 6127: 6124: 6119: 6115: 6109: 6104: 6101: 6098: 6094: 6086: 6085: 6084: 6068: 6064: 6038: 6034: 6010: 6007: 6004: 6001: 5998: 5976: 5972: 5951: 5931: 5922: 5906: 5902: 5892: 5883: 5881: 5877: 5867: 5865: 5860: 5858: 5838: 5831: 5827: 5820: 5812: 5809: 5804: 5800: 5786: 5785: 5784: 5766: 5761: 5756: 5747: 5744: 5741: 5735: 5732: 5727: 5724: 5721: 5716: 5712: 5705: 5696: 5695: 5694: 5677: 5668: 5665: 5662: 5656: 5649: 5638: 5635: 5632: 5626: 5623: 5618: 5614: 5610: 5607: 5598: 5592: 5589: 5582: 5574: 5571: 5568: 5563: 5559: 5545: 5544: 5543: 5538: 5518: 5509: 5506: 5503: 5497: 5494: 5491: 5488: 5485: 5474: 5468: 5465: 5462: 5447: 5446: 5445: 5443: 5438: 5432: 5429: 5426: 5423: 5422: 5421: 5403: 5397: 5394: 5391: 5375: 5369: 5362: 5361: 5360: 5358: 5348: 5346: 5342: 5338: 5333: 5331: 5327: 5323: 5319: 5315: 5298: 5296: 5288: 5284: 5281: 5278: 5273: 5270: 5268:is preferred. 5267: 5263: 5262:Type II error 5258: 5255: 5252: 5247: 5245: 5242: 5241: 5240: 5232: 5230: 5224: 5222: 5218: 5214: 5210: 5206: 5202: 5199: +  5198: 5195: =  5194: 5189: 5175: 5172: 5169: 5161: 5158: 5155: 5151: 5147: 5142: 5139: 5136: 5132: 5109: 5105: 5079: 5074: 5066: 5063: 5059: 5053: 5050: 5046: 5038: 5035: 5031: 5025: 5022: 5018: 5014: 5008: 5004: 4998: 4995: 4992: 4988: 4978: 4971: 4968: 4964: 4958: 4955: 4951: 4945: 4942: 4939: 4935: 4931: 4928: 4909: 4891: 4888: 4885: 4881: 4874: 4864: 4861: 4858: 4854: 4850: 4845: 4842: 4839: 4835: 4823: 4818: 4815: 4812: 4808: 4802: 4797: 4794: 4791: 4787: 4783: 4778: 4774: 4766: 4765: 4764: 4761: 4759: 4755: 4734: 4729: 4726: 4723: 4719: 4711: 4706: 4703: 4700: 4696: 4692: 4687: 4682: 4679: 4675: 4669: 4664: 4661: 4657: 4649: 4648: 4647: 4645: 4626: 4621: 4616: 4613: 4610: 4606: 4598: 4593: 4590: 4587: 4583: 4579: 4574: 4569: 4566: 4562: 4556: 4551: 4548: 4544: 4536: 4535: 4534: 4520: 4497: 4492: 4489: 4485: 4479: 4476: 4472: 4468: 4465: 4460: 4457: 4454: 4450: 4442: 4441: 4440: 4438: 4434: 4430: 4426: 4416: 4414: 4410: 4406: 4402: 4398: 4392: 4382: 4378: 4364: 4361: 4358: 4338: 4335: 4332: 4329: 4326: 4316: 4299: 4296: 4293: 4286: 4282: 4276: 4271: 4267: 4259: 4254: 4251: 4248: 4244: 4240: 4235: 4231: 4223: 4222: 4221: 4218: 4204: 4184: 4176: 4172: 4168: 4164: 4144: 4137: 4121: 4117: 4108: 4104: 4086: 4082: 4078: 4075: 4070: 4066: 4058: 4043: 4036: 4033: 4015: 4011: 4003: 4000: 3984: 3980: 3956: 3952: 3944: 3943: 3942: 3921: 3917: 3911: 3906: 3900: 3896: 3892: 3889: 3885: 3879: 3875: 3870: 3861: 3856: 3853: 3850: 3846: 3842: 3839: 3832: 3828: 3821: 3811: 3807: 3803: 3798: 3794: 3782: 3777: 3774: 3771: 3767: 3763: 3758: 3754: 3746: 3745: 3744: 3736: 3733: 3730: 3727: 3724: 3721: 3720: 3716: 3713: 3710: 3707: 3704: 3701: 3700: 3696: 3693: 3690: 3687: 3684: 3681: 3680: 3676: 3673: 3670: 3667: 3664: 3661: 3660: 3656: 3653: 3650: 3647: 3644: 3641: 3640: 3636: 3633: 3630: 3627: 3624: 3621: 3620: 3616: 3613: 3610: 3607: 3604: 3601: 3600: 3596: 3593: 3590: 3587: 3584: 3581: 3580: 3576: 3573: 3570: 3567: 3564: 3561: 3560: 3556: 3553: 3550: 3547: 3544: 3541: 3540: 3536: 3533: 3530: 3527: 3524: 3521: 3520: 3516: 3513: 3510: 3507: 3504: 3501: 3500: 3496: 3493: 3490: 3487: 3484: 3481: 3480: 3476: 3473: 3470: 3467: 3464: 3461: 3460: 3456: 3453: 3450: 3447: 3444: 3441: 3440: 3436: 3433: 3430: 3427: 3424: 3421: 3420: 3416: 3413: 3410: 3407: 3404: 3401: 3400: 3396: 3393: 3390: 3387: 3384: 3381: 3380: 3376: 3373: 3370: 3367: 3364: 3361: 3360: 3356: 3353: 3350: 3347: 3344: 3341: 3340: 3336: 3333: 3330: 3327: 3324: 3321: 3320: 3316: 3313: 3310: 3307: 3304: 3301: 3300: 3296: 3293: 3290: 3287: 3284: 3281: 3280: 3276: 3273: 3270: 3267: 3264: 3261: 3260: 3256: 3253: 3250: 3247: 3244: 3241: 3240: 3236: 3233: 3230: 3227: 3224: 3221: 3220: 3216: 3213: 3210: 3207: 3204: 3201: 3200: 3196: 3193: 3190: 3187: 3184: 3181: 3180: 3176: 3173: 3170: 3167: 3164: 3161: 3160: 3156: 3153: 3150: 3147: 3144: 3141: 3140: 3136: 3133: 3130: 3127: 3124: 3121: 3120: 3116: 3113: 3110: 3107: 3104: 3101: 3100: 3096: 3093: 3090: 3087: 3084: 3081: 3080: 3076: 3073: 3070: 3067: 3064: 3061: 3060: 3056: 3053: 3050: 3047: 3044: 3041: 3040: 3036: 3033: 3030: 3027: 3024: 3021: 3020: 3016: 3013: 3010: 3007: 3004: 3001: 3000: 2996: 2993: 2990: 2987: 2984: 2981: 2980: 2976: 2973: 2970: 2967: 2964: 2961: 2960: 2956: 2953: 2950: 2947: 2944: 2941: 2940: 2936: 2933: 2930: 2927: 2924: 2921: 2920: 2916: 2913: 2910: 2907: 2904: 2901: 2900: 2896: 2893: 2890: 2887: 2884: 2881: 2880: 2876: 2873: 2870: 2867: 2864: 2861: 2860: 2856: 2853: 2850: 2847: 2844: 2841: 2840: 2836: 2833: 2830: 2827: 2824: 2821: 2820: 2816: 2813: 2810: 2807: 2804: 2801: 2800: 2796: 2793: 2790: 2787: 2784: 2781: 2780: 2776: 2773: 2770: 2767: 2764: 2761: 2760: 2756: 2753: 2750: 2747: 2744: 2741: 2740: 2736: 2733: 2730: 2727: 2724: 2721: 2720: 2716: 2713: 2710: 2707: 2704: 2701: 2700: 2696: 2693: 2690: 2687: 2684: 2681: 2680: 2676: 2673: 2670: 2667: 2664: 2661: 2660: 2656: 2653: 2650: 2647: 2644: 2641: 2640: 2636: 2633: 2630: 2627: 2624: 2621: 2620: 2616: 2613: 2610: 2607: 2604: 2601: 2600: 2596: 2593: 2590: 2587: 2584: 2581: 2580: 2576: 2573: 2570: 2567: 2564: 2561: 2560: 2556: 2553: 2550: 2547: 2544: 2541: 2540: 2536: 2533: 2530: 2527: 2524: 2521: 2520: 2516: 2513: 2510: 2507: 2504: 2501: 2500: 2496: 2493: 2490: 2487: 2484: 2481: 2480: 2476: 2473: 2470: 2467: 2464: 2461: 2460: 2456: 2453: 2450: 2447: 2444: 2441: 2440: 2436: 2433: 2430: 2427: 2424: 2421: 2420: 2416: 2413: 2410: 2407: 2404: 2401: 2400: 2396: 2393: 2390: 2387: 2384: 2381: 2380: 2376: 2373: 2370: 2367: 2364: 2361: 2360: 2356: 2353: 2350: 2347: 2344: 2341: 2340: 2336: 2333: 2330: 2327: 2324: 2321: 2320: 2316: 2313: 2310: 2307: 2304: 2301: 2300: 2296: 2293: 2290: 2287: 2284: 2281: 2280: 2276: 2273: 2270: 2267: 2264: 2261: 2260: 2256: 2253: 2250: 2247: 2244: 2241: 2240: 2236: 2233: 2230: 2227: 2224: 2221: 2220: 2216: 2213: 2210: 2207: 2204: 2201: 2200: 2196: 2193: 2190: 2187: 2184: 2181: 2180: 2176: 2173: 2170: 2167: 2164: 2161: 2160: 2156: 2153: 2150: 2147: 2144: 2141: 2140: 2136: 2133: 2130: 2127: 2124: 2121: 2120: 2116: 2113: 2110: 2107: 2104: 2101: 2100: 2096: 2093: 2090: 2087: 2084: 2081: 2080: 2076: 2073: 2070: 2067: 2064: 2061: 2060: 2056: 2053: 2050: 2047: 2044: 2041: 2040: 2036: 2033: 2030: 2027: 2024: 2021: 2020: 2016: 2013: 2010: 2007: 2004: 2001: 2000: 1996: 1993: 1990: 1987: 1984: 1981: 1980: 1976: 1973: 1970: 1967: 1964: 1961: 1960: 1956: 1953: 1950: 1947: 1944: 1941: 1940: 1936: 1933: 1930: 1927: 1924: 1921: 1920: 1916: 1913: 1910: 1907: 1904: 1901: 1900: 1896: 1893: 1890: 1887: 1884: 1881: 1880: 1876: 1873: 1870: 1867: 1864: 1861: 1860: 1856: 1853: 1850: 1847: 1844: 1841: 1840: 1836: 1833: 1830: 1827: 1824: 1821: 1820: 1816: 1813: 1810: 1807: 1804: 1801: 1800: 1796: 1793: 1790: 1787: 1784: 1781: 1780: 1776: 1773: 1770: 1767: 1764: 1761: 1760: 1756: 1753: 1750: 1747: 1744: 1741: 1740: 1736: 1733: 1730: 1727: 1724: 1723: 1711: 1706: 1700: 1696: 1692: 1683: 1681: 1677: 1673: 1668: 1654: 1634: 1631: 1628: 1608: 1605: 1602: 1582: 1579: 1576: 1556: 1553: 1550: 1542: 1526: 1506: 1503: 1500: 1497: 1494: 1479: 1476: 1462: 1440: 1436: 1415: 1412: 1409: 1386: 1380: 1377: 1372: 1367: 1363: 1355: 1354: 1353: 1351: 1334: 1314: 1307:In this case 1278: 1274: 1265: 1247: 1243: 1234: 1216: 1212: 1189: 1185: 1162: 1158: 1149: 1132: 1128: 1118: 1114: 1096: 1092: 1083: 1080: 1076: 1074: 1069: 1065: 1060: 1056: 1048: 1045: 1041: 1033: 1030: 1026: 1018: 1017: 1015: 1011: 1007: 1004: 1000: 982: 978: 969: 965: 964: 963: 957: 953: 949: 946: 942: 941: 940: 938: 934: 930: 920: 906: 903: 900: 880: 877: 872: 868: 844: 840: 836: 829: 821: 817: 813: 810: 805: 801: 789: 784: 781: 778: 774: 770: 765: 761: 737: 733: 729: 726: 723: 720: 717: 714: 711: 707: 703: 700: 697: 634: 630: 626: 623: 620: 617: 614: 609: 605: 601: 596: 592: 576: 556: 552: 548: 541: 531: 527: 523: 520: 515: 511: 499: 495: 491: 486: 482: 473: 469: 449: 445: 441: 438: 435: 432: 429: 424: 420: 374: 370: 349: 345: 341: 338: 335: 332: 329: 324: 320: 316: 313: 268: 264: 260: 245: 242: 237: 233: 227: 223: 197: 193: 189: 186: 183: 180: 177: 172: 168: 164: 159: 155: 143: 142:observed data 139: 124: 116: 115: 114: 112: 107: 105: 101: 97: 93: 89: 85: 81: 77: 73: 69: 65: 61: 45: 41: 30: 26: 22: 13966: 13954: 13935: 13928: 13840:Econometrics 13790: / 13773:Chemometrics 13750:Epidemiology 13743: / 13716:Applications 13558:ARIMA model 13505:Q-statistic 13454:Stationarity 13350:Multivariate 13293: / 13289: / 13287:Multivariate 13285: / 13225: / 13221: / 12995:Bayes factor 12894:Signed rank 12806: 12780: 12772: 12760: 12455:Completeness 12291:Cohort study 12189:Opinion poll 12124:Missing data 12111:Study design 12066:Scatter plot 11988:Scatter plot 11981:Spearman's ρ 11943:Grouped data 11635: 11603: 11599: 11577: 11573: 11539:Chernoff, H. 11520: 11503: 11499:Jaynes, E.T. 11493: 11472:cite journal 11423: 11411: 11406: 11389: 11377:. Retrieved 11373: 11364: 11329: 11325: 11315: 11305: 11298: 11263: 11259: 11249: 11240: 11231: 11219:. Retrieved 11210: 11168: 11147: 11130: 11129:. Series 5. 11126: 11113: 10987: 10955: 10947: 10926: 10919: 10811: 10780: 10762: 10732: 10724: 10702: 10582: 10575: 10573: 10276: 10264: 10260: 10243: 10183: 10101: 10098: 9800: 9498: 9285: 9047: 8545: 7359: 7186: 7079: 6655: 6397: 6186: 5923: 5893: 5889: 5873: 5861: 5856: 5853: 5781: 5692: 5536: 5534: 5441: 5439: 5436: 5430: 5424: 5419: 5354: 5334: 5329: 5325: 5317: 5313: 5311: 5292: 5282:Independence 5238: 5225: 5220: 5216: 5212: 5208: 5200: 5196: 5192: 5190: 5096: 4762: 4753: 4751: 4643: 4641: 4512: 4436: 4432: 4422: 4394: 4379: 4317: 4314: 4219: 4160: 4106: 4102: 4031: 3999:distribution 3940: 3742: 1698: 1669: 1485: 1477: 1401: 1306: 1263: 1232: 1116: 1072: 1058: 1054: 1043: 1039: 1028: 1024: 1013: 1005:(see below). 961: 937:independence 926: 580: 471: 262: 141: 108: 103: 96:Karl Pearson 32: 28: 27: 25: 13968:WikiProject 13883:Cartography 13845:Jurimetrics 13797:Reliability 13528:Time domain 13507:(Ljung–Box) 13429:Time-series 13307:Categorical 13291:Time-series 13283:Categorical 13218:(Bernoulli) 13053:Correlation 13033:Correlation 12829:Jarque–Bera 12801:Chi-squared 12563:M-estimator 12516:Asymptotics 12460:Sufficiency 12227:Interaction 12139:Replication 12119:Effect size 12076:Violin plot 12056:Radar chart 12036:Forest plot 12026:Correlogram 11976:Kendall's τ 11089:Median test 11078:Lexis ratio 10933:probability 10783:frequencies 6727:we may use 5279:is applied. 5235:Assumptions 4758:frequencies 1672:Student's t 1231:= there is 1079:alpha level 1003:frequencies 933:homogeneity 88:statistical 13984:Categories 13835:Demography 13553:ARMA model 13358:Regression 12935:(Friedman) 12896:(Wilcoxon) 12834:Normality 12824:Lilliefors 12771:Student's 12647:Resampling 12521:Robustness 12509:divergence 12499:Efficiency 12437:(monotone) 12432:Likelihood 12349:Population 12182:Stratified 12134:Population 11953:Dependence 11909:Count data 11840:Percentile 11817:Dispersion 11750:Arithmetic 11685:Statistics 11531:References 11439:1808.09171 11416:Lecture 23 11379:19 October 11221:14 October 11180:2311.08315 11159:2206.14105 11050:CramĂ©r's V 5886:Many cells 5301:Derivation 5097:Note that 1697:, showing 999:normalized 86:, etc.) – 33:Pearson's 13216:Logistic 12983:posterior 12909:Rank sum 12657:Jackknife 12652:Bootstrap 12470:Bootstrap 12405:Parameter 12354:Statistic 12149:Statistic 12061:Run chart 12046:Pie chart 12041:Histogram 12031:Fan chart 12006:Bar chart 11888:L-moments 11775:Geometric 11552:χ 11356:0004-637X 11023:Ψ 10997:χ 10880:− 10846:− 10825:χ 10592:χ 10427:− 10383:− 10224:− 10198:∞ 10195:→ 10166:− 10137:χ 10113:− 10054:− 10036:∑ 10017:− 10009:⁡ 9998:− 9980:∏ 9953:− 9935:∏ 9898:− 9880:∑ 9875:∫ 9868:∼ 9823:χ 9763:− 9745:∑ 9700:− 9676:∑ 9664:so that: 9616:− 9550:− 9541:× 9532:− 9437:δ 9407:− 9398:⋯ 9335:− 9311:∑ 9297:− 9224:− 9116:χ 9057:χ 9000:− 8982:∑ 8950:− 8913:− 8895:∑ 8881:− 8873:⁡ 8862:− 8844:∏ 8817:− 8799:∏ 8707:χ 8702:∫ 8668:∏ 8659:− 8648:π 8633:∼ 8588:χ 8570:, we get 8548:expanding 8473:− 8455:∑ 8448:− 8437:⁡ 8411:− 8393:∑ 8382:− 8361:− 8353:⁡ 8293:⁡ 8244:− 8236:⁡ 8225:− 8207:∏ 8198:× 8186:× 8151:− 8133:∏ 8041:χ 8036:∫ 8006:π 7984:π 7956:∏ 7947:π 7900:− 7882:∑ 7871:− 7850:− 7802:− 7784:∑ 7777:− 7724:− 7665:− 7647:∏ 7606:− 7588:∏ 7496:χ 7491:∫ 7473:π 7450:∏ 7441:π 7431:∼ 7382:χ 7327:− 7309:∑ 7298:− 7166:− 7157:⋯ 7117:− 7051:π 7028:∏ 7019:π 6941:∏ 6877:χ 6851:∑ 6847:∼ 6802:χ 6731:for both 6598:∏ 6578:⋯ 6491:χ 6465:∑ 6416:χ 6381:∞ 6378:→ 6352:− 6323:χ 6269:χ 6196:χ 6139:∑ 6095:∑ 6008:≤ 6002:≤ 5903:χ 5828:σ 5813:μ 5810:− 5745:− 5722:− 5666:− 5636:− 5624:− 5611:− 5569:− 5507:− 5475:≈ 5376:∼ 5351:Two cells 5316:rows and 5266:Cash test 5167:∀ 5106:χ 5064:⋅ 5054:⋅ 5036:⋅ 5026:⋅ 5015:− 4969:⋅ 4959:⋅ 4936:∑ 4851:− 4809:∑ 4788:∑ 4775:χ 4697:∑ 4680:⋅ 4662:⋅ 4584:∑ 4570:⋅ 4552:⋅ 4490:⋅ 4480:⋅ 4435:rows and 4362:− 4336:− 4330:− 4294:− 4245:∑ 4232:χ 3981:χ 3953:χ 3893:− 3847:∑ 3804:− 3768:∑ 3755:χ 1632:− 1275:χ 1186:χ 1159:χ 1129:χ 1093:χ 979:χ 968:statistic 869:χ 811:− 775:∑ 762:χ 521:− 496:∑ 483:χ 224:∑ 42:χ 13930:Category 13623:Survival 13500:Johansen 13223:Binomial 13178:Isotonic 12765:(normal) 12410:location 12217:Blocking 12172:Sampling 12051:Q–Q plot 12016:Box plot 11998:Graphics 11893:Skewness 11883:Kurtosis 11855:Variance 11785:Heronian 11780:Harmonic 11501:(2003). 11456:88524653 11290:23894860 11121:(1900). 11039:See also 10969:or, for 10944:Problems 10713:freedom 10523:−2 10506:−1 10489:−2 10472:−5 10252:Examples 9803:Jacobian 3737:149.449 3717:148.230 3697:147.010 3677:145.789 3657:144.567 3637:143.344 3617:142.119 3597:140.893 3577:139.666 3557:138.438 3537:137.208 3517:135.978 3497:134.746 3477:133.512 3457:132.277 3437:131.041 3417:129.804 3397:128.565 3377:127.324 3357:126.083 3337:124.839 3317:123.594 3297:122.348 3277:121.100 3257:119.850 3237:118.599 3217:117.346 3197:116.092 3177:114.835 3157:113.577 3137:112.317 3117:111.055 3097:109.791 3077:108.526 3057:107.258 3037:105.988 3017:104.716 2997:103.442 2977:102.166 2957:100.888 1717:freedom 1519:, where 1262:= there 1084:Compare 1038:, where 1023:, where 109:It is a 13956:Commons 13903:Kriging 13788:Process 13745:studies 13604:Wavelet 13437:General 12604:Plug-in 12398:L space 12177:Cluster 11878:Moments 11696:Outline 11624:1402731 11464:3239829 11334:Bibcode 11332:: 939. 11281:3900058 10765:p-value 10757:20.515 10754:15.086 10751:12.833 10748:11.070 10709:Degrees 10281:⁠ 10267:⁠ 5864:P-value 4163:p-value 3734:135.807 3731:129.561 3728:124.342 3725:118.498 3714:134.642 3711:128.422 3708:123.225 3705:117.407 3694:133.476 3691:127.282 3688:122.108 3685:116.315 3674:132.309 3671:126.141 3668:120.990 3665:115.223 3654:131.141 3651:125.000 3648:119.871 3645:114.131 3634:129.973 3631:123.858 3628:118.752 3625:113.038 3614:128.803 3611:122.715 3608:117.632 3605:111.944 3594:127.633 3591:121.571 3588:116.511 3585:110.850 3574:126.462 3571:120.427 3568:115.390 3565:109.756 3554:125.289 3551:119.282 3548:114.268 3545:108.661 3534:124.116 3531:118.136 3528:113.145 3525:107.565 3514:122.942 3511:116.989 3508:112.022 3505:106.469 3494:121.767 3491:115.841 3488:110.898 3485:105.372 3474:120.591 3471:114.693 3468:109.773 3465:104.275 3454:119.414 3451:113.544 3448:108.648 3445:103.177 3434:118.236 3431:112.393 3428:107.522 3425:102.079 3414:117.057 3411:111.242 3408:106.395 3405:100.980 3394:115.876 3391:110.090 3388:105.267 3374:114.695 3371:108.937 3368:104.139 3354:113.512 3351:107.783 3348:103.010 3334:112.329 3331:106.629 3328:101.879 3314:111.144 3311:105.473 3308:100.749 3294:109.958 3291:104.316 3274:108.771 3271:103.158 3254:107.583 3251:101.999 3234:106.393 3231:100.839 3214:105.202 3194:104.010 3174:102.816 3154:101.621 3134:100.425 2937:99.607 2917:98.324 2897:97.039 2877:95.751 2857:94.461 2837:93.168 2817:91.872 2797:90.573 2777:89.272 2757:87.968 2737:86.661 2717:85.351 2697:84.037 2677:82.720 2657:81.400 2637:80.077 2617:78.750 2597:77.419 2577:76.084 2557:74.745 2537:73.402 2517:72.055 2497:70.703 2477:69.347 2457:67.985 2437:66.619 2417:65.247 2397:63.870 2377:62.487 2357:61.098 2337:59.703 2317:58.301 2297:56.892 2277:55.476 2257:54.052 2237:52.620 2217:51.179 2197:49.728 2177:48.268 2157:46.797 2137:45.315 2117:43.820 2097:42.312 2077:40.790 2057:39.252 2037:37.697 2017:36.123 1997:34.528 1977:32.910 1957:31.264 1937:29.588 1917:27.877 1897:26.125 1877:24.322 1857:22.458 1837:20.515 1817:18.467 1797:16.266 1777:13.816 1757:10.828 1713:Degrees 371:from a 111:p-value 74:(e.g., 13825:Census 13415:Normal 13363:Manova 13183:Robust 12933:2-way 12925:1-way 12763:-test 12434:  12011:Biplot 11802:Median 11795:Lehmer 11737:Center 11642:  11622:  11511:  11462:  11454:  11354:  11288:  11278:  11202:  11072:G-test 10959:G-test 10745:9.236 10737:0.999 5880:Z-test 5420:where 5379:  5373:  5324:with ( 4926:  4923:  4920:  4917:  4513:where 3941:where 3385:99.880 3365:98.780 3345:97.680 3325:96.578 3305:95.476 3288:99.617 3285:94.374 3268:98.484 3265:93.270 3248:97.351 3245:92.166 3228:96.217 3225:91.061 3211:99.678 3208:95.081 3205:89.956 3191:98.516 3188:93.945 3185:88.850 3171:97.353 3168:92.808 3165:87.743 3151:96.189 3148:91.670 3145:86.635 3131:95.023 3128:90.531 3125:85.527 3114:99.228 3111:93.856 3108:89.391 3105:84.418 3094:98.028 3091:92.689 3088:88.250 3085:83.308 3074:96.828 3071:91.519 3068:87.108 3065:82.197 3054:95.626 3051:90.349 3048:85.965 3045:81.085 3034:94.422 3031:89.177 3028:84.821 3025:79.973 3014:93.217 3011:88.004 3008:83.675 3005:78.860 2994:92.010 2991:86.830 2988:82.529 2985:77.745 2974:90.802 2971:85.654 2968:81.381 2965:76.630 2954:89.591 2951:84.476 2948:80.232 2945:75.514 2934:88.379 2931:83.298 2928:79.082 2925:74.397 2914:87.166 2911:82.117 2908:77.931 2905:73.279 2894:85.950 2891:80.936 2888:76.778 2885:72.160 2874:84.733 2871:79.752 2868:75.624 2865:71.040 2854:83.513 2851:78.567 2848:74.468 2845:69.919 2834:82.292 2831:77.380 2828:73.311 2825:68.796 2814:81.069 2811:76.192 2808:72.153 2805:67.673 2794:79.843 2791:75.002 2788:70.993 2785:66.548 2774:78.616 2771:73.810 2768:69.832 2765:65.422 2754:77.386 2751:72.616 2748:68.669 2745:64.295 2734:76.154 2731:71.420 2728:67.505 2725:63.167 2714:74.919 2711:70.222 2708:66.339 2705:62.038 2694:73.683 2691:69.023 2688:65.171 2685:60.907 2674:72.443 2671:67.821 2668:64.001 2665:59.774 2654:71.201 2651:66.617 2648:62.830 2645:58.641 2634:69.957 2631:65.410 2628:61.656 2625:57.505 2614:68.710 2611:64.201 2608:60.481 2605:56.369 2594:67.459 2591:62.990 2588:59.304 2585:55.230 2574:66.206 2571:61.777 2568:58.124 2565:54.090 2554:64.950 2551:60.561 2548:56.942 2545:52.949 2534:63.691 2531:59.342 2528:55.758 2525:51.805 2514:62.428 2511:58.120 2508:54.572 2505:50.660 2494:61.162 2491:56.896 2488:53.384 2485:49.513 2474:59.893 2471:55.668 2468:52.192 2465:48.363 2454:58.619 2451:54.437 2448:50.998 2445:47.212 2434:57.342 2431:53.203 2428:49.802 2425:46.059 2414:56.061 2411:51.966 2408:48.602 2405:44.903 2394:54.776 2391:50.725 2388:47.400 2385:43.745 2374:53.486 2371:49.480 2368:46.194 2365:42.585 2354:52.191 2351:48.232 2348:44.985 2345:41.422 2334:50.892 2331:46.979 2328:43.773 2325:40.256 2314:49.588 2311:45.722 2308:42.557 2305:39.087 2294:48.278 2291:44.461 2288:41.337 2285:37.916 2274:46.963 2271:43.195 2268:40.113 2265:36.741 2254:45.642 2251:41.923 2248:38.885 2245:35.563 2234:44.314 2231:40.646 2228:37.652 2225:34.382 2214:42.980 2211:39.364 2208:36.415 2205:33.196 2194:41.638 2191:38.076 2188:35.172 2185:32.007 2174:40.289 2171:36.781 2168:33.924 2165:30.813 2154:38.932 2151:35.479 2148:32.671 2145:29.615 2134:37.566 2131:34.170 2128:31.410 2125:28.412 2114:36.191 2111:32.852 2108:30.144 2105:27.204 2094:34.805 2091:31.526 2088:28.869 2085:25.989 2074:33.409 2071:30.191 2068:27.587 2065:24.769 2054:32.000 2051:28.845 2048:26.296 2045:23.542 2034:30.578 2031:27.488 2028:24.996 2025:22.307 2014:29.141 2011:26.119 2008:23.685 2005:21.064 1994:27.688 1991:24.736 1988:22.362 1985:19.812 1974:26.217 1971:23.337 1968:21.026 1965:18.549 1954:24.725 1951:21.920 1948:19.675 1945:17.275 1934:23.209 1931:20.483 1928:18.307 1925:15.987 1914:21.666 1911:19.023 1908:16.919 1905:14.684 1894:20.090 1891:17.535 1888:15.507 1885:13.362 1874:18.475 1871:16.013 1868:14.067 1865:12.017 1854:16.812 1851:14.449 1848:12.592 1845:10.645 1834:15.086 1831:12.833 1828:11.070 1814:13.277 1811:11.143 1794:11.345 1737:0.999 1075:-value 1029:Params 935:, and 753:, and 13449:Trend 12978:prior 12920:anova 12809:-test 12783:-test 12775:-test 12682:Power 12627:Pivot 12420:shape 12415:scale 11865:Shape 11845:Range 11790:Heinz 11765:Cubic 11701:Index 11620:JSTOR 11606:(1). 11452:S2CID 11434:arXiv 11398:(PDF) 11175:arXiv 11154:arXiv 11105:Notes 10905:1.44. 10729:0.975 10155:with 4169:to a 1825:9.236 1808:9.488 1805:7.779 1791:9.348 1788:7.815 1785:6.251 1774:9.210 1771:7.378 1768:5.991 1765:4.605 1754:6.635 1751:5.024 1748:3.841 1745:2.706 1731:0.975 1115:with 923:Usage 881:11.07 76:Yates 62:is a 13682:Test 12882:Sign 12734:Wald 11807:Mode 11745:Mean 11640:ISBN 11509:ISBN 11485:help 11460:SSRN 11381:2021 11352:ISSN 11302:See 11286:PMID 11223:2014 11200:ISBN 10961:, a 10733:0.99 10725:0.95 10721:0.90 10689:13.4 10568:134 10565:Sum 10560:100 9921:> 9859:> 8785:> 8624:> 8119:> 7574:> 7418:> 6932:> 6838:> 6754:and 6546:> 6452:> 6187:Let 5924:Let 5535:Let 4351:and 3722:100 1734:0.99 1728:0.95 1725:0.90 1059:Cols 1055:Rows 1044:Cols 1040:Rows 1025:Cats 907:0.05 904:< 878:> 261:The 140:The 60:test 12862:BIC 12857:AIC 11612:doi 11582:doi 11444:doi 11342:doi 11330:228 11276:PMC 11268:doi 11135:doi 10675:100 10475:25 10006:exp 9283:). 8870:exp 8546:By 8350:exp 8233:exp 6133:and 5859:). 5456:Bin 5440:If 5384:Bin 4403:as 4395:In 4165:by 3702:99 3682:98 3662:97 3642:96 3622:95 3602:94 3582:93 3562:92 3542:91 3522:90 3502:89 3482:88 3462:87 3442:86 3422:85 3402:84 3382:83 3362:82 3342:81 3322:80 3302:79 3282:78 3262:77 3242:76 3222:75 3202:74 3182:73 3162:72 3142:71 3122:70 3102:69 3082:68 3062:67 3042:66 3022:65 3002:64 2982:63 2962:62 2942:61 2922:60 2902:59 2882:58 2862:57 2842:56 2822:55 2802:54 2782:53 2762:52 2742:51 2722:50 2702:49 2682:48 2662:47 2642:46 2622:45 2602:44 2582:43 2562:42 2542:41 2522:40 2502:39 2482:38 2462:37 2442:36 2422:35 2402:34 2382:33 2362:32 2342:31 2322:30 2302:29 2282:28 2262:27 2242:26 2222:25 2202:24 2182:23 2162:22 2142:21 2122:20 2102:19 2082:18 2062:17 2042:16 2022:15 2002:14 1982:13 1962:12 1942:11 1922:10 1680:die 1674:or 369:IID 144:is 31:or 13986:: 11618:. 11604:51 11602:. 11578:25 11576:. 11572:. 11523:.) 11476:: 11474:}} 11470:{{ 11458:. 11450:. 11442:. 11414:. 11372:. 11350:. 11340:. 11328:. 11324:. 11284:. 11274:. 11264:23 11262:. 11258:. 11239:. 11189:^ 11131:50 11125:. 10985:. 10973:, 10953:. 10897:50 10883:50 10877:56 10863:50 10849:50 10843:44 10742:5 10711:of 10683:10 10669:10 10655:10 10641:10 10627:10 10613:10 10605:25 10557:10 10554:10 10551:20 10543:0 10537:10 10534:10 10526:4 10520:10 10509:1 10503:10 10492:4 10486:10 10469:10 10270:60 10248:. 8434:ln 8290:ln 6172:1. 5359:, 5347:. 5209:rc 4217:. 1902:9 1882:8 1862:7 1842:6 1822:5 1802:4 1782:3 1762:2 1742:1 1715:of 1543:, 1475:. 1264:is 1233:no 1117:df 1070:, 1014:df 1012:, 970:, 939:. 931:, 919:. 771::= 492::= 82:, 78:, 12807:G 12781:F 12773:t 12761:Z 12480:V 12475:U 11677:e 11670:t 11663:v 11648:. 11626:. 11614:: 11590:. 11584:: 11556:2 11519:( 11517:. 11487:) 11483:( 11466:. 11446:: 11436:: 11383:. 11358:. 11344:: 11336:: 11308:. 11292:. 11270:: 11225:. 11183:. 11177:: 11162:. 11156:: 11141:. 11137:: 11001:2 10902:= 10891:2 10887:) 10874:( 10868:+ 10857:2 10853:) 10840:( 10834:= 10829:2 10793:N 10686:= 10679:/ 10672:+ 10665:/ 10661:0 10658:+ 10651:/ 10647:4 10644:+ 10637:/ 10633:1 10630:+ 10623:/ 10619:4 10616:+ 10609:/ 10602:= 10596:2 10548:6 10540:0 10531:5 10517:8 10514:4 10500:9 10497:3 10483:8 10480:2 10466:5 10463:1 10445:2 10441:) 10435:i 10431:E 10422:i 10418:O 10414:( 10391:i 10387:E 10378:i 10374:O 10350:i 10346:E 10322:i 10318:O 10296:i 10277:n 10273:/ 10227:1 10221:m 10201:, 10192:n 10169:1 10163:m 10141:2 10116:1 10110:m 10083:] 10078:) 10072:2 10067:i 10063:y 10057:1 10051:m 10046:1 10043:= 10040:i 10031:( 10025:2 10022:1 10013:[ 10001:1 9995:m 9990:1 9987:= 9984:i 9975:} 9969:i 9965:y 9961:d 9956:1 9950:m 9945:1 9942:= 9939:i 9930:{ 9924:T 9916:2 9911:i 9907:y 9901:1 9895:m 9890:1 9887:= 9884:i 9871:C 9865:) 9862:T 9856:) 9853:} 9848:i 9844:p 9840:{ 9837:( 9832:2 9827:P 9819:( 9816:P 9786:. 9781:2 9776:i 9772:y 9766:1 9760:m 9755:1 9752:= 9749:i 9741:= 9736:j 9732:x 9726:j 9723:i 9719:A 9713:i 9709:x 9703:1 9697:m 9692:1 9689:= 9686:j 9683:, 9680:i 9652:} 9647:i 9643:y 9639:{ 9619:1 9613:m 9593:} 9588:i 9584:x 9580:{ 9556:) 9553:1 9547:m 9544:( 9538:) 9535:1 9529:m 9526:( 9506:A 9484:. 9476:m 9472:p 9468:1 9462:+ 9454:i 9450:p 9444:j 9441:i 9430:= 9425:j 9422:i 9418:A 9413:, 9410:1 9404:m 9401:, 9395:, 9392:1 9389:= 9386:j 9383:, 9380:i 9376:, 9371:j 9367:x 9361:j 9358:i 9354:A 9348:i 9344:x 9338:1 9332:m 9327:1 9324:= 9321:j 9318:, 9315:i 9305:2 9302:1 9271:) 9266:m 9262:p 9258:n 9255:( 9251:/ 9245:2 9241:) 9235:m 9231:p 9227:n 9219:m 9215:k 9211:( 9191:) 9188:} 9183:i 9179:p 9175:{ 9172:, 9169:} 9164:i 9160:p 9156:n 9153:+ 9148:i 9144:x 9138:n 9133:{ 9130:( 9125:2 9120:P 9112:= 9109:) 9106:} 9101:i 9097:p 9093:{ 9090:, 9087:} 9082:i 9078:k 9074:{ 9071:( 9066:2 9061:P 9032:] 9026:2 9021:) 9014:i 9010:x 9003:1 8997:m 8992:1 8989:= 8986:i 8977:( 8967:m 8963:p 8959:2 8955:1 8943:i 8939:p 8933:2 8928:i 8924:x 8916:1 8910:m 8905:1 8902:= 8899:i 8889:2 8886:1 8877:[ 8865:1 8859:m 8854:1 8851:= 8848:i 8839:} 8833:i 8829:x 8825:d 8820:1 8814:m 8809:1 8806:= 8803:i 8794:{ 8788:T 8782:) 8779:} 8774:i 8770:p 8766:{ 8763:, 8760:} 8755:i 8751:p 8747:n 8744:+ 8739:i 8735:x 8729:n 8724:{ 8721:( 8716:2 8711:P 8693:i 8689:p 8683:m 8678:1 8675:= 8672:i 8662:1 8656:m 8652:) 8645:2 8642:( 8638:1 8630:) 8627:T 8621:) 8618:} 8613:i 8609:p 8605:{ 8602:( 8597:2 8592:P 8584:( 8581:P 8558:n 8526:} 8521:] 8516:) 8507:m 8503:p 8497:n 8487:i 8483:x 8476:1 8470:m 8465:1 8462:= 8459:i 8445:1 8441:( 8430:) 8424:i 8420:x 8414:1 8408:m 8403:1 8400:= 8397:i 8387:n 8377:m 8373:p 8369:n 8365:( 8357:[ 8346:] 8341:) 8332:i 8328:p 8322:n 8314:i 8310:x 8304:+ 8301:1 8297:( 8286:) 8280:i 8276:x 8270:n 8265:+ 8260:i 8256:p 8252:n 8248:( 8240:[ 8228:1 8222:m 8217:1 8214:= 8211:i 8202:{ 8182:} 8175:i 8171:x 8167:d 8162:n 8154:1 8148:m 8143:1 8140:= 8137:i 8128:{ 8122:T 8116:) 8113:} 8108:i 8104:p 8100:{ 8097:, 8094:} 8089:i 8085:p 8081:n 8078:+ 8073:i 8069:x 8063:n 8058:{ 8055:( 8050:2 8045:P 8027:) 8021:i 8017:x 8011:n 8003:2 8000:+ 7995:i 7991:p 7987:n 7981:2 7977:( 7971:m 7966:1 7963:= 7960:i 7950:n 7944:2 7937:= 7926:} 7919:) 7913:i 7909:x 7903:1 7897:m 7892:1 7889:= 7886:i 7876:n 7866:m 7862:p 7858:n 7854:( 7845:) 7836:m 7832:p 7826:n 7816:i 7812:x 7805:1 7799:m 7794:1 7791:= 7788:i 7774:1 7770:( 7763:) 7758:i 7754:x 7748:n 7743:+ 7738:i 7734:p 7730:n 7727:( 7719:) 7710:i 7706:p 7700:n 7692:i 7688:x 7682:+ 7679:1 7675:( 7668:1 7662:m 7657:1 7654:= 7651:i 7642:{ 7637:} 7630:i 7626:x 7622:d 7617:n 7609:1 7603:m 7598:1 7595:= 7592:i 7583:{ 7577:T 7571:) 7568:} 7563:i 7559:p 7555:{ 7552:, 7549:} 7544:i 7540:p 7536:n 7533:+ 7528:i 7524:x 7518:n 7513:{ 7510:( 7505:2 7500:P 7481:i 7477:k 7470:2 7465:m 7460:1 7457:= 7454:i 7444:n 7438:2 7424:) 7421:T 7415:) 7412:} 7407:i 7403:p 7399:{ 7396:( 7391:2 7386:P 7378:( 7375:P 7345:, 7340:i 7336:x 7330:1 7324:m 7319:1 7316:= 7313:i 7303:n 7293:m 7289:p 7285:n 7282:= 7277:m 7273:k 7247:i 7243:x 7220:i 7216:k 7195:n 7172:, 7169:1 7163:m 7160:, 7154:, 7151:1 7148:= 7145:i 7141:, 7135:n 7128:i 7124:p 7120:n 7112:i 7108:k 7101:= 7096:i 7092:x 7059:i 7055:k 7048:2 7043:m 7038:1 7035:= 7032:i 7022:n 7016:2 7005:i 7001:k 6995:) 6988:i 6984:k 6977:i 6973:p 6969:n 6963:( 6956:m 6951:1 6948:= 6945:i 6935:T 6929:) 6926:} 6921:i 6917:p 6913:{ 6910:, 6907:} 6902:i 6898:k 6894:{ 6891:( 6886:2 6881:P 6872:| 6868:} 6863:i 6859:k 6855:{ 6844:) 6841:T 6835:) 6832:} 6827:i 6823:p 6819:{ 6816:( 6811:2 6806:P 6798:( 6795:P 6772:! 6767:i 6763:k 6742:! 6739:n 6715:n 6695:n 6673:i 6669:k 6637:i 6633:k 6625:i 6621:p 6613:m 6608:1 6605:= 6602:i 6591:! 6586:m 6582:k 6575:! 6570:1 6566:k 6560:! 6557:n 6549:T 6543:) 6540:} 6535:i 6531:p 6527:{ 6524:, 6521:} 6516:i 6512:k 6508:{ 6505:( 6500:2 6495:P 6486:| 6482:} 6477:i 6473:k 6469:{ 6461:= 6458:) 6455:T 6449:) 6446:} 6441:i 6437:p 6433:{ 6430:( 6425:2 6420:P 6412:( 6409:P 6384:. 6375:n 6355:1 6349:m 6327:2 6302:) 6299:} 6294:i 6290:p 6286:{ 6283:( 6278:2 6273:P 6248:) 6245:} 6240:i 6236:p 6232:{ 6229:, 6226:} 6221:i 6217:k 6213:{ 6210:( 6205:2 6200:P 6169:= 6164:i 6160:p 6154:m 6149:1 6146:= 6143:i 6128:n 6125:= 6120:i 6116:k 6110:m 6105:1 6102:= 6099:i 6069:i 6065:k 6044:} 6039:i 6035:k 6031:{ 6011:m 6005:i 5999:1 5977:i 5973:p 5952:m 5932:n 5907:2 5857:n 5839:. 5832:2 5821:2 5817:) 5805:1 5801:O 5797:( 5767:. 5762:2 5757:) 5751:) 5748:p 5742:1 5739:( 5736:p 5733:n 5728:p 5725:n 5717:1 5713:O 5706:( 5678:, 5672:) 5669:p 5663:1 5660:( 5657:n 5650:2 5646:) 5642:) 5639:p 5633:1 5630:( 5627:n 5619:1 5615:O 5608:n 5605:( 5599:+ 5593:p 5590:n 5583:2 5579:) 5575:p 5572:n 5564:1 5560:O 5556:( 5540:1 5537:O 5519:. 5516:) 5513:) 5510:p 5504:1 5501:( 5498:p 5495:n 5492:, 5489:p 5486:n 5483:( 5479:N 5472:) 5469:p 5466:, 5463:n 5460:( 5442:n 5431:n 5425:p 5404:, 5401:) 5398:p 5395:, 5392:n 5389:( 5370:O 5330:j 5326:k 5318:k 5314:j 5253:. 5221:c 5217:r 5213:p 5201:c 5197:r 5193:p 5176:j 5173:, 5170:i 5162:j 5159:, 5156:i 5152:E 5148:= 5143:j 5140:, 5137:i 5133:O 5110:2 5080:2 5075:) 5067:j 5060:p 5051:i 5047:p 5039:j 5032:p 5023:i 5019:p 5012:) 5009:N 5005:/ 4999:j 4996:, 4993:i 4989:O 4985:( 4979:( 4972:j 4965:p 4956:i 4952:p 4946:j 4943:, 4940:i 4932:N 4929:= 4892:j 4889:, 4886:i 4882:E 4875:2 4871:) 4865:j 4862:, 4859:i 4855:E 4846:j 4843:, 4840:i 4836:O 4832:( 4824:c 4819:1 4816:= 4813:j 4803:r 4798:1 4795:= 4792:i 4784:= 4779:2 4754:j 4735:N 4730:j 4727:, 4724:i 4720:O 4712:r 4707:1 4704:= 4701:i 4693:= 4688:N 4683:j 4676:O 4670:= 4665:j 4658:p 4644:i 4627:, 4622:N 4617:j 4614:, 4611:i 4607:O 4599:c 4594:1 4591:= 4588:j 4580:= 4575:N 4567:i 4563:O 4557:= 4549:i 4545:p 4521:N 4498:, 4493:j 4486:p 4477:i 4473:p 4469:N 4466:= 4461:j 4458:, 4455:i 4451:E 4437:c 4433:r 4365:1 4359:n 4339:p 4333:1 4327:n 4300:. 4297:N 4287:i 4283:E 4277:2 4272:i 4268:O 4260:n 4255:1 4252:= 4249:i 4241:= 4236:2 4205:p 4185:n 4145:n 4122:i 4118:p 4107:i 4103:i 4087:i 4083:p 4079:N 4076:= 4071:i 4067:E 4044:N 4034:. 4032:i 4016:i 4012:O 4001:. 3985:2 3957:2 3922:i 3918:p 3912:2 3907:) 3901:i 3897:p 3890:N 3886:/ 3880:i 3876:O 3871:( 3862:n 3857:1 3854:= 3851:i 3843:N 3840:= 3833:i 3829:E 3822:2 3818:) 3812:i 3808:E 3799:i 3795:O 3791:( 3783:n 3778:1 3775:= 3772:i 3764:= 3759:2 1699:X 1655:n 1635:p 1629:n 1609:2 1606:= 1603:p 1583:3 1580:= 1577:p 1557:4 1554:= 1551:p 1527:s 1507:1 1504:+ 1501:s 1498:= 1495:p 1463:N 1441:i 1437:O 1416:1 1413:= 1410:p 1387:, 1381:n 1378:N 1373:= 1368:i 1364:E 1335:n 1315:N 1279:2 1248:1 1244:H 1217:0 1213:H 1190:2 1163:2 1147:. 1133:2 1097:2 1073:p 983:2 901:p 873:2 845:6 841:/ 837:N 830:2 826:) 822:6 818:/ 814:N 806:i 802:O 798:( 790:6 785:1 782:= 779:i 766:2 741:) 738:6 734:/ 730:1 727:, 724:. 721:. 718:. 715:, 712:6 708:/ 704:1 701:; 698:N 695:( 691:l 688:a 685:i 682:m 679:o 676:n 673:i 670:t 667:l 664:u 661:M 640:) 635:6 631:O 627:, 624:. 621:. 618:. 615:, 610:2 606:O 602:, 597:1 593:O 589:( 557:i 553:p 549:N 542:2 538:) 532:i 528:p 524:N 516:i 512:O 508:( 500:i 487:2 455:) 450:n 446:p 442:, 439:. 436:. 433:. 430:, 425:1 421:p 417:( 413:l 410:a 407:c 404:i 401:r 398:o 395:g 392:e 389:t 386:a 383:C 355:) 350:n 346:p 342:, 339:. 336:. 333:. 330:, 325:1 321:p 317:; 314:N 311:( 307:l 304:a 301:i 298:m 295:o 292:n 289:i 286:t 283:l 280:u 277:M 258:. 246:N 243:= 238:i 234:O 228:i 203:) 198:n 194:O 190:, 187:. 184:. 181:. 178:, 173:2 169:O 165:, 160:1 156:O 152:( 125:N 46:2 23:.

Index

Chi-squared test
statistical test
categorical data
chi-squared tests
Yates
likelihood ratio
portmanteau test in time series
statistical
chi-squared distribution
Karl Pearson
test statistic
p-value
multinomial distribution
IID
categorical distribution
goodness of fit
homogeneity
independence
frequency distribution
contingency table
statistic
normalized
frequencies
degrees of freedom
significance level
p-value
alpha level
chi-squared distribution
discrete uniform distribution
Generalized gamma distribution

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