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 activityâcollege, military, employment, travelâof graduates of a high school reported a year after graduation, sorted by graduation year, to see if number of graduates
10812:
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
9494:
5248:
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
5226:
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
4380:
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
10948:
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
6790:
4318:
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
5092:
1486:
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
10956:
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
3936:
5890:
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.
5259:
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
5274:
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,
5782:
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
10940:(0.01 or 0.05), so normally we would not reject the null hypothesis that the number of men in the population is the same as the number of women (i.e., we would consider our sample within the range of what we would expect for a 50/50 male/female ratio.)
9201:
10261:
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
4906:
1119:
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
4637:
4747:
9811:
6182:
5688:
9292:
9796:
7182:
7070:{\displaystyle P(\chi _{P}^{2}(\{p_{i}\})>T)\sim \sum _{\{k_{i}\}|\chi _{P}^{2}(\{k_{i}\},\{p_{i}\})>T}\prod _{i=1}^{m}\left({\frac {np_{i}}{k_{i}}}\right)^{k_{i}}{\sqrt {\frac {2\pi n}{\prod _{i=1}^{m}2\pi k_{i}}}}}
10915:
858:
572:
4912:
1347:
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
4310:
5777:
10949:
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
5530:
3749:
10699:
10935:
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.
5415:
1150:
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
5444:
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,
9281:
5186:
10977:. This test uses the conditional distribution of the test statistic given the marginal totals, and thus assumes that the margins were determined before the study; alternatives such as
6312:
5285:
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,
1031:
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.
1397:
650:
213:
891:
10457:
9566:
581:
A simple example is testing the hypothesis that an ordinary six-sided dice is "fair" (i.âe., 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
10819:
5087:{\displaystyle \ \ \ \ =N\sum _{i,j}p_{i\cdot }p_{\cdot j}\left({\frac {(O_{i,j}/N)-p_{i\cdot }p_{\cdot j}}{p_{i\cdot }p_{\cdot j}}}\right)^{2}}
13060:
10580:
table, the tabular value refers to the sum of the squared variables each divided by the expected outcomes. For the present example, this means
11415:
5239:
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions:
756:
477:
13565:
11198:
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
13715:
5265:
5450:
13339:
11980:
10585:
5437:
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,
5866:, which is equal to the probability of getting a statistic equal or bigger than the observed one, assuming the null hypothesis.
271:
70:
to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many
5789:
5231:
corresponds to the variables having an association or relationship where the structure of this relationship is not specified.
11512:
377:
11975:
11675:
10950:
10785:
of both theoretical and empirical distributions are unnormalised counts, and for a chi-squared test the total sample sizes
5276:
655:
75:
10245:
13999:
12579:
11727:
11607:
5542:
be the number of observations from the sample that are in the first cell. The
Pearson test statistic can be expressed as
6190:
4445:
13362:
13254:
11643:
11203:
936:
5365:
13967:
13540:
13414:
5344:
5335:
This approximation arises as the true distribution, under the null hypothesis, if the expected value is given by a
10767:). Specifically, getting 20 rolls of 6, when the expectation is only 10 such values, is unlikely with a fair die.
13598:
13259:
13004:
12375:
11965:
11055:
10921:
9802:
9206:
5204:
4174:
1009:
5127:
13649:
12861:
12668:
12557:
12515:
1540:
12589:
10128:
independent normally distributed variables of zero mean and unit variance will be greater than T, namely that
6263:
13892:
12851:
11754:
11098:
11093:
6657:
1358:
1349:
954:
A test of independence assesses whether observations consisting of measures on two variables, expressed in a
584:
147:
1539:
is the number of parameters used in fitting the distribution. For instance, when checking a three-parameter
13443:
13392:
13377:
13367:
13236:
13108:
13075:
12901:
12856:
12686:
11035:
test. The above reasons for the above issues become apparent when the higher order terms are investigated.
13955:
13787:
13588:
13512:
12813:
12567:
12236:
11700:
10763:
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
998:
218:
13404:
13172:
12893:
12818:
12747:
12676:
12596:
12584:
12454:
12442:
12435:
12143:
11864:
4424:
11484:
10576:
13994:
13887:
13654:
13517:
13202:
13167:
13131:
12916:
12358:
12267:
12226:
12138:
11829:
11668:
11236:
11215:
10937:
10928:
10187:
6370:
5994:
5336:
5321:
4170:
3972:
1694:
1112:
1046:
corresponds to the number of independent groups (i.e. columns in the associated contingency table).
932:
372:
266:
91:
11394:
11369:
11152:
Loukas, Orestis; Chung, Ho Ryun (2022). "Entropy-based
Characterization of Modeling Constraints".
5862:
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
6026:
5897:
5294:
5228:
5100:
4757:
4400:
3975:
3947:
1269:
1180:
1153:
1123:
1087:
1002:
973:
944:
896:
36:
11463:
11429:
5355:
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
1595:, and when checking a Poisson distribution (where the parameter is the expected value),
13943:
13754:
13608:
13504:
13453:
13329:
13226:
13210:
13187:
12964:
12698:
12681:
12641:
12552:
12447:
12409:
12380:
12340:
12300:
12246:
12163:
11849:
11844:
11619:
11451:
11433:
11280:
11255:
11174:
11153:
10978:
10970:
10806:
10788:
10291:
9501:
8553:
7190:
6710:
6690:
6177:{\displaystyle \sum _{i=1}^{m}k_{i}=n\qquad {\text{and}}\qquad \sum _{i=1}^{m}p_{i}=1.}
5947:
5927:
5250:
4516:
4200:
4180:
4140:
4039:
1650:
1522:
1458:
1330:
1310:
1235:
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
215:, the count number of samples from a finite set of given categories. They satisfy
13791:
13535:
13397:
13324:
12999:
12873:
12846:
12823:
12792:
12419:
12414:
12368:
12098:
11749:
11631:
11538:
10776:
4412:
4404:
928:
13281:
11502:
11173:
Loukas, Orestis; Chung, Ho Ryun (2023). "Total
Empiricism: Learning from Data".
5191:
Fitting the model of "independence" reduces the number of degrees of freedom by
98:
in 1900. In contexts where it is important to improve a distinction between the
16:
Evaluates how likely it is that any difference between data sets arose by chance
13740:
13735:
12198:
12128:
11774:
11595:
11322:"Parameter estimation in astronomy through application of the likelihood ratio"
9791:{\displaystyle \sum _{i,j=1}^{m-1}x_{i}A_{ij}x_{j}=\sum _{i=1}^{m-1}y_{i}^{2}.}
9569:
7177:{\displaystyle x_{i}={\frac {k_{i}-np_{i}}{\sqrt {n}}},\qquad i=1,\cdots ,m-1,}
1675:
1671:
962:
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
5261:
1670:
The degrees of freedom are not based on the number of observations as with a
5894:
Let us now prove that the distribution indeed approaches asymptotically the
13839:
13772:
13749:
13664:
12994:
12290:
12188:
12123:
12065:
12050:
11987:
11942:
11289:
11118:
95:
13882:
13844:
13527:
13428:
13290:
13103:
13070:
12562:
12479:
12474:
12118:
12075:
12055:
12035:
12025:
11794:
11447:
11271:
11088:
11077:
10932:
6260:
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
927:
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
967:
11615:
11122:
10805:
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 "
5525:{\displaystyle {\text{Bin}}(n,p)\approx {\text{N}}(np,np(1-p)).\,}
4533:
is the total sample size (the sum of all cells in the table), and
4377:
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
5863:
5227:
that the row variable is independent of the column variable. The
4162:
1071:
110:
5991:
the probability of an observation to fall in the i-th cell, for
5921:
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.
117:
Before the experiment, the experimenter fixes a certain number
11653:
1057:
corresponds to the number of categories in one variable, and
4646:
ignoring the column attribute (fraction of row totals), and
4431:) according to the values of the two outcomes. If there are
4105:, asserted by the null hypothesis that the fraction of type
893:, then the fairness of dice can be rejected at the level of
11744:
11216:"1.3.6.7.4. Critical Values of the Chi-Square Distribution"
1679:
1001:
sum of squared deviations between observed and theoretical
90:
procedures whose results are evaluated by reference to the
4161:
The chi-squared statistic can then be used to calculate a
943:
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
10412:
10371:
10343:
10315:
10294:
10219:
10190:
10161:
10134:
10108:
9814:
9673:
9637:
9611:
9578:
9524:
9504:
9295:
9209:
9054:
8579:
8556:
7369:
7270:
7240:
7213:
7193:
7089:
6793:
6760:
6737:
6713:
6693:
6666:
6407:
6373:
6347:
6320:
6266:
6193:
6092:
6062:
6029:
5997:
5970:
5950:
5930:
5900:
5792:
5702:
5551:
5453:
5368:
5130:
5103:
4915:
4772:
4655:
4542:
4519:
4448:
4357:
4325:
4229:
4203:
4183:
4143:
4115:
4064:
4042:
4009:
3978:
3950:
3752:
1653:
1627:
1601:
1575:
1549:
1525:
1493:
1461:
1434:
1408:
1361:
1333:
1313:
1272:
1241:
1210:
1183:
1156:
1126:
1090:
976:
899:
866:
759:
746:{\displaystyle \mathrm {Multinomial} (N;1/6,...,1/6)}
658:
587:
480:
380:
274:
221:
150:
123:
39:
13566:
Autoregressive conditional heteroskedasticity (ARCH)
11074:, test to which chi-squared test is an approximation
5312:
The null distribution of the Pearson statistic with
4220:
The chi-squared statistic can be also calculated as
11052:â 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:KaplanâMeier 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)Ă(Cols − 1)
1036:df = (Rows − 1)Ă(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: â 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:CochranâMantelâHaenszel 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: â 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 MoivreâLaplace 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:HodgesâLehmann 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:LehmannâScheffĂ© 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:NelsonâAalen 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:(JonckheereâTerpstra)
12842:Likelihood-ratio test
12531:Frequentist inference
12443:Locationâscale 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:RaoâBlackwellization
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:MannâWhitney 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:KolmogorovâSmirnov
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: â 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 Ï-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:(KruskalâWallis)
12912:
12897:
12852:Cross validation
12837:
12819:AndersonâDarling
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): 157â175.
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: â 1)(
5219: â 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:BreuschâGodfrey
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:(MannâWhitney)
12906:
12905:
12904:
12891:
12890:
12889:
12878:
12876:
12870:
12869:
12867:
12866:
12865:
12864:
12859:
12854:
12844:
12839:
12836:(ShapiroâWilk)
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): 59â72.
11592:
11580:(3): 579â586.
11557:
11553:
11534:
11532:
11529:
11526:
11525:
11513:
11490:
11481:|journal=
11420:
11403:
11386:
11361:
11347:10.1086/156922
11312:
11295:
11266:(2): 143â149.
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:(BoxâJenkins)
13556:
13554:
13551:
13549:
13546:
13542:
13539:
13538:
13537:
13534:
13533:
13531:
13529:
13525:
13519:
13516:
13514:
13513:DurbinâWatson
13511:
13509:
13503:
13501:
13498:
13496:
13495:DickeyâFuller
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 Ï
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:(LjungâBox)
13429:Time-series
13307:Categorical
13291:Time-series
13283:Categorical
13218:(Bernoulli)
13053:Correlation
13033:Correlation
12829:JarqueâBera
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 Ï
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:Cramér's V
5886:Many cells
5301:Derivation
5097:Note that
1697:, showing
999:normalized
86:, etc.) â
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:QâQ 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:(
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10840:(
10834:=
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10686:=
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10637:/
10633:1
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10623:/
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7101:=
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6441:i
6437:p
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6213:{
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5560:O
5556:(
5540:1
5537:O
5519:.
5516:)
5513:)
5510:p
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5501:(
5498:p
5495:n
5492:,
5489:p
5486:n
5483:(
5479:N
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5469:p
5466:,
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5460:(
5442:n
5431:n
5425:p
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5398:p
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5330:j
5326:k
5318:k
5314:j
5253:.
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5217:r
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5201:c
5197:r
5193:p
5176:j
5173:,
5170:i
5162:j
5159:,
5156:i
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5148:=
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5140:,
5137:i
5133:O
5110:2
5080:2
5075:)
5067:j
5060:p
5051:i
5047:p
5039:j
5032:p
5023:i
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5012:)
5009:N
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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
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640:)
635:6
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627:,
624:.
621:.
618:.
615:,
610:2
606:O
602:,
597:1
593:O
589:(
557:i
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549:N
542:2
538:)
532:i
528:p
524:N
516:i
512:O
508:(
500:i
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455:)
450:n
446:p
442:,
439:.
436:.
433:.
430:,
425:1
421:p
417:(
413:l
410:a
407:c
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398:o
395:g
392:e
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350:n
346:p
342:,
339:.
336:.
333:.
330:,
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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
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152:(
125:N
46:2
23:.
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