686:-test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure-lowering medication. By comparing the same patient's numbers before and after treatment, we are effectively using each patient as their own control. That way the correct rejection of the null hypothesis (here: of no difference made by the treatment) can become much more likely, with statistical power increasing simply because the random interpatient variation has now been eliminated. However, an increase of statistical power comes at a price: more tests are required, each subject having to be tested twice. Because half of the sample now depends on the other half, the paired version of Student's
7511:
6906:
power in detecting an alternative by which group B has the same distribution as A but after some shift by a constant (in which case there would indeed be a difference in the means of the two groups). However, there could be cases where group A and B will have different distributions but with the same means (such as two distributions, one with positive skewness and the other with a negative one, but shifted so to have the same means). In such cases, MW could have more than alpha level power in rejecting the Null hypothesis but attributing the interpretation of difference in means to such a result would be incorrect.
12035:
8390:
737:-test based on a "matched-pairs sample" results from an unpaired sample that is subsequently used to form a paired sample, by using additional variables that were measured along with the variable of interest. The matching is carried out by identifying pairs of values consisting of one observation from each of the two samples, where the pair is similar in terms of other measured variables. This approach is sometimes used in observational studies to reduce or eliminate the effects of confounding factors.
13207:
12021:
95:
234:
2464:
537:
6258:
13231:
12059:
241:
13219:
12047:
525:
1317:, sample means of moderately large samples are often well-approximated by a normal distribution even if the data are not normally distributed. However, the sample size required for the sample means to converge to normality depends on the skewness of the distribution of the original data. The sample can vary from 30 to 100 or higher values depending on the skewness. F
7480:
1893:
2232:
4262:
2221:
5604:
6905:
discussed below, typically do not test for a difference of means, so should be used carefully if a difference of means is of primary scientific interest. For example, Mann-Whitney U test will keep the type 1 error at the desired level alpha if both groups have the same distribution. It will also have
6964:
When both paired observations and independent observations are present in the two sample design, assuming data are missing completely at random (MCAR), the paired observations or independent observations may be discarded in order to proceed with the standard tests above. Alternatively making use of
646:
samples are obtained, and one variable from each of the two populations is compared. For example, suppose we are evaluating the effect of a medical treatment, and we enroll 100 subjects into our study, then randomly assign 50 subjects to the treatment group and 50 subjects to the
7505:
A clinical trial examines 6 patients given drug or placebo. Three (3) patients get 0 units of drug (the placebo group). Three (3) patients get 1 unit of drug (the active treatment group). At the end of treatment, the researchers measure the change from baseline in the number of words that each
1262:
The data used to carry out the test should either be sampled independently from the two populations being compared or be fully paired. This is in general not testable from the data, but if the data are known to be dependent (e.g. paired by test design), a dependent test has to be applied. For
2459:{\displaystyle {\begin{aligned}{\hat {\varepsilon }}_{i}&=y_{i}-{\hat {y}}_{i}=y_{i}-({\hat {\alpha }}+{\hat {\beta }}x_{i})={\text{residuals}}={\text{estimated errors}},\\{\text{SSR}}&=\sum _{i=1}^{n}{{\hat {\varepsilon }}_{i}}^{2}={\text{sum of squares of residuals}}.\end{aligned}}}
7192:
1769:
7262:
2638:
6055:
are the average and standard deviation of the differences between all pairs. The pairs are e.g. either one person's pre-test and post-test scores or between-pairs of persons matched into meaningful groups (for instance, drawn from the same family or age group: see table). The constant
2857:
181:, and was interested in the problems of small samples – for example, the chemical properties of barley with small sample sizes. Hence a second version of the etymology of the term Student is that Guinness did not want their competitors to know that they were using the
4018:
3274:
This test is used only when it can be assumed that the two distributions have the same variance (when this assumption is violated, see below). The previous formulae are a special case of the formulae below, one recovers them when both samples are equal in size:
3434:
5300:
2005:
5875:
2031:
5146:
3600:
544:-tests as a function of the correlation. The simulated random numbers originate from a bivariate normal distribution with a variance of 1 and a deviation of the expected value of 0.4. The significance level is 5% and the number of cases is 60.
6593:
for the two samples are approximately 0.05 and 0.11, respectively. For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample
3918:
6995:, allows for the testing of hypotheses on multiple (often correlated) measures within the same sample. For instance, a researcher might submit a number of subjects to a personality test consisting of multiple personality scales (e.g. the
6695:
5440:
1582:
1084:
905:
5432:
3006:
4980:
5889:
This test is used when the samples are dependent; that is, when there is only one sample that has been tested twice (repeated measures) or when there are two samples that have been matched or "paired". This is an example of a
7950:
3807:
1888:{\displaystyle {\begin{aligned}{\hat {\alpha }},{\hat {\beta }}&={\text{least-squares estimators}},\\SE_{\hat {\alpha }},SE_{\hat {\beta }}&={\text{the standard errors of least-squares estimators}}.\end{aligned}}}
7475:{\displaystyle t^{2}={\frac {n_{1}n_{2}}{n_{1}+n_{2}}}\left({\bar {\mathbf {x} }}_{1}-{\bar {\mathbf {x} }}_{2}\right)'{\mathbf {S} _{\text{pooled}}}^{-1}\left({\bar {\mathbf {x} }}_{1}-{\bar {\mathbf {x} }}_{2}\right).}
1435:
2726:
7937:
The estimate value of 4 for the drug dose indicates that for a 1-unit change in drug dose (from 0 to 1) there is a 4-unit change in mean word recall (from 2 to 6). This is the slope of the line joining the two group
5708:
2484:
6491:
6392:
5987:
3103:
7068:
2766:
13017:
356:
532:-tests as a function of the correlation. The simulated random numbers originate from a bivariate normal distribution with a variance of 1. The significance level is 5% and the number of cases is 60.
4287:, i.e., comparing the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.
6584:
4257:{\displaystyle {\text{d.f.}}={\frac {\left({\frac {s_{1}^{2}}{n_{1}}}+{\frac {s_{2}^{2}}{n_{2}}}\right)^{2}}{{\frac {(s_{1}^{2}/n_{1})^{2}}{n_{1}-1}}+{\frac {(s_{2}^{2}/n_{2})^{2}}{n_{2}-1}}}}.}
2237:
1774:
1488:
1692:
3310:
7945:
The coefficients for the linear regression specify the slope and intercept of the line that joins the two group means, as illustrated in the graph. The intercept is 2 and the slope is 4.
6729:
4652:
4598:
2216:{\displaystyle SE_{\hat {\beta }}={\frac {\sqrt {\displaystyle {\frac {1}{n-2}}\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2}}}{\sqrt {\displaystyle \sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}}
5157:
1904:
5716:
4006:
217:
Guinness had a policy of allowing technical staff leave for study (so-called "study leave"), which Gosset used during the first two terms of the 1906â1907 academic year in
Professor
9296:"Central limit theorem and the normality assumption > Normality > Continuous distributions > Distribution > Statistical Reference Guide | Analyse-itÂŽ 6.15 documentation"
717:
being the total number of observations). Pairs become individual test units, and the sample has to be doubled to achieve the same number of degrees of freedom. Normally, there are
6780:
4805:
4701:
8573:
Schlyvitch, B. (October 1937). "Untersuchungen Ăźber den anastomotischen Kanal zwischen der
Arteria coeliaca und mesenterica superior und damit in Zusammenhang stehende Fragen".
6814:
4356:
510:
6026:
3710:-test, is used only when the two population variances are not assumed to be equal (the two sample sizes may or may not be equal) and hence must be estimated separately. The
4863:
4759:
4988:
3445:
3818:
937:
444:
388:
4831:
4727:
5599:{\displaystyle {\frac {\sum _{i=2}^{n}Z_{i}^{2}}{n-1}}\sim {\frac {\chi _{n-1}^{2}}{n-1}}\times \left({\frac {\sigma _{1}^{2}}{m}}+{\frac {\sigma _{2}^{2}}{n}}\right)}
4544:
6875:
4518:
4440:
614:(probability of avoiding a type II error, also known as a false negative) than unpaired tests when the paired units are similar with respect to "noise factors" (see
6612:
6053:
643:
1499:
1349:
987:
471:
821:
9542:"How to compare the means of two samples that include paired observations and independent observations: A companion to Derrick, Russ, Toher and White (2017)"
5308:
2914:
7970:
From the regression, the slope is also 4 indicating that a 1-unit change in drug dose (from 0 to 1) gives a 4-unit change in mean word recall (from 2 to 6).
185:-test to determine the quality of raw material. Although it was William Gosset after whom the term "Student" is penned, it was actually through the work of
4871:
13012:
6852:
is a nearly exact test for the case where the data are normal but the variances may differ.) For moderately large samples and a one tailed test, the
13002:
7003:-tests to test hypotheses, as these would neglect the covariance among measures and inflate the chance of falsely rejecting at least one hypothesis (
3722:
8559:
8008:
that are associated with the response. Including such additional explanatory variables using regression or anova reduces the otherwise unexplained
1357:
9413:
Zimmerman, Donald W. (January 1998). "Invalidation of
Parametric and Nonparametric Statistical Tests by Concurrent Violation of Two Assumptions".
2658:
2633:{\displaystyle t_{\text{score}}={\frac {({\hat {\beta }}-\beta _{0}){\sqrt {n-2}}}{\sqrt {\frac {SSR}{\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}}.}
11156:
7187:{\displaystyle t^{2}=n({\bar {\mathbf {x} }}-{{\boldsymbol {\mu }}_{0}})'{\mathbf {S} }^{-1}({\bar {\mathbf {x} }}-{{\boldsymbol {\mu }}_{0}})}
5612:
2852:{\displaystyle t_{\text{score,intercept}}={\frac {\alpha }{\beta }}{\frac {t_{\text{score,slope}}}{\sqrt {s_{\text{x}}^{2}+{\bar {x}}^{2}}}},}
11661:
7250:
6412:
6313:
5904:
3017:
8340:
8323:
7985:
This example shows that, for the special case of a simple linear regression where there is a single x-variable that has values 0 and 1, the
8618:"Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Beobachtungsfehlers directer Beobachtungen gleicher Genauigkeit"
4008:
is not a pooled variance. For use in significance testing, the distribution of the test statistic is approximated as an ordinary
Student's
6917:-test is not robust. For example, for two independent samples when the data distributions are asymmetric (that is, the distributions are
1331:
implies that the distribution of the sample variance has little effect on the distribution of the test statistic. That is, as sample size
11811:
6996:
792:
may be sensitive to the alternative hypothesis (i.e., its magnitude tends to be larger when the alternative hypothesis is true), whereas
13052:
11435:
10076:
287:
11209:
7981:-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods give identical results.
568:
of the two populations are also assumed to be equal; the form of the test used when this assumption is dropped is sometimes called
8357:
1624:
13085:
13057:
12097:
11648:
6844:-test provides an exact test for the equality of the means of two i.i.d. normal populations with unknown, but equal, variances. (
13062:
12378:
9734:
9448:
Blair, R. Clifford; Higgins, James J. (1980). "A Comparison of the Power of
Wilcoxon's Rank-Sum Statistic to That of Student's
9382:
Sawilowsky, Shlomo S.; Blair, R. Clifford (1992). "A More
Realistic Look at the Robustness and Type II Error Properties of the
8171:
8137:
417:. Although the parent population does not need to be normally distributed, the distribution of the population of sample means
78:-test's most common application is to test whether the means of two populations are significantly different. In many cases, a
13120:
13027:
9279:
9012:
8543:
8510:
7008:
6978:
1597:-tests are given below. In each case, the formula for a test statistic that either exactly follows or closely approximates a
13110:
10071:
9771:
8417:
6065:
is zero if we want to test whether the average of the difference is significantly different. The degree of freedom used is
6525:
1639:(usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.
13067:
12631:
12219:
10675:
9823:
8005:
9190:
Markowski, Carol A.; Markowski, Edward P. (1990). "Conditions for the
Effectiveness of a Preliminary Test of Variance".
2022:
12135:
8821:
7056:
6999:). Because measures of this type are usually positively correlated, it is not advisable to conduct separate univariate
6988:
4271:. The true distribution of the test statistic actually depends (slightly) on the two unknown population variances (see
1446:
3429:{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{p}\cdot {\sqrt {{\frac {1}{n_{1}}}+{\frac {1}{n_{2}}}}}}},}
13125:
12651:
12234:
11458:
11350:
9623:
9037:
8929:
6285:
1653:
1310:
12063:
11636:
11510:
9594:
9541:
9225:
Guo, Beibei; Yuan, Ying (2017). "A comparative review of methods for comparing means using partially paired data".
8459:
4268:
7013:
5295:{\displaystyle Z_{1}={\bar {X}}-{\bar {Y}}={\frac {1}{m}}\sum _{i=1}^{m}X_{i}-{\frac {1}{n}}\sum _{j=1}^{n}Y_{j},}
2000:{\displaystyle t_{\text{score}}={\frac {{\hat {\beta }}-\beta _{0}}{SE_{\hat {\beta }}}}\sim {\mathcal {T}}_{n-2}}
12768:
12396:
12373:
11694:
11355:
11100:
10471:
10061:
8255:
6706:
5870:{\displaystyle T_{e}:={\frac {Z_{1}-(\mu _{1}-\mu _{2})}{\sqrt {(\sum _{i=2}^{n}Z_{i}^{2})/(n-1)}}}\sim t_{n-1}.}
4603:
4549:
3197:
2736:
1602:
1225:
1166:
407:
7949:
13264:
13223:
13042:
12992:
12804:
12701:
12462:
12363:
12276:
11745:
10957:
10764:
10653:
10611:
35:
10685:
3964:
13235:
12875:
12646:
11988:
10947:
9850:
9716:
9295:
8232:
8069:
6856:-test is relatively robust to moderate violations of the normality assumption. In large enough samples, the
12740:
12467:
11539:
11488:
11473:
11463:
11332:
11204:
11171:
10997:
10952:
10782:
9321:"Comparison of Normality Tests in Terms of Sample Sizes under Different Skewness and Kurtosis Coefficients"
8346:
8209:
7612:
functions for the t-test and linear regression. Here are the same (fictitious) data above generated in R.
6752:
12887:
12780:
12691:
12504:
12492:
12401:
12090:
12051:
11883:
11684:
11608:
10909:
10663:
10332:
9796:
9711:
8329:
7989:-test gives the same results as the linear regression. The relationship can also be shown algebraically.
4764:
4660:
3190:
150:
43:
13259:
12957:
12882:
12787:
12323:
11768:
11740:
11735:
11483:
11242:
11148:
11128:
11036:
10747:
10565:
10048:
9920:
9740:
9611:
8306:
7934:
The estimate value of 2 for the intercept is the mean value of the word recall when the drug dose is 0.
6791:
4284:
4272:
981:
8778:"X. Contributions to the mathematical theory of evolution.âII. Skew variation in homogeneous material"
6965:
all of the available data, assuming normality and MCAR, the generalized partially overlapping samples
4309:
618:) that are independent of membership in the two groups being compared. In a different context, paired
13079:
13074:
12942:
12641:
12348:
12306:
12270:
12177:
11500:
11268:
10989:
10914:
10843:
10772:
10692:
10680:
10550:
10538:
10531:
10239:
9960:
9358:
Wang, Chang; Jia, Jinzhu (2022). "Te Test: A New Non-asymptotic T-test for
Behrens-Fisher Problems".
8694:
Pfanzagl, J. (1996). "Studies in the history of probability and statistics XLIV. A forerunner of the
6938:
6496:
These could be, for example, the weights of screws that were manufactured by two different machines.
3606:
3118:
476:
222:
8188:
5995:
5141:{\displaystyle Z\sim N((\mu _{1}-\mu _{2},0,...,0)^{T},(\sigma _{1}^{2}/m+\sigma _{2}^{2}/n)I_{n}).}
3643:
3595:{\displaystyle s_{p}={\sqrt {\frac {(n_{1}-1)s_{X_{1}}^{2}+(n_{2}-1)s_{X_{2}}^{2}}{n_{1}+n_{2}-2}}}}
647:
control group. In this case, we have two independent samples and would use the unpaired form of the
12917:
12616:
12328:
12224:
11983:
11750:
11613:
11298:
11263:
11227:
11012:
10454:
10363:
10322:
10234:
9925:
9764:
8427:
8403:
8295:
8065:
7227:
4836:
4732:
3913:{\displaystyle s_{\bar {\Delta }}={\sqrt {{\frac {s_{1}^{2}}{n_{1}}}+{\frac {s_{2}^{2}}{n_{2}}}}}.}
1636:
1303:
1194:
1151:
126:
31:
9706:
3623:
is the number of degrees of freedom for each group, and the total sample size minus two (that is,
397:
13188:
13115:
12947:
11892:
11505:
11445:
11382:
11020:
11004:
10742:
10604:
10594:
10444:
10358:
8449:
7807:
Perform a linear regression of the same data. Calculations may be performed using the R function
6922:
6902:
3217:
1240:
9615:
9605:
9159:
9142:
8953:
Raju, T. N. (2005). "William Sealy Gosset and
William A. Silverman: Two 'Students' of Science".
6959:
6901:
control than some non-parametric alternatives. Furthermore, non-parametric methods, such as the
913:
420:
364:
225:. Gosset's identity was then known to fellow statisticians and to editor-in-chief Karl Pearson.
13211:
13183:
12962:
12686:
12172:
12083:
11930:
11860:
11653:
11590:
11345:
11232:
10229:
10126:
10033:
9912:
9811:
7601:
7025:
distribution. However, in practice the distribution is rarely used, since tabulated values for
6519:, which appears in the numerator for all the two-sample testing approaches discussed above, is
5891:
4810:
4706:
1313:. Normality of the individual data values is not required if these conditions are met. By the
1259:
is insensitive to equality of the variances regardless of whether the sample sizes are similar.
1205:-test comparing the means of two independent samples, the following assumptions should be met:
660:
9002:
8500:
6690:{\displaystyle {\sqrt {{\frac {s_{1}^{2}}{n_{1}}}+{\frac {s_{2}^{2}}{n_{2}}}}}\approx 0.04849}
1320:
For non-normal data, the distribution of the sample variance may deviate substantially from a
13168:
12952:
12487:
12388:
12281:
12130:
11955:
11897:
11840:
11666:
11559:
11468:
11194:
11078:
10937:
10929:
10819:
10811:
10626:
10522:
10500:
10459:
10424:
10391:
10337:
10312:
10267:
10206:
10166:
9968:
9791:
4523:
3613:
of the common variance, whether or not the population means are the same. In these formulae,
1438:
1314:
1214:
607:
450:
122:
7996:-test and linear regression facilitates the use of multiple linear regression and multi-way
6921:) or the distributions have large tails, then the Wilcoxon rank-sum test (also known as the
6276:
4445:
4367:
62:
in the test statistic were known (typically, the scaling term is unknown and is therefore a
13143:
12927:
12792:
12758:
12706:
12531:
12526:
12472:
12428:
12318:
12256:
12145:
12140:
11878:
11453:
11402:
11378:
11340:
11258:
11237:
11189:
11068:
11046:
11015:
10924:
10801:
10752:
10670:
10643:
10599:
10555:
10317:
10093:
9973:
9069:
8955:
8789:
8719:
8668:
8629:
8479:
7997:
6949:
6031:
1577:{\displaystyle \therefore {\frac {{\sqrt {n}}({\bar {X}}-\mu )}{s}}\xrightarrow {d} N(0,1)}
1491:
1328:
1210:
158:
138:
98:
9604:
Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (1992).
9493:-test? On assumptions for hypothesis tests and multiple interpretations of decision rules"
1079:{\displaystyle {\hat {\sigma }}={\sqrt {{\frac {1}{n-1}}\sum _{i}(X_{i}-{\bar {X}})^{2}}}}
8:
13153:
13148:
12922:
12711:
12546:
12155:
12025:
11950:
11873:
11554:
11318:
11311:
11273:
11181:
11161:
11133:
10732:
10727:
10717:
10709:
10527:
10488:
10378:
10368:
10277:
10056:
10012:
9930:
9855:
9757:
8077:
6590:
900:{\displaystyle t={\frac {Z}{s}}={\frac {{\bar {X}}-\mu }{{\hat {\sigma }}/{\sqrt {n}}}},}
627:
55:
8793:
8672:
8633:
8289:
1224:-test, the two populations being compared should have the same variance (testable using
272:. In testing the null hypothesis that the population mean is equal to a specified value
12775:
12358:
12207:
12039:
11850:
11704:
11600:
11549:
11425:
11322:
11306:
11283:
11060:
10794:
10777:
10737:
10648:
10543:
10505:
10476:
10436:
10396:
10342:
10259:
9945:
9940:
9517:
9469:
9359:
9250:
9207:
9112:
8980:
8758:
8598:
8553:
8395:
5427:{\displaystyle Z_{1}-(\mu _{1}-\mu _{2})\sim N(0,\sigma _{1}^{2}/m+\sigma _{2}^{2}/n),}
3933:
3610:
3180:
3001:{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{p}{\sqrt {\frac {2}{n}}}}},}
1334:
1236:
456:
86:-test because the latter converges to the former as the size of the dataset increases.
63:
7485:
1247:). If the sample sizes in the two groups being compared are equal, Student's original
12937:
12932:
12860:
12809:
12583:
12563:
12551:
12511:
12482:
12450:
12368:
12261:
12229:
12125:
12034:
11945:
11915:
11907:
11727:
11718:
11643:
11574:
11430:
11415:
11390:
11278:
11219:
11085:
11073:
10699:
10616:
10560:
10483:
10327:
10249:
10028:
9902:
9724:
9674:
Edgell, Stephen E.; Noon, Sheila M. (1984). "Effect of violation of normality on the
9662:
9619:
9590:
9522:
9488:
9430:
9340:
9275:
9242:
9172:
9164:
9033:
9008:
8972:
8935:
8925:
8902:
8762:
8750:
8590:
8539:
8506:
8469:
8389:
7499:
6890:
6845:
6606:
If the approach for unequal variances (discussed above) is followed, the results are
6268:
3697:
1252:
672:
611:
588:
569:
9254:
8984:
8602:
7510:
4975:{\displaystyle Z:=(Q^{T})_{n\times m}X/{\sqrt {m}}-(P^{T})_{n\times n}Y/{\sqrt {n}}}
4361:
The statistic to test whether the means are different can be calculated as follows:
3640:) is the total number of degrees of freedom, which is used in significance testing.
13102:
12855:
12814:
12626:
12601:
12413:
12343:
12187:
11970:
11925:
11689:
11676:
11569:
11544:
11478:
11410:
11288:
10896:
10789:
10722:
10635:
10582:
10401:
10272:
10066:
9950:
9865:
9832:
9687:
9654:
9556:
9512:
9504:
9461:
9422:
9395:
9332:
9234:
9199:
9154:
9104:
8964:
8894:
8846:
8838:
8797:
8742:
8707:
8676:
8637:
8582:
8531:
8194:
8037:
7738:, is required to make the analysis exactly equivalent to simple linear regression.
6746:
If the approach for equal variances (discussed above) is followed, the results are
1605:
are given in each case. Each of these statistics can be used to carry out either a
1232:
598:-tests for a difference in means involve independent samples (unpaired samples) or
189:
that the distribution became well known as "Student's distribution" and "Student's
170:
27:
8898:
13163:
12865:
12668:
12661:
12596:
12536:
12418:
12408:
12338:
12311:
12296:
12251:
12241:
12192:
11887:
11631:
11493:
11420:
11095:
10969:
10942:
10919:
10888:
10515:
10510:
10464:
10194:
9845:
9641:
Boneau, C. Alan (1960). "The effects of violations of assumptions underlying the
9269:
8715:
8535:
8272:
8226:
8143:
8109:
8041:
8013:
7007:). In this case a single multivariate test is preferable for hypothesis testing.
6500:
1606:
1097:
799:
269:
59:
51:
11377:
9399:
3304:
statistic to test whether the means are different can be calculated as follows:
2908:
statistic to test whether the means are different can be calculated as follows:
130:
117:-statistic" is abbreviated from "hypothesis test statistic". In statistics, the
12850:
12636:
12573:
12558:
12541:
12499:
12301:
12182:
11836:
11831:
10294:
10224:
9870:
9691:
8312:
8057:
8045:
6893:. However, when data are non-normal with differing variances between groups, a
6882:
1733:
is the outcome of interest. We want to test the null hypothesis that the slope
553:
39:
9426:
8850:
8711:
6878:
for some theory related to one particular family of non-normal distributions.
3802:{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{\bar {\Delta }}}},}
3716:
statistic to test whether the population means are different is calculated as
13253:
13158:
13037:
12845:
12819:
12696:
12656:
12621:
12611:
12591:
12333:
12291:
12266:
12214:
12202:
12197:
12106:
11993:
11960:
11823:
11784:
11595:
11564:
11028:
10982:
10587:
10289:
10116:
9880:
9875:
9434:
9344:
9238:
9168:
9143:"The Importance of the Normality Assumption in Large Public Health Data Sets"
8998:
8939:
8754:
8680:
8641:
8594:
8215:
8177:
7800:
The difference between treatment groups in the mean word.recall is 6 â 2 = 4.
7233:
For a two-sample multivariate test, the hypothesis is that the mean vectors (
6960:
A design which includes both paired observations and independent observations
6819:
The test statistic is approximately equal to 1.959, which gives a two-tailed
1430:{\displaystyle {\sqrt {n}}({\bar {X}}-\mu )\xrightarrow {d} N(0,\sigma ^{2})}
665:
599:
265:
186:
9561:
9320:
7803:
The difference in word.recall between drug doses is significant (p=0.00805).
7516:
A table of the patients' word recall and drug dose values are shown below.
7040:
For a one-sample multivariate test, the hypothesis is that the mean vector (
7017:
reduced for positive correlation among tests is one. Another is
Hotelling's
13178:
12606:
12455:
12445:
12423:
12353:
12246:
12160:
11935:
11868:
11845:
11760:
11090:
10386:
10284:
10219:
10161:
10146:
10083:
10038:
9666:
9526:
9336:
9246:
9176:
8976:
8968:
8906:
8842:
8802:
8777:
8526:
SzabĂł, IstvĂĄn (2003). "Systeme aus einer endlichen Anzahl starrer KĂśrper".
8374:
7004:
6898:
6870:
If the data are substantially non-normal and the sample size is small, the
2721:{\displaystyle t_{\text{score}}={\frac {r{\sqrt {n-2}}}{\sqrt {1-r^{2}}}},}
1721:
is a normally distributed random variable with mean 0 and unknown variance
1244:
218:
142:
675:, or one group of units that has been tested twice (a "repeated measures"
165:
using the pseudonym "Student" because his employer preferred staff to use
30:
used to test whether the difference between the response of two groups is
13173:
12870:
12568:
12477:
12440:
11978:
11940:
11623:
11524:
11386:
11199:
11166:
10658:
10575:
10570:
10214:
10171:
10151:
10131:
10121:
9890:
9138:
8278:
8029:
6734:
The test statistic is approximately 1.959, which gives a two-tailed test
1267:-tests may give invalid results as the test statistic might not follow a
1217:, even when the distribution of observations in each group is non-normal.
940:
623:
453:, if the observations are independent and the second moment exists, then
9032:. High-Yield Series. Hagerstown, MD: Lippincott Williams & Wilkins.
5703:{\displaystyle Z_{1}-(\mu _{1}-\mu _{2})\perp \sum _{i=2}^{n}Z_{i}^{2}.}
1601:-distribution under the null hypothesis is given. Also, the appropriate
137:-distribution also appeared in a more general form as Pearson type
12799:
12521:
10824:
10304:
10004:
9935:
9885:
9860:
9780:
9744:
9473:
9211:
9116:
8829:
8746:
8586:
8414: â Statistical hypothesis test, mostly using multiple restrictions
6486:{\displaystyle A_{2}=\{29.89,\ 29.93,\ 29.72,\ 29.98,\ 30.02,\ 29.98\}}
6387:{\displaystyle A_{1}=\{30.02,\ 29.99,\ 30.11,\ 29.97,\ 30.01,\ 29.99\}}
5982:{\displaystyle t={\frac {{\bar {X}}_{D}-\mu _{0}}{s_{D}/{\sqrt {n}}}},}
4291:
3609:
of the two samples: it is defined in this way so that its square is an
3098:{\displaystyle s_{p}={\sqrt {\frac {s_{X_{1}}^{2}+s_{X_{2}}^{2}}{2}}}.}
1287:
615:
210:
162:
94:
6307:
denote a set obtained by drawing a random sample of six measurements:
4278:
1302:-test additionally requires that the sample variance follows a scaled
161:, who first published it in English in 1908 in the scientific journal
12897:
12716:
12286:
12167:
10977:
10829:
10449:
10244:
10156:
10141:
10136:
10101:
9658:
9586:
9508:
8871:
7955:
Compare the result from the linear regression to the result from the
7872:
The linear regression provides a table of coefficients and p-values.
106:
54:. It is most commonly applied when the test statistic would follow a
9465:
9203:
9108:
8656:
8617:
8476: â Statistical test of whether two populations have equal means
6503:
of the populations from which the two samples were taken are equal.
2895:
it can be assumed that the two distributions have the same variance.
1550:
1464:
1396:
1283:-tests are robust to all but large deviations from the assumptions.
233:
12763:
12516:
12150:
12120:
10493:
10111:
9988:
9983:
9978:
9364:
8009:
7941:
The p-value that the slope of 4 is different from 0 is p = 0.00805.
6918:
6831:
4302:
of two populations. The exact property still holds even with small
3937:
1169:. This assumption is met when the observations used for estimating
1087:
565:
536:
166:
70:, the test statisticâunder certain conditionsâfollows a Student's
12435:
11998:
11699:
8733:
Sheynin, Oscar (1995). "Helmert's work in the theory of errors".
8085:
8033:
6945:-test and nonparametric alternatives, see Lumley, et al. (2002).
6910:
1617:
1213:. Under weak assumptions, this follows in large samples from the
671:-tests typically consist of a sample of matched pairs of similar
178:
12075:
9603:
1748:(often taken to be 0, in which case the null hypothesis is that
564:, though strictly speaking that name should only be used if the
556:
of two populations are equal. All such tests are usually called
240:
12730:
11920:
10901:
10875:
10855:
10106:
9897:
8440:
8408:
8261:
8081:
6861:
1176:
591:
underlying the two samples being compared are non-overlapping.
524:
351:{\displaystyle t={\frac {{\bar {x}}-\mu _{0}}{s/{\sqrt {n}}}},}
268:
of whether the mean of a population has a value specified in a
174:
79:
9583:
Sensory Evaluation of Food: Statistical Methods and Procedures
8815:
8813:
6867:, and becomes robust even to large deviations from normality.
1209:
The means of the two populations being compared should follow
12892:
9749:
8363:
8061:
8053:
6941:
for paired samples. For a discussion on choosing between the
6506:
The difference between the two sample means, each denoted by
1251:-test is highly robust to the presence of unequal variances.
201:
8657:"Vergleichung von zwei Werthen des wahrscheinlichen Fehlers"
2888:
Given two groups (1, 2), this test is only applicable when:
13018:
Committee on the Environment, Public Health and Food Safety
12824:
9840:
9007:. Springer Science & Business Media. pp. 234â235.
8922:
Probability & statistics for engineers & scientists
8810:
8782:
Philosophical Transactions of the Royal Society of London A
8530:(in German). Springer Berlin Heidelberg. pp. 196â199.
8073:
8049:
6933:-test. The nonparametric counterpart to the paired samples
4833:
orthogonal matrix (whose elements of the first row are all
4012:-distribution with the degrees of freedom calculated using
1593:
Explicit expressions that can be used to carry out various
67:
4729:
orthogonal matrix whose elements of the first row are all
9091:
David, H. A.; Gunnink, Jason L. (1997). "The Paired
8183:
TTEST(sample-1-values, sample-2-values, tails, test-type)
8924:. Myers, H. Raymond (7th ed.). New Delhi: Pearson.
6499:
We will carry out tests of the null hypothesis that the
208:-test work was submitted to and accepted in the journal
169:
when publishing scientific papers. Gosset worked at the
9607:
Numerical Recipes in C: The Art of Scientific Computing
8436:
Pages displaying short descriptions of redirect targets
7967:-test, the difference between the group means is 6-2=4.
7930:
The table of coefficients gives the following results.
2021:
degrees of freedom if the null hypothesis is true. The
9325:
International Journal of Assessment Tools in Education
9136:
6876:
Location test for Gaussian scale mixture distributions
5880:
1275:-test is sub-optimal as it discards the unpaired data.
479:
7734:-test. Notice that the assumption of equal variance,
7265:
7071:
6929:) can have three to four times higher power than the
6794:
6755:
6709:
6615:
6528:
6415:
6316:
6034:
5998:
5907:
5719:
5615:
5443:
5311:
5160:
4991:
4874:
4839:
4813:
4767:
4735:
4709:
4663:
4606:
4552:
4526:
4448:
4370:
4312:
4021:
3967:
3821:
3725:
3448:
3313:
3020:
2917:
2899:
Violations of these assumptions are discussed below.
2769:
2661:
2487:
2235:
2149:
2061:
2034:
1907:
1772:
1656:
1502:
1449:
1360:
1337:
1298:-test require normality of the sample means, and the
990:
916:
824:
459:
423:
367:
290:
200:-test as an economical way to monitor the quality of
11662:
Autoregressive conditional heteroskedasticity (ARCH)
8385:
6956:-test when the data belong to more than two groups.
6579:{\displaystyle {\bar {X}}_{1}-{\bar {X}}_{2}=0.095.}
9377:
9375:
8575:
Zeitschrift fĂźr Anatomie und Entwicklungsgeschichte
7797:
The mean word.recall in the 1 drug.dose group is 6.
7794:
The mean word.recall in the 0 drug.dose group is 2.
7600:Data and code are given for the analysis using the
7490:-test is a special case of simple linear regression
4279:
Exact method for unequal variances and sample sizes
744:-tests are often referred to as "dependent samples
552:location test of the null hypothesis such that the
66:). When the scaling term is estimated based on the
11124:
9452:Statistic Under Various Nonnormal Distributions".
9189:
8919:
7474:
7249:) of two samples are equal. The test statistic is
7186:
6808:
6774:
6723:
6689:
6578:
6485:
6386:
6047:
6020:
5981:
5869:
5702:
5598:
5426:
5294:
5140:
4974:
4857:
4825:
4799:
4753:
4721:
4695:
4646:
4592:
4538:
4512:
4434:
4350:
4256:
4000:
3912:
3801:
3644:Equal or unequal sample sizes, unequal variances (
3594:
3428:
3218:Equal or unequal sample sizes, similar variances (
3097:
3000:
2883:
2851:
2720:
2632:
2458:
2215:
1999:
1887:
1686:
1576:
1482:
1429:
1343:
1309:, and that the sample mean and sample variance be
1078:
931:
899:
504:
465:
438:
382:
350:
9539:
8456: â Nonparametric test of the null hypothesis
1483:{\displaystyle s^{2}\xrightarrow {p} \sigma ^{2}}
1263:partially paired data, the classical independent
633:
13251:
9736:Econometrics lecture (topic: hypothesis testing)
9372:
8482: â Collection of statistical models (ANOVA)
7790:Running the R code gives the following results.
6271:its corresponding main article in better quality
2874:
11210:Multivariate adaptive regression splines (MARS)
9386:Test to Departures From Population Normality".
9381:
8885:Wendl, Michael C. (2016). "Pseudonymous fame".
6881:When the normality assumption does not hold, a
3183:of the population variance. The denominator of
1875:the standard errors of least-squares estimators
1687:{\displaystyle Y=\alpha +\beta x+\varepsilon ,}
1616:value and degrees of freedom are determined, a
587:-tests, as they are typically applied when the
528:Type I error of unpaired and paired two-sample
9487:Fay, Michael P.; Proschan, Michael A. (2010).
6598:-test will perform similarly in this example.
2226:can be written in terms of the residuals. Let
1220:If using Student's original definition of the
12091:
9765:
8004:-tests allow for the inclusion of additional
1642:
9580:
9447:
9090:
8558:: CS1 maint: DOI inactive as of June 2024 (
6826:
6480:
6429:
6381:
6330:
622:-tests can be used to reduce the effects of
9486:
9160:10.1146/annurev.publhealth.23.100901.140546
8505:. Academic Press. 2020-05-29. p. 397.
8023:
6997:Minnesota Multiphasic Personality Inventory
6724:{\displaystyle {\text{d.f.}}\approx 7.031.}
4647:{\displaystyle N(\mu _{2},\sigma _{2}^{2})}
4593:{\displaystyle N(\mu _{1},\sigma _{1}^{2})}
4304:extremely small and unbalanced sample sizes
1107:-test in the simplest form above are that:
682:A typical example of the repeated measures
13053:Centers for Disease Control and Prevention
12098:
12084:
9810:
9772:
9758:
9673:
8572:
8032:programs and statistics packages, such as
7992:Recognizing this relationship between the
4982:is an n-dimensional normal random vector.
13013:Centre for Disease Prevention and Control
13003:Center for Disease Control and Prevention
10423:
9560:
9516:
9412:
9363:
9261:
9158:
9055:Mathematical Statistics and Data Analysis
8991:
8801:
8016:to detect differences than do two-sample
7502:as illustrated by the following example.
6286:Learn how and when to remove this message
1635:-value is below the threshold chosen for
730:being the total number of observations).
9533:
9274:. Oxford University Press. p. 168.
8693:
6406:denote a second set obtained similarly:
5151:From the above distribution we see that
4001:{\displaystyle (s_{\bar {\Delta }})^{2}}
1118:follows a normal distribution with mean
642:-test is used when two separate sets of
540:Power of unpaired and paired two-sample
535:
523:
239:
232:
93:
13058:Health departments in the United States
9549:The Quantitative Methods for Psychology
9540:Derrick, B; Toher, D; White, P (2017).
9357:
9227:Statistical Methods in Medical Research
9224:
9218:
9141:; Emerson, Scott; Chen, Lu (May 2002).
8819:
8775:
8732:
8615:
8088:, include implementations of Student's
7170:
7111:
6972:
6874:-test can give misleading results. See
2023:standard error of the slope coefficient
644:independent and identically distributed
576:. These tests are often referred to as
105:-statistic" and published it under the
13252:
13063:Council on Education for Public Health
11736:KaplanâMeier estimator (product limit)
9678:test of the correlation coefficient".
9640:
9004:The Concise Encyclopedia of Statistics
8654:
1327:However, if the sample size is large,
13121:Professional degrees of public health
13028:Ministry of Health and Family Welfare
12079:
11809:
11376:
11123:
10422:
10192:
9809:
9753:
9415:The Journal of Experimental Education
9318:
9271:An Introduction to Medical Statistics
9267:
9132:
9130:
9128:
9126:
9067:
9027:
9021:
8997:
8884:
8735:Archive for History of Exact Sciences
8528:EinfĂźhrung in die Technische Mechanik
8525:
7506:patient can recall in a memory test.
6279:and make improvements to the summary.
3193:of the difference between two means.
1175:come from a normal distribution (and
515:
121:-distribution was first derived as a
82:will yield very similar results to a
13218:
13111:Bachelor of Science in Public Health
12046:
11746:Accelerated failure time (AFT) model
9052:
8952:
8502:The Microbiome in Health and Disease
8352:EqualVarianceTTest(sample1, sample2)
8301:t.test(data1, data2, var.equal=TRUE)
6860:-test asymptotically approaches the
6775:{\displaystyle s_{p}\approx 0.08399}
6601:
6251:
1243:; or assessable graphically using a
247:
13230:
12379:Workers' right to access the toilet
12220:Human right to water and sanitation
12058:
11341:Analysis of variance (ANOVA, anova)
10193:
6952:(ANOVA) generalizes the two-sample
4800:{\displaystyle (Q^{T})_{n\times m}}
4696:{\displaystyle (P^{T})_{n\times n}}
758:Most test statistics have the form
13:
11436:CochranâMantelâHaenszel statistics
10062:Pearson product-moment correlation
9634:
9123:
8221:TTEST(range1, range2, tails, type)
7498:-test is a special case of simple
7211:is the vector of column means and
7011:for combining multiple tests with
6979:Hotelling's T-squared distribution
6741:
6247:
3978:
3949:= number of participants in group
3829:
3784:
1980:
1271:distribution, while the dependent
482:
14:
13276:
12652:Commercial determinants of health
12105:
9699:
9454:Journal of Educational Statistics
9057:(3rd ed.). Duxbury Advanced.
6809:{\displaystyle {\text{d.f.}}=10.}
3706:This test, also known as Welch's
1739:is equal to some specified value
1647:Suppose one is fitting the model
811:As an example, in the one-sample
654:
13229:
13217:
13206:
13205:
12235:National public health institute
12057:
12045:
12033:
12020:
12019:
11810:
9095:Test Under Artificial Pairing".
8424: â Probability distribution
8388:
7948:
7509:
7448:
7424:
7394:
7365:
7341:
7154:
7133:
7095:
6256:
6078:represents the number of pairs.
4351:{\displaystyle n_{1}=5,n_{2}=50}
3940:of each of the two samples with
802:that allows the distribution of
505:{\textstyle {\mathcal {N}}(0,1)}
12632:Open-source healthcare software
12374:Sociology of health and illness
11695:Least-squares spectral analysis
9729:Research Methods Knowledge Base
9480:
9441:
9406:
9351:
9312:
9288:
9183:
9084:
9061:
9046:
8946:
8913:
8878:
8864:
8422:-distribution in power analysis
4283:The test deals with the famous
2892:the two sample sizes are equal,
2884:Equal sample sizes and variance
2737:Pearson correlation coefficient
1625:table of values from Student's
1588:
12993:Caribbean Public Health Agency
12805:Sexually transmitted infection
12702:Statistical hypothesis testing
12463:Occupational safety and health
12364:Sexual and reproductive health
12277:Occupational safety and health
10676:Mean-unbiased minimum-variance
9779:
9319:DEMÄ°R, SĂźleyman (2022-06-26).
9147:Annual Review of Public Health
8822:"The Probable Error of a Mean"
8769:
8726:
8687:
8648:
8609:
8566:
8519:
8493:
8012:, and commonly yields greater
7452:
7428:
7369:
7345:
7181:
7158:
7147:
7123:
7099:
7088:
7046:) is equal to a given vector (
6983:A generalization of Student's
6558:
6536:
6165:
6021:{\displaystyle {\bar {X}}_{D}}
6006:
5924:
5839:
5827:
5819:
5780:
5775:
5749:
5655:
5629:
5418:
5360:
5351:
5325:
5195:
5180:
5132:
5119:
5067:
5055:
5004:
5001:
4942:
4928:
4895:
4881:
4782:
4768:
4678:
4664:
4641:
4610:
4587:
4556:
4520:be the i.i.d. sample vectors (
4501:
4455:
4423:
4377:
4218:
4184:
4148:
4114:
3989:
3981:
3968:
3832:
3787:
3764:
3742:
3532:
3513:
3485:
3466:
3352:
3330:
3196:For significance testing, the
2956:
2934:
2831:
2613:
2606:
2584:
2532:
2513:
2504:
2422:
2354:
2338:
2323:
2314:
2286:
2247:
2200:
2193:
2171:
2137:
2124:
2101:
2048:
1964:
1930:
1859:
1836:
1798:
1783:
1571:
1559:
1537:
1525:
1516:
1424:
1405:
1389:
1377:
1368:
1065:
1058:
1036:
997:
923:
873:
853:
751:
634:Independent (unpaired) samples
499:
487:
430:
374:
306:
1:
12647:Social determinants of health
11989:Geographic information system
11205:Simultaneous equations models
9030:High-Yield Behavioral Science
8899:10.1126/science.351.6280.1406
8486:
6167:Example of repeated measures
4858:{\displaystyle 1/{\sqrt {m}}}
4754:{\displaystyle 1/{\sqrt {n}}}
2643:Another way to determine the
1607:one-tailed or two-tailed test
1103:The assumptions underlying a
473:will be approximately normal
149:-distribution, also known as
12707:Analysis of variance (ANOVA)
12468:Human factors and ergonomics
11172:Coefficient of determination
10783:Uniformly most powerful test
8536:10.1007/978-3-642-61925-0_16
4290:The test is developed as an
4269:WelchâSatterthwaite equation
145:'s 1895 paper. However, the
7:
12888:Good manufacturing practice
12692:Randomized controlled trial
11741:Proportional hazards models
11685:Spectral density estimation
11667:Vector autoregression (VAR)
11101:Maximum posterior estimator
10333:Randomized controlled trial
9712:Encyclopedia of Mathematics
9400:10.1037/0033-2909.111.2.352
8920:Walpole, Ronald E. (2006).
8434: â Ratio in statistics
8381:
7033:is converted instead to an
7029:are hard to find. Usually,
6836:-test for location problems
6785:and the degrees of freedom
6700:and the degrees of freedom
5898:statistic is calculated as
2751:can be determined from the
2446:sum of squares of residuals
784:are functions of the data.
221:'s Biometric Laboratory at
36:statistical hypothesis test
16:Statistical hypothesis test
10:
13281:
12958:Theory of planned behavior
12883:Good agricultural practice
12788:Public health surveillance
12680:epidemiological statistics
12324:Public health intervention
11501:Multivariate distributions
9921:Average absolute deviation
9692:10.1037/0033-2909.95.3.576
9612:Cambridge University Press
9581:O'Mahony, Michael (1986).
9573:
9489:"WilcoxonâMannâWhitney or
8466: â Statistical method
6976:
4807:be the first n rows of an
3695:
1643:Slope of a regression line
982:standard error of the mean
932:{\displaystyle {\bar {X}}}
658:
439:{\displaystyle {\bar {x}}}
383:{\displaystyle {\bar {x}}}
89:
13201:
13136:
13095:
13080:World Toilet Organization
13075:World Health Organization
12982:
12971:
12908:
12833:
12749:
12677:
12642:Public health informatics
12582:
12387:
12349:Right to rest and leisure
12178:Globalization and disease
12113:
12015:
11969:
11906:
11859:
11822:
11818:
11805:
11777:
11759:
11726:
11717:
11675:
11622:
11583:
11532:
11523:
11489:Structural equation model
11444:
11401:
11397:
11372:
11331:
11297:
11251:
11218:
11180:
11147:
11143:
11119:
11059:
10968:
10887:
10851:
10842:
10825:Score/Lagrange multiplier
10810:
10763:
10708:
10634:
10625:
10435:
10431:
10418:
10377:
10351:
10303:
10258:
10240:Sample size determination
10205:
10201:
10188:
10092:
10047:
10021:
10003:
9959:
9911:
9831:
9822:
9818:
9805:
9787:
9427:10.1080/00220979809598344
9192:The American Statistician
9097:The American Statistician
8661:Astronomische Nachrichten
8622:Astronomische Nachrichten
7055:). The test statistic is
6939:Wilcoxon signed-rank test
6827:Related statistical tests
6088:Example of matched pairs
4826:{\displaystyle m\times m}
4722:{\displaystyle n\times n}
3607:pooled standard deviation
3119:pooled standard deviation
1311:statistically independent
724:degrees of freedom (with
711:degrees of freedom (with
446:is assumed to be normal.
398:sample standard deviation
281:, one uses the statistic
223:University College London
32:statistically significant
13126:Schools of public health
12918:Diffusion of innovations
12617:Health impact assessment
12329:Public health laboratory
12225:Management of depression
11984:Environmental statistics
11506:Elliptical distributions
11299:Generalized linear model
11228:Simple linear regression
10998:HodgesâLehmann estimator
10455:Probability distribution
10364:Stochastic approximation
9926:Coefficient of variation
9239:10.1177/0962280215577111
8681:10.1002/asna.18760871402
8642:10.1002/asna.18760880802
8446: â Statistical test
8404:Conditional change model
8202:Data1; Data2; Mode; Type
8024:Software implementations
8000:. These alternatives to
7813:
7740:
7614:
7228:sample covariance matrix
5885:-test for paired samples
3961:= 1 or 2). In this case
2871:is the sample variance.
1813:least-squares estimators
1637:statistical significance
638:The independent samples
406:is the sample size. The
13189:Social hygiene movement
13116:Doctor of Public Health
12948:Social cognitive theory
12750:Infectious and epidemic
12532:Fecalâoral transmission
11644:Cross-correlation (XCF)
11252:Non-standard predictors
10686:LehmannâScheffĂŠ theorem
10359:Adaptive clinical trial
9723:Trochim, William M.K. "
9562:10.20982/tqmp.13.2.p120
9028:Fadem, Barbara (2008).
8712:10.1093/biomet/83.4.891
8538:(inactive 2024-06-28).
8335:tTest(sample1, sample2)
7251:Hotelling's two-sample
4539:{\displaystyle m\geq n}
2875:Independent two-sample
1090:of the population, and
1086:is the estimate of the
228:
214:and published in 1908.
13184:Germ theory of disease
12963:Transtheoretical model
12040:Mathematics portal
11861:Engineering statistics
11769:NelsonâAalen estimator
11346:Analysis of covariance
11233:Ordinary least squares
11157:Pearson product-moment
10561:Statistical functional
10472:Empirical distribution
10305:Controlled experiments
10034:Frequency distribution
9812:Descriptive statistics
9680:Psychological Bulletin
9647:Psychological Bulletin
9388:Psychological Bulletin
9337:10.21449/ijate.1101295
9268:Bland, Martin (1995).
9053:Rice, John A. (2006).
8969:10.1542/peds.2005-1134
8803:10.1098/rsta.1895.0010
8776:Pearson, Karl (1895).
8238:scipy.stats.ttest_ind(
7602:R programming language
7476:
7188:
6909:In the presence of an
6897:-test may have better
6889:-test may have better
6810:
6776:
6725:
6691:
6580:
6487:
6388:
6049:
6022:
5983:
5892:paired difference test
5871:
5803:
5704:
5681:
5600:
5467:
5428:
5296:
5278:
5234:
5142:
4976:
4859:
4827:
4801:
4755:
4723:
4697:
4648:
4594:
4540:
4514:
4513:{\displaystyle Y=^{T}}
4436:
4435:{\displaystyle X=^{T}}
4352:
4285:BehrensâFisher problem
4273:BehrensâFisher problem
4258:
4002:
3914:
3803:
3596:
3430:
3099:
3002:
2853:
2722:
2634:
2583:
2460:
2412:
2217:
2170:
2100:
2001:
1889:
1688:
1578:
1484:
1431:
1345:
1080:
933:
901:
661:Paired difference test
545:
533:
506:
467:
440:
410:used in this test are
384:
352:
244:
237:
123:posterior distribution
110:
13265:Parametric statistics
13068:Public Health Service
12953:Social norms approach
12943:PRECEDEâPROCEED model
12389:Preventive healthcare
12282:Pharmaceutical policy
12131:Chief Medical Officer
11956:Population statistics
11898:System identification
11632:Autocorrelation (ACF)
11560:Exponential smoothing
11474:Discriminant analysis
11469:Canonical correlation
11333:Partition of variance
11195:Regression validation
11039:(JonckheereâTerpstra)
10938:Likelihood-ratio test
10627:Frequentist inference
10539:Locationâscale family
10460:Sampling distribution
10425:Statistical inference
10392:Cross-sectional study
10379:Observational studies
10338:Randomized experiment
10167:Stem-and-leaf display
9969:Central limit theorem
9078:mathworld.wolfram.com
8460:Ĺ idĂĄk correction for
8006:explanatory variables
7811:for a linear model.
7477:
7189:
6969:-test could be used.
6811:
6777:
6726:
6692:
6581:
6488:
6389:
6050:
6048:{\displaystyle s_{D}}
6023:
5984:
5872:
5783:
5705:
5661:
5601:
5447:
5429:
5297:
5258:
5214:
5143:
4977:
4860:
4828:
4802:
4756:
4724:
4698:
4649:
4595:
4541:
4515:
4437:
4353:
4267:This is known as the
4259:
4003:
3915:
3804:
3597:
3431:
3100:
3003:
2854:
2723:
2635:
2563:
2461:
2392:
2218:
2150:
2080:
2002:
1890:
1689:
1623:can be found using a
1579:
1485:
1439:Central limit theorem
1432:
1346:
1315:central limit theorem
1215:central limit theorem
1081:
934:
902:
606:-tests are a form of
539:
527:
507:
468:
451:central limit theorem
441:
385:
353:
258:one-sample Student's
243:
236:
157:, gets its name from
101:, who developed the "
97:
13144:Sara Josephine Baker
13043:Public Health Agency
12928:Health communication
12793:Disease surveillance
12759:Asymptomatic carrier
12741:Statistical software
12429:Preventive nutrition
12257:Medical anthropology
12146:Environmental health
11879:Probabilistic design
11464:Principal components
11307:Exponential families
11259:Nonlinear regression
11238:General linear model
11200:Mixed effects models
11190:Errors and residuals
11167:Confounding variable
11069:Bayesian probability
11047:Van der Waerden test
11037:Ordered alternative
10802:Multiple comparisons
10681:RaoâBlackwellization
10644:Estimating equations
10600:Statistical distance
10318:Factorial experiment
9851:Arithmetic-Geometric
8843:10.1093/biomet/6.1.1
8480:Analysis of variance
8369:ttest data1 == data2
7998:analysis of variance
7263:
7203:is the sample size,
7069:
7021:statistic follows a
6973:Multivariate testing
6950:analysis of variance
6832:Alternatives to the
6792:
6753:
6707:
6613:
6526:
6413:
6314:
6032:
5996:
5905:
5717:
5613:
5441:
5309:
5158:
4989:
4872:
4837:
4811:
4765:
4733:
4707:
4661:
4604:
4550:
4524:
4446:
4368:
4310:
4296:unequal sample sizes
4019:
3965:
3819:
3723:
3446:
3311:
3018:
2915:
2767:
2659:
2485:
2233:
2032:
1905:
1770:
1654:
1631:. If the calculated
1500:
1492:law of large numbers
1447:
1358:
1335:
1211:normal distributions
988:
914:
822:
477:
457:
421:
390:is the sample mean,
365:
288:
159:William Sealy Gosset
99:William Sealy Gosset
13154:Carl Rogers Darnall
13149:Samuel Jay Crumbine
12923:Health belief model
12776:Notifiable diseases
12712:Regression analysis
12547:Waterborne diseases
12136:Cultural competence
11951:Official statistics
11874:Methods engineering
11555:Seasonal adjustment
11323:Poisson regressions
11243:Bayesian regression
11182:Regression analysis
11162:Partial correlation
11134:Regression analysis
10733:Prediction interval
10728:Likelihood interval
10718:Confidence interval
10710:Interval estimation
10671:Unbiased estimators
10489:Model specification
10369:Up-and-down designs
10057:Partial correlation
10013:Index of dispersion
9931:Interquartile range
8794:1895RSPTA.186..343P
8673:1876AN.....87..209L
8655:LĂźroth, J. (1876).
8634:1876AN.....88..113H
8267:ttest(data1, data2)
8078:Wolfram Mathematica
7864:word.recall.data.lm
7819:word.recall.data.lm
6903:Mann-Whitney U test
6885:alternative to the
6823:-value of 0.07857.
6738:-value of 0.09077.
6666:
6634:
6591:standard deviations
6275:Please help out to
6168:
6089:
5818:
5696:
5585:
5560:
5522:
5482:
5409:
5383:
5110:
5084:
4640:
4586:
4201:
4131:
4086:
4054:
3892:
3860:
3556:
3509:
3181:unbiased estimators
3084:
3059:
2820:
2014:-distribution with
1760:are uncorrelated).
1554:
1468:
1400:
1241:BrownâForsythe test
628:observational study
624:confounding factors
610:, and have greater
582:independent samples
196:Gosset devised the
56:normal distribution
12752:disease prevention
12687:Caseâcontrol study
12359:Security of person
12208:Health care reform
11971:Spatial statistics
11851:Medical statistics
11751:First hitting time
11705:Whittle likelihood
11356:Degrees of freedom
11351:Multivariate ANOVA
11284:Heteroscedasticity
11096:Bayesian estimator
11061:Bayesian inference
10910:KolmogorovâSmirnov
10795:Randomization test
10765:Testing hypotheses
10738:Tolerance interval
10649:Maximum likelihood
10544:Exponential family
10477:Density estimation
10437:Statistical theory
10397:Natural experiment
10343:Scientific control
10260:Survey methodology
9946:Standard deviation
9497:Statistics Surveys
8851:10338.dmlcz/143545
8747:10.1007/BF00374700
8587:10.1007/bf02118337
8396:Mathematics portal
7472:
7184:
6993:-squared statistic
6987:statistic, called
6806:
6772:
6721:
6687:
6652:
6620:
6576:
6483:
6384:
6166:
6087:
6045:
6018:
5979:
5867:
5804:
5700:
5682:
5596:
5571:
5546:
5502:
5468:
5424:
5395:
5369:
5292:
5138:
5096:
5070:
4972:
4855:
4823:
4797:
4751:
4719:
4693:
4644:
4626:
4590:
4572:
4536:
4510:
4432:
4348:
4254:
4187:
4117:
4072:
4040:
3998:
3934:unbiased estimator
3910:
3878:
3846:
3799:
3611:unbiased estimator
3592:
3535:
3488:
3426:
3198:degrees of freedom
3095:
3063:
3038:
2998:
2849:
2806:
2718:
2630:
2456:
2454:
2213:
2209:
2146:
1997:
1885:
1883:
1684:
1603:degrees of freedom
1574:
1480:
1427:
1341:
1167:degrees of freedom
1088:standard deviation
1076:
1035:
929:
897:
808:to be determined.
546:
534:
502:
463:
436:
408:degrees of freedom
380:
348:
245:
238:
111:
74:distribution. The
64:nuisance parameter
58:if the value of a
34:or not. It is any
13260:Statistical tests
13245:
13244:
13197:
13196:
13107:Higher education
12938:Positive deviance
12933:Health psychology
12909:Health behavioral
12836:safety management
12810:Social distancing
12584:Population health
12564:Smoking cessation
12512:Pharmacovigilance
12483:Injury prevention
12451:Infection control
12369:Social psychology
12319:Prisoners' rights
12262:Medical sociology
12230:Public health law
12126:Biological hazard
12073:
12072:
12011:
12010:
12007:
12006:
11946:National accounts
11916:Actuarial science
11908:Social statistics
11801:
11800:
11797:
11796:
11793:
11792:
11728:Survival function
11713:
11712:
11575:Granger causality
11416:Contingency table
11391:Survival analysis
11368:
11367:
11364:
11363:
11220:Linear regression
11115:
11114:
11111:
11110:
11086:Credible interval
11055:
11054:
10838:
10837:
10654:Method of moments
10523:Parametric family
10484:Statistical model
10414:
10413:
10410:
10409:
10328:Random assignment
10250:Statistical power
10184:
10183:
10180:
10179:
10029:Contingency table
9999:
9998:
9866:Generalized/power
9281:978-0-19-262428-4
9068:Weisstein, Eric.
9014:978-0-387-31742-7
8545:978-3-540-13293-6
8512:978-0-12-820001-8
8379:
8378:
7928:
7927:
7598:
7597:
7500:linear regression
7455:
7431:
7401:
7372:
7348:
7328:
7161:
7102:
6891:statistical power
6798:
6713:
6679:
6677:
6645:
6602:Unequal variances
6561:
6539:
6476:
6467:
6458:
6449:
6440:
6377:
6368:
6359:
6350:
6341:
6296:
6295:
6288:
6277:edit this article
6245:
6244:
6241:
6240:
6162:
6161:
6009:
5974:
5971:
5927:
5843:
5842:
5589:
5564:
5534:
5495:
5256:
5212:
5198:
5183:
4970:
4923:
4853:
4761:, similarly, let
4749:
4300:unequal variances
4249:
4246:
4176:
4097:
4065:
4025:
3984:
3905:
3903:
3871:
3835:
3794:
3790:
3767:
3745:
3590:
3589:
3421:
3418:
3416:
3396:
3355:
3333:
3200:for this test is
3090:
3089:
2993:
2990:
2989:
2959:
2937:
2844:
2843:
2834:
2813:
2802:
2791:
2777:
2713:
2712:
2692:
2669:
2625:
2624:
2623:
2609:
2546:
2516:
2495:
2447:
2425:
2383:
2371:
2363:
2341:
2326:
2289:
2250:
2211:
2210:
2196:
2147:
2127:
2078:
2051:
1972:
1967:
1933:
1915:
1876:
1862:
1839:
1814:
1801:
1786:
1555:
1544:
1528:
1514:
1469:
1401:
1380:
1366:
1344:{\displaystyle n}
1329:Slutsky's theorem
1074:
1061:
1026:
1024:
1000:
926:
892:
889:
876:
856:
839:
800:scaling parameter
733:A paired samples
589:statistical units
466:{\displaystyle t}
433:
377:
343:
340:
309:
13272:
13233:
13232:
13221:
13220:
13209:
13208:
13103:Health education
12980:
12979:
12834:Food hygiene and
12815:Tropical disease
12627:Infant mortality
12602:Community health
12478:Controlled Drugs
12414:Health promotion
12344:Right to housing
12188:Health economics
12100:
12093:
12086:
12077:
12076:
12061:
12060:
12049:
12048:
12038:
12037:
12023:
12022:
11926:Crime statistics
11820:
11819:
11807:
11806:
11724:
11723:
11690:Fourier analysis
11677:Frequency domain
11657:
11604:
11570:Structural break
11530:
11529:
11479:Cluster analysis
11426:Log-linear model
11399:
11398:
11374:
11373:
11315:
11289:Homoscedasticity
11145:
11144:
11121:
11120:
11040:
11032:
11024:
11023:(KruskalâWallis)
11008:
10993:
10948:Cross validation
10933:
10915:AndersonâDarling
10862:
10849:
10848:
10820:Likelihood-ratio
10812:Parametric tests
10790:Permutation test
10773:1- & 2-tails
10664:Minimum distance
10636:Point estimation
10632:
10631:
10583:Optimal decision
10534:
10433:
10432:
10420:
10419:
10402:Quasi-experiment
10352:Adaptive designs
10203:
10202:
10190:
10189:
10067:Rank correlation
9829:
9828:
9820:
9819:
9807:
9806:
9774:
9767:
9760:
9751:
9750:
9737:
9720:
9695:
9670:
9659:10.1037/h0041412
9629:
9600:
9567:
9566:
9564:
9546:
9537:
9531:
9530:
9520:
9509:10.1214/09-SS051
9484:
9478:
9477:
9445:
9439:
9438:
9410:
9404:
9403:
9379:
9370:
9369:
9367:
9355:
9349:
9348:
9316:
9310:
9309:
9307:
9306:
9292:
9286:
9285:
9265:
9259:
9258:
9233:(3): 1323â1340.
9222:
9216:
9215:
9187:
9181:
9180:
9162:
9137:Lumley, Thomas;
9134:
9121:
9120:
9088:
9082:
9081:
9065:
9059:
9058:
9050:
9044:
9043:
9025:
9019:
9018:
8995:
8989:
8988:
8950:
8944:
8943:
8917:
8911:
8910:
8882:
8876:
8875:
8868:
8862:
8861:
8859:
8857:
8826:
8820:Student (1908).
8817:
8808:
8807:
8805:
8773:
8767:
8766:
8730:
8724:
8723:
8698:-distribution".
8691:
8685:
8684:
8652:
8646:
8645:
8628:(8â9): 113â131.
8616:Helmert (1876).
8613:
8607:
8606:
8570:
8564:
8563:
8557:
8549:
8523:
8517:
8516:
8497:
8437:
8398:
8393:
8392:
8370:
8353:
8336:
8319:
8302:
8285:
8268:
8251:
8222:
8205:
8195:LibreOffice Calc
8184:
8167:
8133:
8098:Language/Program
8095:
8094:
8038:LibreOffice Calc
7952:
7875:
7874:
7868:
7865:
7862:
7859:
7856:
7853:
7850:
7849:word.recall.data
7847:
7844:
7841:
7838:
7835:
7832:
7829:
7826:
7823:
7820:
7817:
7810:
7786:
7783:
7780:
7777:
7774:
7771:
7768:
7765:
7762:
7759:
7756:
7753:
7752:word.recall.data
7750:
7747:
7744:
7737:
7726:
7723:
7720:
7717:
7714:
7711:
7708:
7705:
7702:
7699:
7696:
7693:
7690:
7687:
7684:
7681:
7678:
7675:
7672:
7669:
7666:
7663:
7660:
7657:
7654:
7651:
7648:
7645:
7642:
7639:
7636:
7633:
7630:
7627:
7624:
7621:
7620:word.recall.data
7618:
7611:
7607:
7519:
7518:
7513:
7481:
7479:
7478:
7473:
7468:
7464:
7463:
7462:
7457:
7456:
7451:
7446:
7439:
7438:
7433:
7432:
7427:
7422:
7413:
7412:
7404:
7403:
7402:
7399:
7397:
7389:
7385:
7381:
7380:
7379:
7374:
7373:
7368:
7363:
7356:
7355:
7350:
7349:
7344:
7339:
7329:
7327:
7326:
7325:
7313:
7312:
7302:
7301:
7300:
7291:
7290:
7280:
7275:
7274:
7248:
7226:
7216:
7210:
7209:
7202:
7193:
7191:
7190:
7185:
7180:
7179:
7178:
7173:
7163:
7162:
7157:
7152:
7146:
7145:
7137:
7136:
7129:
7121:
7120:
7119:
7114:
7104:
7103:
7098:
7093:
7081:
7080:
7054:
7045:
6815:
6813:
6812:
6807:
6799:
6796:
6781:
6779:
6778:
6773:
6765:
6764:
6730:
6728:
6727:
6722:
6714:
6711:
6696:
6694:
6693:
6688:
6680:
6678:
6676:
6675:
6665:
6660:
6651:
6646:
6644:
6643:
6633:
6628:
6619:
6617:
6585:
6583:
6582:
6577:
6569:
6568:
6563:
6562:
6554:
6547:
6546:
6541:
6540:
6532:
6518:
6512:
6492:
6490:
6489:
6484:
6474:
6465:
6456:
6447:
6438:
6425:
6424:
6405:
6393:
6391:
6390:
6385:
6375:
6366:
6357:
6348:
6339:
6326:
6325:
6306:
6291:
6284:
6280:
6260:
6259:
6252:
6169:
6090:
6086:
6083:
6082:
6077:
6071:
6064:
6054:
6052:
6051:
6046:
6044:
6043:
6027:
6025:
6024:
6019:
6017:
6016:
6011:
6010:
6002:
5988:
5986:
5985:
5980:
5975:
5973:
5972:
5967:
5965:
5960:
5959:
5949:
5948:
5947:
5935:
5934:
5929:
5928:
5920:
5915:
5876:
5874:
5873:
5868:
5863:
5862:
5844:
5826:
5817:
5812:
5802:
5797:
5779:
5778:
5774:
5773:
5761:
5760:
5745:
5744:
5734:
5729:
5728:
5709:
5707:
5706:
5701:
5695:
5690:
5680:
5675:
5654:
5653:
5641:
5640:
5625:
5624:
5605:
5603:
5602:
5597:
5595:
5591:
5590:
5584:
5579:
5570:
5565:
5559:
5554:
5545:
5535:
5533:
5521:
5516:
5501:
5496:
5494:
5483:
5481:
5476:
5466:
5461:
5445:
5433:
5431:
5430:
5425:
5414:
5408:
5403:
5388:
5382:
5377:
5350:
5349:
5337:
5336:
5321:
5320:
5301:
5299:
5298:
5293:
5288:
5287:
5277:
5272:
5257:
5249:
5244:
5243:
5233:
5228:
5213:
5205:
5200:
5199:
5191:
5185:
5184:
5176:
5170:
5169:
5147:
5145:
5144:
5139:
5131:
5130:
5115:
5109:
5104:
5089:
5083:
5078:
5063:
5062:
5029:
5028:
5016:
5015:
4981:
4979:
4978:
4973:
4971:
4966:
4964:
4956:
4955:
4940:
4939:
4924:
4919:
4917:
4909:
4908:
4893:
4892:
4864:
4862:
4861:
4856:
4854:
4849:
4847:
4832:
4830:
4829:
4824:
4806:
4804:
4803:
4798:
4796:
4795:
4780:
4779:
4760:
4758:
4757:
4752:
4750:
4745:
4743:
4728:
4726:
4725:
4720:
4702:
4700:
4699:
4694:
4692:
4691:
4676:
4675:
4653:
4651:
4650:
4645:
4639:
4634:
4622:
4621:
4599:
4597:
4596:
4591:
4585:
4580:
4568:
4567:
4545:
4543:
4542:
4537:
4519:
4517:
4516:
4511:
4509:
4508:
4499:
4498:
4480:
4479:
4467:
4466:
4441:
4439:
4438:
4433:
4431:
4430:
4421:
4420:
4402:
4401:
4389:
4388:
4357:
4355:
4354:
4349:
4341:
4340:
4322:
4321:
4294:that allows for
4263:
4261:
4260:
4255:
4250:
4248:
4247:
4245:
4238:
4237:
4227:
4226:
4225:
4216:
4215:
4206:
4200:
4195:
4182:
4177:
4175:
4168:
4167:
4157:
4156:
4155:
4146:
4145:
4136:
4130:
4125:
4112:
4109:
4108:
4103:
4099:
4098:
4096:
4095:
4085:
4080:
4071:
4066:
4064:
4063:
4053:
4048:
4039:
4031:
4026:
4023:
4007:
4005:
4004:
3999:
3997:
3996:
3987:
3986:
3985:
3977:
3960:
3954:
3948:
3931:
3919:
3917:
3916:
3911:
3906:
3904:
3902:
3901:
3891:
3886:
3877:
3872:
3870:
3869:
3859:
3854:
3845:
3843:
3838:
3837:
3836:
3828:
3808:
3806:
3805:
3800:
3795:
3793:
3792:
3791:
3783:
3776:
3775:
3774:
3769:
3768:
3760:
3753:
3752:
3747:
3746:
3738:
3733:
3715:
3639:
3622:
3601:
3599:
3598:
3593:
3591:
3588:
3581:
3580:
3568:
3567:
3557:
3555:
3550:
3549:
3548:
3525:
3524:
3508:
3503:
3502:
3501:
3478:
3477:
3464:
3463:
3458:
3457:
3435:
3433:
3432:
3427:
3422:
3420:
3419:
3417:
3415:
3414:
3402:
3397:
3395:
3394:
3382:
3380:
3375:
3374:
3364:
3363:
3362:
3357:
3356:
3348:
3341:
3340:
3335:
3334:
3326:
3321:
3303:
3294:
3269:
3267:
3266:
3253:
3250:
3233:
3231:
3230:
3227:
3224:
3214:is sample size.
3213:
3207:
3188:
3178:
3177:
3176:
3159:
3158:
3157:
3140:
3116:
3104:
3102:
3101:
3096:
3091:
3085:
3083:
3078:
3077:
3076:
3058:
3053:
3052:
3051:
3036:
3035:
3030:
3029:
3007:
3005:
3004:
2999:
2994:
2992:
2991:
2982:
2981:
2979:
2978:
2968:
2967:
2966:
2961:
2960:
2952:
2945:
2944:
2939:
2938:
2930:
2925:
2907:
2870:
2858:
2856:
2855:
2850:
2845:
2842:
2841:
2836:
2835:
2827:
2819:
2814:
2811:
2805:
2804:
2803:
2800:
2794:
2792:
2784:
2779:
2778:
2775:
2756:
2749:score, intercept
2747:
2727:
2725:
2724:
2719:
2714:
2711:
2710:
2695:
2694:
2693:
2682:
2676:
2671:
2670:
2667:
2648:
2639:
2637:
2636:
2631:
2626:
2622:
2621:
2620:
2611:
2610:
2602:
2596:
2595:
2582:
2577:
2561:
2550:
2549:
2548:
2547:
2536:
2531:
2530:
2518:
2517:
2509:
2502:
2497:
2496:
2493:
2474:
2465:
2463:
2462:
2457:
2455:
2448:
2445:
2440:
2439:
2434:
2433:
2432:
2427:
2426:
2418:
2411:
2406:
2384:
2381:
2372:
2370:estimated errors
2369:
2364:
2361:
2353:
2352:
2343:
2342:
2334:
2328:
2327:
2319:
2310:
2309:
2297:
2296:
2291:
2290:
2282:
2275:
2274:
2258:
2257:
2252:
2251:
2243:
2222:
2220:
2219:
2214:
2212:
2208:
2207:
2198:
2197:
2189:
2183:
2182:
2169:
2164:
2148:
2145:
2144:
2135:
2134:
2129:
2128:
2120:
2113:
2112:
2099:
2094:
2079:
2077:
2063:
2060:
2059:
2054:
2053:
2052:
2044:
2020:
2006:
2004:
2003:
1998:
1996:
1995:
1984:
1983:
1973:
1971:
1970:
1969:
1968:
1960:
1949:
1948:
1947:
1935:
1934:
1926:
1922:
1917:
1916:
1913:
1894:
1892:
1891:
1886:
1884:
1877:
1874:
1865:
1864:
1863:
1855:
1842:
1841:
1840:
1832:
1815:
1812:
1803:
1802:
1794:
1788:
1787:
1779:
1759:
1753:
1747:
1738:
1732:
1726:
1720:
1714:
1708:
1702:
1693:
1691:
1690:
1685:
1583:
1581:
1580:
1575:
1546:
1545:
1540:
1530:
1529:
1521:
1515:
1510:
1507:
1489:
1487:
1486:
1481:
1479:
1478:
1460:
1459:
1458:
1436:
1434:
1433:
1428:
1423:
1422:
1392:
1382:
1381:
1373:
1367:
1362:
1350:
1348:
1347:
1342:
1279:Most two-sample
1192:
1186:
1179:for each group).
1174:
1165:
1156:
1149:
1145: â 1)/
1133:
1123:
1117:
1116:
1095:
1085:
1083:
1082:
1077:
1075:
1073:
1072:
1063:
1062:
1054:
1048:
1047:
1034:
1025:
1023:
1009:
1007:
1002:
1001:
993:
979:
973:
967:
938:
936:
935:
930:
928:
927:
919:
906:
904:
903:
898:
893:
891:
890:
885:
883:
878:
877:
869:
865:
858:
857:
849:
845:
840:
832:
807:
797:
791:
783:
777:
771:
729:
723:
716:
710:
708:
706:
705:
702:
699:
511:
509:
508:
503:
486:
485:
472:
470:
469:
464:
445:
443:
442:
437:
435:
434:
426:
416:
405:
395:
389:
387:
386:
381:
379:
378:
370:
357:
355:
354:
349:
344:
342:
341:
336:
334:
325:
324:
323:
311:
310:
302:
298:
280:
171:Guinness Brewery
141:distribution in
28:statistical test
13280:
13279:
13275:
13274:
13273:
13271:
13270:
13269:
13250:
13249:
13246:
13241:
13193:
13164:Margaret Sanger
13132:
13091:
12975:
12973:
12967:
12910:
12904:
12876:Safety scandals
12835:
12829:
12751:
12745:
12679:
12673:
12669:Social medicine
12662:Race and health
12597:Child mortality
12578:
12537:Open defecation
12419:Human nutrition
12409:Family planning
12397:Behavior change
12383:
12339:Right to health
12252:Maternal health
12242:Health politics
12193:Health literacy
12109:
12104:
12074:
12069:
12032:
12003:
11965:
11902:
11888:quality control
11855:
11837:Clinical trials
11814:
11789:
11773:
11761:Hazard function
11755:
11709:
11671:
11655:
11618:
11614:BreuschâGodfrey
11602:
11579:
11519:
11494:Factor analysis
11440:
11421:Graphical model
11393:
11360:
11327:
11313:
11293:
11247:
11214:
11176:
11139:
11138:
11107:
11051:
11038:
11030:
11022:
11006:
10991:
10970:Rank statistics
10964:
10943:Model selection
10931:
10889:Goodness of fit
10883:
10860:
10834:
10806:
10759:
10704:
10693:Median unbiased
10621:
10532:
10465:Order statistic
10427:
10406:
10373:
10347:
10299:
10254:
10197:
10195:Data collection
10176:
10088:
10043:
10017:
9995:
9955:
9907:
9824:Continuous data
9814:
9801:
9783:
9778:
9735:
9705:
9702:
9637:
9635:Further reading
9632:
9626:
9597:
9589:. p. 487.
9576:
9571:
9570:
9544:
9538:
9534:
9485:
9481:
9466:10.2307/1164905
9446:
9442:
9411:
9407:
9380:
9373:
9356:
9352:
9317:
9313:
9304:
9302:
9294:
9293:
9289:
9282:
9266:
9262:
9223:
9219:
9204:10.2307/2684360
9188:
9184:
9135:
9124:
9109:10.2307/2684684
9089:
9085:
9066:
9062:
9051:
9047:
9040:
9026:
9022:
9015:
8996:
8992:
8951:
8947:
8932:
8918:
8914:
8883:
8879:
8870:
8869:
8865:
8855:
8853:
8824:
8818:
8811:
8774:
8770:
8731:
8727:
8692:
8688:
8667:(14): 209â220.
8653:
8649:
8614:
8610:
8571:
8567:
8551:
8550:
8546:
8524:
8520:
8513:
8499:
8498:
8494:
8489:
8435:
8394:
8387:
8384:
8368:
8351:
8334:
8317:
8300:
8283:
8266:
8237:
8220:
8199:
8182:
8149:
8144:Microsoft Excel
8115:
8110:Microsoft Excel
8042:Microsoft Excel
8026:
7870:
7869:
7866:
7863:
7860:
7857:
7854:
7851:
7848:
7845:
7842:
7839:
7836:
7833:
7830:
7827:
7824:
7821:
7818:
7815:
7808:
7788:
7787:
7784:
7781:
7778:
7775:
7772:
7769:
7766:
7763:
7760:
7757:
7754:
7751:
7748:
7745:
7742:
7735:
7728:
7727:
7724:
7721:
7718:
7715:
7712:
7709:
7706:
7703:
7700:
7697:
7694:
7691:
7688:
7685:
7682:
7679:
7676:
7673:
7670:
7667:
7664:
7661:
7658:
7655:
7652:
7649:
7646:
7643:
7640:
7637:
7634:
7631:
7628:
7625:
7622:
7619:
7616:
7609:
7605:
7494:The two-sample
7492:
7486:The two-sample
7458:
7447:
7445:
7444:
7443:
7434:
7423:
7421:
7420:
7419:
7418:
7414:
7405:
7398:
7393:
7392:
7391:
7390:
7375:
7364:
7362:
7361:
7360:
7351:
7340:
7338:
7337:
7336:
7335:
7331:
7330:
7321:
7317:
7308:
7304:
7303:
7296:
7292:
7286:
7282:
7281:
7279:
7270:
7266:
7264:
7261:
7260:
7247:
7240:
7234:
7218:
7212:
7205:
7204:
7198:
7174:
7169:
7168:
7167:
7153:
7151:
7150:
7138:
7132:
7131:
7130:
7122:
7115:
7110:
7109:
7108:
7094:
7092:
7091:
7076:
7072:
7070:
7067:
7066:
7053:
7047:
7041:
7009:Fisher's Method
6981:
6975:
6962:
6838:
6829:
6795:
6793:
6790:
6789:
6760:
6756:
6754:
6751:
6750:
6744:
6742:Equal variances
6710:
6708:
6705:
6704:
6671:
6667:
6661:
6656:
6650:
6639:
6635:
6629:
6624:
6618:
6616:
6614:
6611:
6610:
6604:
6564:
6553:
6552:
6551:
6542:
6531:
6530:
6529:
6527:
6524:
6523:
6517:
6508:
6507:
6420:
6416:
6414:
6411:
6410:
6404:
6398:
6321:
6317:
6315:
6312:
6311:
6305:
6299:
6292:
6281:
6274:
6261:
6257:
6250:
6248:Worked examples
6073:
6066:
6063:
6057:
6039:
6035:
6033:
6030:
6029:
6012:
6001:
6000:
5999:
5997:
5994:
5993:
5966:
5961:
5955:
5951:
5950:
5943:
5939:
5930:
5919:
5918:
5917:
5916:
5914:
5906:
5903:
5902:
5887:
5852:
5848:
5822:
5813:
5808:
5798:
5787:
5769:
5765:
5756:
5752:
5740:
5736:
5735:
5733:
5724:
5720:
5718:
5715:
5714:
5691:
5686:
5676:
5665:
5649:
5645:
5636:
5632:
5620:
5616:
5614:
5611:
5610:
5580:
5575:
5569:
5555:
5550:
5544:
5543:
5539:
5523:
5517:
5506:
5500:
5484:
5477:
5472:
5462:
5451:
5446:
5444:
5442:
5439:
5438:
5410:
5404:
5399:
5384:
5378:
5373:
5345:
5341:
5332:
5328:
5316:
5312:
5310:
5307:
5306:
5283:
5279:
5273:
5262:
5248:
5239:
5235:
5229:
5218:
5204:
5190:
5189:
5175:
5174:
5165:
5161:
5159:
5156:
5155:
5126:
5122:
5111:
5105:
5100:
5085:
5079:
5074:
5058:
5054:
5024:
5020:
5011:
5007:
4990:
4987:
4986:
4965:
4960:
4945:
4941:
4935:
4931:
4918:
4913:
4898:
4894:
4888:
4884:
4873:
4870:
4869:
4848:
4843:
4838:
4835:
4834:
4812:
4809:
4808:
4785:
4781:
4775:
4771:
4766:
4763:
4762:
4744:
4739:
4734:
4731:
4730:
4708:
4705:
4704:
4681:
4677:
4671:
4667:
4662:
4659:
4658:
4635:
4630:
4617:
4613:
4605:
4602:
4601:
4581:
4576:
4563:
4559:
4551:
4548:
4547:
4525:
4522:
4521:
4504:
4500:
4494:
4490:
4475:
4471:
4462:
4458:
4447:
4444:
4443:
4426:
4422:
4416:
4412:
4397:
4393:
4384:
4380:
4369:
4366:
4365:
4336:
4332:
4317:
4313:
4311:
4308:
4307:
4281:
4233:
4229:
4228:
4221:
4217:
4211:
4207:
4202:
4196:
4191:
4183:
4181:
4163:
4159:
4158:
4151:
4147:
4141:
4137:
4132:
4126:
4121:
4113:
4111:
4110:
4104:
4091:
4087:
4081:
4076:
4070:
4059:
4055:
4049:
4044:
4038:
4037:
4033:
4032:
4030:
4022:
4020:
4017:
4016:
3992:
3988:
3976:
3975:
3971:
3966:
3963:
3962:
3956:
3950:
3946:
3941:
3929:
3924:
3897:
3893:
3887:
3882:
3876:
3865:
3861:
3855:
3850:
3844:
3842:
3827:
3826:
3822:
3820:
3817:
3816:
3782:
3781:
3777:
3770:
3759:
3758:
3757:
3748:
3737:
3736:
3735:
3734:
3732:
3724:
3721:
3720:
3711:
3704:
3694:
3691:
3690:
3679:
3678:
3667:
3666:
3655:
3654:
3637:
3630:
3624:
3619:
3614:
3576:
3572:
3563:
3559:
3558:
3551:
3544:
3540:
3539:
3520:
3516:
3504:
3497:
3493:
3492:
3473:
3469:
3465:
3462:
3453:
3449:
3447:
3444:
3443:
3410:
3406:
3401:
3390:
3386:
3381:
3379:
3370:
3366:
3365:
3358:
3347:
3346:
3345:
3336:
3325:
3324:
3323:
3322:
3320:
3312:
3309:
3308:
3299:
3293:
3286:
3276:
3272:
3265:
3264:
3254:
3251:
3249:
3248:
3238:
3237:
3235:
3228:
3225:
3222:
3221:
3219:
3209:
3201:
3184:
3175:
3174:
3167:
3166:
3165:
3161:
3156:
3155:
3148:
3147:
3146:
3142:
3139:
3132:
3122:
3114:
3109:
3079:
3072:
3068:
3067:
3054:
3047:
3043:
3042:
3037:
3034:
3025:
3021:
3019:
3016:
3015:
2980:
2974:
2970:
2969:
2962:
2951:
2950:
2949:
2940:
2929:
2928:
2927:
2926:
2924:
2916:
2913:
2912:
2903:
2886:
2881:
2869:
2863:
2837:
2826:
2825:
2824:
2815:
2810:
2799:
2795:
2793:
2783:
2776:score,intercept
2774:
2770:
2768:
2765:
2764:
2759:
2752:
2750:
2743:
2706:
2702:
2681:
2677:
2675:
2666:
2662:
2660:
2657:
2656:
2651:
2644:
2616:
2612:
2601:
2600:
2591:
2587:
2578:
2567:
2562:
2551:
2535:
2526:
2522:
2508:
2507:
2503:
2501:
2492:
2488:
2486:
2483:
2482:
2477:
2470:
2453:
2452:
2444:
2435:
2428:
2417:
2416:
2415:
2414:
2413:
2407:
2396:
2385:
2380:
2377:
2376:
2368:
2360:
2348:
2344:
2333:
2332:
2318:
2317:
2305:
2301:
2292:
2281:
2280:
2279:
2270:
2266:
2259:
2253:
2242:
2241:
2240:
2236:
2234:
2231:
2230:
2203:
2199:
2188:
2187:
2178:
2174:
2165:
2154:
2140:
2136:
2130:
2119:
2118:
2117:
2108:
2104:
2095:
2084:
2067:
2062:
2058:
2043:
2042:
2038:
2033:
2030:
2029:
2015:
1985:
1979:
1978:
1977:
1959:
1958:
1954:
1950:
1943:
1939:
1925:
1924:
1923:
1921:
1912:
1908:
1906:
1903:
1902:
1882:
1881:
1873:
1866:
1854:
1853:
1849:
1831:
1830:
1826:
1820:
1819:
1811:
1804:
1793:
1792:
1778:
1777:
1773:
1771:
1768:
1767:
1755:
1749:
1746:
1740:
1734:
1728:
1722:
1716:
1710:
1704:
1698:
1655:
1652:
1651:
1645:
1591:
1520:
1519:
1509:
1508:
1506:
1501:
1498:
1497:
1474:
1470:
1454:
1450:
1448:
1445:
1444:
1418:
1414:
1372:
1371:
1361:
1359:
1356:
1355:
1336:
1333:
1332:
1237:Bartlett's test
1188:
1182:
1170:
1160:
1152:
1137:
1125:
1119:
1112:
1111:
1098:population mean
1091:
1068:
1064:
1053:
1052:
1043:
1039:
1030:
1013:
1008:
1006:
992:
991:
989:
986:
985:
975:
969:
966:
957:
950:
944:
918:
917:
915:
912:
911:
884:
879:
868:
867:
866:
848:
847:
846:
844:
831:
823:
820:
819:
803:
793:
787:
779:
773:
759:
754:
740:Paired samples
725:
718:
712:
703:
700:
695:
694:
692:
691:
690:-test has only
663:
657:
636:
522:
481:
480:
478:
475:
474:
458:
455:
454:
425:
424:
422:
419:
418:
411:
401:
391:
369:
368:
366:
363:
362:
335:
330:
326:
319:
315:
301:
300:
299:
297:
289:
286:
285:
279:
273:
270:null hypothesis
254:
231:
92:
52:null hypothesis
17:
12:
11:
5:
13278:
13268:
13267:
13262:
13248:
13247:
13243:
13242:
13240:
13239:
13227:
13215:
13202:
13199:
13198:
13195:
13194:
13192:
13191:
13186:
13181:
13176:
13171:
13166:
13161:
13156:
13151:
13146:
13140:
13138:
13134:
13133:
13131:
13130:
13129:
13128:
13123:
13118:
13113:
13105:
13099:
13097:
13093:
13092:
13090:
13089:
13082:
13077:
13072:
13071:
13070:
13065:
13060:
13055:
13047:
13046:
13045:
13040:
13032:
13031:
13030:
13022:
13021:
13020:
13015:
13007:
13006:
13005:
12997:
12996:
12995:
12986:
12984:
12977:
12972:Organizations,
12969:
12968:
12966:
12965:
12960:
12955:
12950:
12945:
12940:
12935:
12930:
12925:
12920:
12914:
12912:
12906:
12905:
12903:
12902:
12901:
12900:
12895:
12885:
12880:
12879:
12878:
12873:
12868:
12863:
12858:
12853:
12848:
12839:
12837:
12831:
12830:
12828:
12827:
12822:
12817:
12812:
12807:
12802:
12797:
12796:
12795:
12785:
12784:
12783:
12773:
12772:
12771:
12761:
12755:
12753:
12747:
12746:
12744:
12743:
12738:
12737:
12736:
12728:
12719:
12714:
12709:
12699:
12694:
12689:
12683:
12681:
12678:Biological and
12675:
12674:
12672:
12671:
12666:
12665:
12664:
12659:
12654:
12644:
12639:
12637:Multimorbidity
12634:
12629:
12624:
12619:
12614:
12609:
12604:
12599:
12594:
12588:
12586:
12580:
12579:
12577:
12576:
12574:Vector control
12571:
12566:
12561:
12559:School hygiene
12556:
12555:
12554:
12549:
12544:
12542:Sanitary sewer
12539:
12534:
12529:
12519:
12514:
12509:
12508:
12507:
12500:Patient safety
12497:
12496:
12495:
12490:
12485:
12480:
12475:
12470:
12460:
12459:
12458:
12453:
12448:
12443:
12433:
12432:
12431:
12426:
12416:
12411:
12406:
12405:
12404:
12393:
12391:
12385:
12384:
12382:
12381:
12376:
12371:
12366:
12361:
12356:
12351:
12346:
12341:
12336:
12331:
12326:
12321:
12316:
12315:
12314:
12309:
12304:
12299:
12294:
12284:
12279:
12274:
12264:
12259:
12254:
12249:
12244:
12239:
12238:
12237:
12232:
12222:
12217:
12212:
12211:
12210:
12205:
12195:
12190:
12185:
12183:Harm reduction
12180:
12175:
12170:
12165:
12164:
12163:
12158:
12148:
12143:
12138:
12133:
12128:
12123:
12117:
12115:
12111:
12110:
12103:
12102:
12095:
12088:
12080:
12071:
12070:
12068:
12067:
12055:
12043:
12029:
12016:
12013:
12012:
12009:
12008:
12005:
12004:
12002:
12001:
11996:
11991:
11986:
11981:
11975:
11973:
11967:
11966:
11964:
11963:
11958:
11953:
11948:
11943:
11938:
11933:
11928:
11923:
11918:
11912:
11910:
11904:
11903:
11901:
11900:
11895:
11890:
11881:
11876:
11871:
11865:
11863:
11857:
11856:
11854:
11853:
11848:
11843:
11834:
11832:Bioinformatics
11828:
11826:
11816:
11815:
11803:
11802:
11799:
11798:
11795:
11794:
11791:
11790:
11788:
11787:
11781:
11779:
11775:
11774:
11772:
11771:
11765:
11763:
11757:
11756:
11754:
11753:
11748:
11743:
11738:
11732:
11730:
11721:
11715:
11714:
11711:
11710:
11708:
11707:
11702:
11697:
11692:
11687:
11681:
11679:
11673:
11672:
11670:
11669:
11664:
11659:
11651:
11646:
11641:
11640:
11639:
11637:partial (PACF)
11628:
11626:
11620:
11619:
11617:
11616:
11611:
11606:
11598:
11593:
11587:
11585:
11584:Specific tests
11581:
11580:
11578:
11577:
11572:
11567:
11562:
11557:
11552:
11547:
11542:
11536:
11534:
11527:
11521:
11520:
11518:
11517:
11516:
11515:
11514:
11513:
11498:
11497:
11496:
11486:
11484:Classification
11481:
11476:
11471:
11466:
11461:
11456:
11450:
11448:
11442:
11441:
11439:
11438:
11433:
11431:McNemar's test
11428:
11423:
11418:
11413:
11407:
11405:
11395:
11394:
11370:
11369:
11366:
11365:
11362:
11361:
11359:
11358:
11353:
11348:
11343:
11337:
11335:
11329:
11328:
11326:
11325:
11309:
11303:
11301:
11295:
11294:
11292:
11291:
11286:
11281:
11276:
11271:
11269:Semiparametric
11266:
11261:
11255:
11253:
11249:
11248:
11246:
11245:
11240:
11235:
11230:
11224:
11222:
11216:
11215:
11213:
11212:
11207:
11202:
11197:
11192:
11186:
11184:
11178:
11177:
11175:
11174:
11169:
11164:
11159:
11153:
11151:
11141:
11140:
11137:
11136:
11131:
11125:
11117:
11116:
11113:
11112:
11109:
11108:
11106:
11105:
11104:
11103:
11093:
11088:
11083:
11082:
11081:
11076:
11065:
11063:
11057:
11056:
11053:
11052:
11050:
11049:
11044:
11043:
11042:
11034:
11026:
11010:
11007:(MannâWhitney)
11002:
11001:
11000:
10987:
10986:
10985:
10974:
10972:
10966:
10965:
10963:
10962:
10961:
10960:
10955:
10950:
10940:
10935:
10932:(ShapiroâWilk)
10927:
10922:
10917:
10912:
10907:
10899:
10893:
10891:
10885:
10884:
10882:
10881:
10873:
10864:
10852:
10846:
10844:Specific tests
10840:
10839:
10836:
10835:
10833:
10832:
10827:
10822:
10816:
10814:
10808:
10807:
10805:
10804:
10799:
10798:
10797:
10787:
10786:
10785:
10775:
10769:
10767:
10761:
10760:
10758:
10757:
10756:
10755:
10750:
10740:
10735:
10730:
10725:
10720:
10714:
10712:
10706:
10705:
10703:
10702:
10697:
10696:
10695:
10690:
10689:
10688:
10683:
10668:
10667:
10666:
10661:
10656:
10651:
10640:
10638:
10629:
10623:
10622:
10620:
10619:
10614:
10609:
10608:
10607:
10597:
10592:
10591:
10590:
10580:
10579:
10578:
10573:
10568:
10558:
10553:
10548:
10547:
10546:
10541:
10536:
10520:
10519:
10518:
10513:
10508:
10498:
10497:
10496:
10491:
10481:
10480:
10479:
10469:
10468:
10467:
10457:
10452:
10447:
10441:
10439:
10429:
10428:
10416:
10415:
10412:
10411:
10408:
10407:
10405:
10404:
10399:
10394:
10389:
10383:
10381:
10375:
10374:
10372:
10371:
10366:
10361:
10355:
10353:
10349:
10348:
10346:
10345:
10340:
10335:
10330:
10325:
10320:
10315:
10309:
10307:
10301:
10300:
10298:
10297:
10295:Standard error
10292:
10287:
10282:
10281:
10280:
10275:
10264:
10262:
10256:
10255:
10253:
10252:
10247:
10242:
10237:
10232:
10227:
10225:Optimal design
10222:
10217:
10211:
10209:
10199:
10198:
10186:
10185:
10182:
10181:
10178:
10177:
10175:
10174:
10169:
10164:
10159:
10154:
10149:
10144:
10139:
10134:
10129:
10124:
10119:
10114:
10109:
10104:
10098:
10096:
10090:
10089:
10087:
10086:
10081:
10080:
10079:
10074:
10064:
10059:
10053:
10051:
10045:
10044:
10042:
10041:
10036:
10031:
10025:
10023:
10022:Summary tables
10019:
10018:
10016:
10015:
10009:
10007:
10001:
10000:
9997:
9996:
9994:
9993:
9992:
9991:
9986:
9981:
9971:
9965:
9963:
9957:
9956:
9954:
9953:
9948:
9943:
9938:
9933:
9928:
9923:
9917:
9915:
9909:
9908:
9906:
9905:
9900:
9895:
9894:
9893:
9888:
9883:
9878:
9873:
9868:
9863:
9858:
9856:Contraharmonic
9853:
9848:
9837:
9835:
9826:
9816:
9815:
9803:
9802:
9800:
9799:
9794:
9788:
9785:
9784:
9777:
9776:
9769:
9762:
9754:
9748:
9747:
9732:
9721:
9707:"Student test"
9701:
9700:External links
9698:
9697:
9696:
9686:(3): 576â583.
9671:
9636:
9633:
9631:
9630:
9624:
9601:
9595:
9577:
9575:
9572:
9569:
9568:
9555:(2): 120â126.
9532:
9479:
9460:(4): 309â335.
9440:
9405:
9394:(2): 352â360.
9371:
9350:
9331:(2): 397â409.
9311:
9300:analyse-it.com
9287:
9280:
9260:
9217:
9198:(4): 322â326.
9182:
9153:(1): 151â169.
9122:
9083:
9074:-Distribution"
9060:
9045:
9038:
9020:
9013:
8999:Dodge, Yadolah
8990:
8963:(3): 732â735.
8945:
8930:
8912:
8893:(6280): 1406.
8877:
8863:
8809:
8768:
8725:
8706:(4): 891â898.
8686:
8647:
8608:
8581:(6): 709â737.
8565:
8544:
8518:
8511:
8491:
8490:
8488:
8485:
8484:
8483:
8477:
8467:
8457:
8447:
8438:
8425:
8415:
8406:
8400:
8399:
8383:
8380:
8377:
8376:
8371:
8366:
8360:
8359:
8354:
8349:
8343:
8342:
8337:
8332:
8326:
8325:
8320:
8315:
8309:
8308:
8303:
8298:
8292:
8291:
8286:
8281:
8275:
8274:
8269:
8264:
8258:
8257:
8252:
8248:equal_var=True
8235:
8229:
8228:
8223:
8218:
8212:
8211:
8206:
8197:
8191:
8190:
8185:
8180:
8174:
8173:
8168:
8147:
8146:2010 and later
8140:
8139:
8134:
8113:
8106:
8105:
8102:
8099:
8025:
8022:
7983:
7982:
7971:
7968:
7943:
7942:
7939:
7935:
7926:
7925:
7922:
7919:
7916:
7913:
7909:
7908:
7905:
7902:
7899:
7896:
7892:
7891:
7888:
7885:
7882:
7879:
7814:
7805:
7804:
7801:
7798:
7795:
7741:
7615:
7596:
7595:
7592:
7589:
7585:
7584:
7581:
7578:
7574:
7573:
7570:
7567:
7563:
7562:
7559:
7556:
7552:
7551:
7548:
7545:
7541:
7540:
7537:
7534:
7530:
7529:
7526:
7523:
7491:
7484:
7483:
7482:
7471:
7467:
7461:
7454:
7450:
7442:
7437:
7430:
7426:
7417:
7411:
7408:
7396:
7388:
7384:
7378:
7371:
7367:
7359:
7354:
7347:
7343:
7334:
7324:
7320:
7316:
7311:
7307:
7299:
7295:
7289:
7285:
7278:
7273:
7269:
7245:
7238:
7195:
7194:
7183:
7177:
7172:
7166:
7160:
7156:
7149:
7144:
7141:
7135:
7128:
7125:
7118:
7113:
7107:
7101:
7097:
7090:
7087:
7084:
7079:
7075:
7051:
6977:Main article:
6974:
6971:
6961:
6958:
6883:non-parametric
6837:
6830:
6828:
6825:
6817:
6816:
6805:
6802:
6783:
6782:
6771:
6768:
6763:
6759:
6743:
6740:
6732:
6731:
6720:
6717:
6698:
6697:
6686:
6683:
6674:
6670:
6664:
6659:
6655:
6649:
6642:
6638:
6632:
6627:
6623:
6603:
6600:
6587:
6586:
6575:
6572:
6567:
6560:
6557:
6550:
6545:
6538:
6535:
6513:
6494:
6493:
6482:
6479:
6473:
6470:
6464:
6461:
6455:
6452:
6446:
6443:
6437:
6434:
6431:
6428:
6423:
6419:
6402:
6395:
6394:
6383:
6380:
6374:
6371:
6365:
6362:
6356:
6353:
6347:
6344:
6338:
6335:
6332:
6329:
6324:
6320:
6303:
6294:
6293:
6264:
6262:
6255:
6249:
6246:
6243:
6242:
6239:
6238:
6235:
6232:
6229:
6225:
6224:
6221:
6218:
6215:
6211:
6210:
6207:
6204:
6201:
6197:
6196:
6193:
6190:
6187:
6183:
6182:
6179:
6176:
6173:
6163:
6160:
6159:
6156:
6153:
6150:
6146:
6145:
6142:
6139:
6136:
6132:
6131:
6128:
6125:
6122:
6118:
6117:
6114:
6111:
6108:
6104:
6103:
6100:
6097:
6094:
6061:
6042:
6038:
6015:
6008:
6005:
5990:
5989:
5978:
5970:
5964:
5958:
5954:
5946:
5942:
5938:
5933:
5926:
5923:
5913:
5910:
5886:
5879:
5878:
5877:
5866:
5861:
5858:
5855:
5851:
5847:
5841:
5838:
5835:
5832:
5829:
5825:
5821:
5816:
5811:
5807:
5801:
5796:
5793:
5790:
5786:
5782:
5777:
5772:
5768:
5764:
5759:
5755:
5751:
5748:
5743:
5739:
5732:
5727:
5723:
5711:
5710:
5699:
5694:
5689:
5685:
5679:
5674:
5671:
5668:
5664:
5660:
5657:
5652:
5648:
5644:
5639:
5635:
5631:
5628:
5623:
5619:
5607:
5606:
5594:
5588:
5583:
5578:
5574:
5568:
5563:
5558:
5553:
5549:
5542:
5538:
5532:
5529:
5526:
5520:
5515:
5512:
5509:
5505:
5499:
5493:
5490:
5487:
5480:
5475:
5471:
5465:
5460:
5457:
5454:
5450:
5435:
5434:
5423:
5420:
5417:
5413:
5407:
5402:
5398:
5394:
5391:
5387:
5381:
5376:
5372:
5368:
5365:
5362:
5359:
5356:
5353:
5348:
5344:
5340:
5335:
5331:
5327:
5324:
5319:
5315:
5303:
5302:
5291:
5286:
5282:
5276:
5271:
5268:
5265:
5261:
5255:
5252:
5247:
5242:
5238:
5232:
5227:
5224:
5221:
5217:
5211:
5208:
5203:
5197:
5194:
5188:
5182:
5179:
5173:
5168:
5164:
5149:
5148:
5137:
5134:
5129:
5125:
5121:
5118:
5114:
5108:
5103:
5099:
5095:
5092:
5088:
5082:
5077:
5073:
5069:
5066:
5061:
5057:
5053:
5050:
5047:
5044:
5041:
5038:
5035:
5032:
5027:
5023:
5019:
5014:
5010:
5006:
5003:
5000:
4997:
4994:
4969:
4963:
4959:
4954:
4951:
4948:
4944:
4938:
4934:
4930:
4927:
4922:
4916:
4912:
4907:
4904:
4901:
4897:
4891:
4887:
4883:
4880:
4877:
4852:
4846:
4842:
4822:
4819:
4816:
4794:
4791:
4788:
4784:
4778:
4774:
4770:
4748:
4742:
4738:
4718:
4715:
4712:
4690:
4687:
4684:
4680:
4674:
4670:
4666:
4643:
4638:
4633:
4629:
4625:
4620:
4616:
4612:
4609:
4589:
4584:
4579:
4575:
4571:
4566:
4562:
4558:
4555:
4535:
4532:
4529:
4507:
4503:
4497:
4493:
4489:
4486:
4483:
4478:
4474:
4470:
4465:
4461:
4457:
4454:
4451:
4429:
4425:
4419:
4415:
4411:
4408:
4405:
4400:
4396:
4392:
4387:
4383:
4379:
4376:
4373:
4347:
4344:
4339:
4335:
4331:
4328:
4325:
4320:
4316:
4280:
4277:
4265:
4264:
4253:
4244:
4241:
4236:
4232:
4224:
4220:
4214:
4210:
4205:
4199:
4194:
4190:
4186:
4180:
4174:
4171:
4166:
4162:
4154:
4150:
4144:
4140:
4135:
4129:
4124:
4120:
4116:
4107:
4102:
4094:
4090:
4084:
4079:
4075:
4069:
4062:
4058:
4052:
4047:
4043:
4036:
4029:
3995:
3991:
3983:
3980:
3974:
3970:
3944:
3927:
3921:
3920:
3909:
3900:
3896:
3890:
3885:
3881:
3875:
3868:
3864:
3858:
3853:
3849:
3841:
3834:
3831:
3825:
3810:
3809:
3798:
3789:
3786:
3780:
3773:
3766:
3763:
3756:
3751:
3744:
3741:
3731:
3728:
3696:Main article:
3693:
3688:
3684:
3676:
3672:
3664:
3660:
3652:
3648:
3642:
3638: â 2
3635:
3628:
3621: â 1
3617:
3603:
3602:
3587:
3584:
3579:
3575:
3571:
3566:
3562:
3554:
3547:
3543:
3538:
3534:
3531:
3528:
3523:
3519:
3515:
3512:
3507:
3500:
3496:
3491:
3487:
3484:
3481:
3476:
3472:
3468:
3461:
3456:
3452:
3437:
3436:
3425:
3413:
3409:
3405:
3400:
3393:
3389:
3385:
3378:
3373:
3369:
3361:
3354:
3351:
3344:
3339:
3332:
3329:
3319:
3316:
3291:
3284:
3271:
3262:
3258:
3246:
3242:
3216:
3191:standard error
3172:
3168:
3153:
3149:
3137:
3130:
3112:
3106:
3105:
3094:
3088:
3082:
3075:
3071:
3066:
3062:
3057:
3050:
3046:
3041:
3033:
3028:
3024:
3009:
3008:
2997:
2988:
2985:
2977:
2973:
2965:
2958:
2955:
2948:
2943:
2936:
2933:
2923:
2920:
2897:
2896:
2893:
2885:
2882:
2880:
2873:
2867:
2860:
2859:
2848:
2840:
2833:
2830:
2823:
2818:
2809:
2798:
2790:
2787:
2782:
2773:
2757:
2748:
2729:
2728:
2717:
2709:
2705:
2701:
2698:
2691:
2688:
2685:
2680:
2674:
2665:
2649:
2641:
2640:
2629:
2619:
2615:
2608:
2605:
2599:
2594:
2590:
2586:
2581:
2576:
2573:
2570:
2566:
2560:
2557:
2554:
2545:
2542:
2539:
2534:
2529:
2525:
2521:
2515:
2512:
2506:
2500:
2491:
2475:
2467:
2466:
2451:
2443:
2438:
2431:
2424:
2421:
2410:
2405:
2402:
2399:
2395:
2391:
2388:
2386:
2379:
2378:
2375:
2367:
2359:
2356:
2351:
2347:
2340:
2337:
2331:
2325:
2322:
2316:
2313:
2308:
2304:
2300:
2295:
2288:
2285:
2278:
2273:
2269:
2265:
2262:
2260:
2256:
2249:
2246:
2239:
2238:
2224:
2223:
2206:
2202:
2195:
2192:
2186:
2181:
2177:
2173:
2168:
2163:
2160:
2157:
2153:
2143:
2139:
2133:
2126:
2123:
2116:
2111:
2107:
2103:
2098:
2093:
2090:
2087:
2083:
2076:
2073:
2070:
2066:
2057:
2050:
2047:
2041:
2037:
2008:
2007:
1994:
1991:
1988:
1982:
1976:
1966:
1963:
1957:
1953:
1946:
1942:
1938:
1932:
1929:
1920:
1911:
1896:
1895:
1880:
1872:
1869:
1867:
1861:
1858:
1852:
1848:
1845:
1838:
1835:
1829:
1825:
1822:
1821:
1818:
1810:
1807:
1805:
1800:
1797:
1791:
1785:
1782:
1776:
1775:
1744:
1695:
1694:
1683:
1680:
1677:
1674:
1671:
1668:
1665:
1662:
1659:
1644:
1641:
1590:
1587:
1586:
1585:
1573:
1570:
1567:
1564:
1561:
1558:
1553:
1549:
1543:
1539:
1536:
1533:
1527:
1524:
1518:
1513:
1505:
1495:
1477:
1473:
1467:
1463:
1457:
1453:
1442:
1426:
1421:
1417:
1413:
1410:
1407:
1404:
1399:
1395:
1391:
1388:
1385:
1379:
1376:
1370:
1365:
1340:
1324:distribution.
1277:
1276:
1260:
1218:
1199:
1198:
1180:
1164: â 1
1135:
1071:
1067:
1060:
1057:
1051:
1046:
1042:
1038:
1033:
1029:
1022:
1019:
1016:
1012:
1005:
999:
996:
962:
955:
948:
943:from a sample
925:
922:
908:
907:
896:
888:
882:
875:
872:
864:
861:
855:
852:
843:
838:
835:
830:
827:
753:
750:
666:Paired samples
659:Main article:
656:
655:Paired samples
653:
635:
632:
600:paired samples
521:
514:
501:
498:
495:
492:
489:
484:
462:
432:
429:
415: â 1
376:
373:
359:
358:
347:
339:
333:
329:
322:
318:
314:
308:
305:
296:
293:
277:
253:
246:
230:
227:
91:
88:
40:test statistic
15:
9:
6:
4:
3:
2:
13277:
13266:
13263:
13261:
13258:
13257:
13255:
13238:
13237:
13228:
13226:
13225:
13216:
13214:
13213:
13204:
13203:
13200:
13190:
13187:
13185:
13182:
13180:
13177:
13175:
13172:
13170:
13167:
13165:
13162:
13160:
13159:Joseph Lister
13157:
13155:
13152:
13150:
13147:
13145:
13142:
13141:
13139:
13135:
13127:
13124:
13122:
13119:
13117:
13114:
13112:
13109:
13108:
13106:
13104:
13101:
13100:
13098:
13094:
13087:
13083:
13081:
13078:
13076:
13073:
13069:
13066:
13064:
13061:
13059:
13056:
13054:
13051:
13050:
13048:
13044:
13041:
13039:
13038:Health Canada
13036:
13035:
13033:
13029:
13026:
13025:
13023:
13019:
13016:
13014:
13011:
13010:
13008:
13004:
13001:
13000:
12998:
12994:
12991:
12990:
12988:
12987:
12985:
12983:Organizations
12981:
12978:
12970:
12964:
12961:
12959:
12956:
12954:
12951:
12949:
12946:
12944:
12941:
12939:
12936:
12934:
12931:
12929:
12926:
12924:
12921:
12919:
12916:
12915:
12913:
12907:
12899:
12896:
12894:
12891:
12890:
12889:
12886:
12884:
12881:
12877:
12874:
12872:
12869:
12867:
12864:
12862:
12859:
12857:
12854:
12852:
12849:
12847:
12844:
12843:
12841:
12840:
12838:
12832:
12826:
12823:
12821:
12820:Vaccine trial
12818:
12816:
12813:
12811:
12808:
12806:
12803:
12801:
12798:
12794:
12791:
12790:
12789:
12786:
12782:
12779:
12778:
12777:
12774:
12770:
12767:
12766:
12765:
12762:
12760:
12757:
12756:
12754:
12748:
12742:
12739:
12735:
12733:
12729:
12727:
12725:
12720:
12718:
12715:
12713:
12710:
12708:
12705:
12704:
12703:
12700:
12698:
12697:Relative risk
12695:
12693:
12690:
12688:
12685:
12684:
12682:
12676:
12670:
12667:
12663:
12660:
12658:
12657:Health equity
12655:
12653:
12650:
12649:
12648:
12645:
12643:
12640:
12638:
12635:
12633:
12630:
12628:
12625:
12623:
12622:Health system
12620:
12618:
12615:
12613:
12612:Global health
12610:
12608:
12605:
12603:
12600:
12598:
12595:
12593:
12592:Biostatistics
12590:
12589:
12587:
12585:
12581:
12575:
12572:
12570:
12567:
12565:
12562:
12560:
12557:
12553:
12550:
12548:
12545:
12543:
12540:
12538:
12535:
12533:
12530:
12528:
12525:
12524:
12523:
12520:
12518:
12515:
12513:
12510:
12506:
12503:
12502:
12501:
12498:
12494:
12491:
12489:
12486:
12484:
12481:
12479:
12476:
12474:
12471:
12469:
12466:
12465:
12464:
12461:
12457:
12454:
12452:
12449:
12447:
12444:
12442:
12439:
12438:
12437:
12434:
12430:
12427:
12425:
12422:
12421:
12420:
12417:
12415:
12412:
12410:
12407:
12403:
12400:
12399:
12398:
12395:
12394:
12392:
12390:
12386:
12380:
12377:
12375:
12372:
12370:
12367:
12365:
12362:
12360:
12357:
12355:
12352:
12350:
12347:
12345:
12342:
12340:
12337:
12335:
12334:Right to food
12332:
12330:
12327:
12325:
12322:
12320:
12317:
12313:
12310:
12308:
12305:
12303:
12300:
12298:
12295:
12293:
12290:
12289:
12288:
12285:
12283:
12280:
12278:
12275:
12272:
12268:
12267:Mental health
12265:
12263:
12260:
12258:
12255:
12253:
12250:
12248:
12245:
12243:
12240:
12236:
12233:
12231:
12228:
12227:
12226:
12223:
12221:
12218:
12216:
12215:Housing First
12213:
12209:
12206:
12204:
12203:Health system
12201:
12200:
12199:
12198:Health policy
12196:
12194:
12191:
12189:
12186:
12184:
12181:
12179:
12176:
12174:
12171:
12169:
12166:
12162:
12159:
12157:
12154:
12153:
12152:
12149:
12147:
12144:
12142:
12139:
12137:
12134:
12132:
12129:
12127:
12124:
12122:
12119:
12118:
12116:
12112:
12108:
12107:Public health
12101:
12096:
12094:
12089:
12087:
12082:
12081:
12078:
12066:
12065:
12056:
12054:
12053:
12044:
12042:
12041:
12036:
12030:
12028:
12027:
12018:
12017:
12014:
12000:
11997:
11995:
11994:Geostatistics
11992:
11990:
11987:
11985:
11982:
11980:
11977:
11976:
11974:
11972:
11968:
11962:
11961:Psychometrics
11959:
11957:
11954:
11952:
11949:
11947:
11944:
11942:
11939:
11937:
11934:
11932:
11929:
11927:
11924:
11922:
11919:
11917:
11914:
11913:
11911:
11909:
11905:
11899:
11896:
11894:
11891:
11889:
11885:
11882:
11880:
11877:
11875:
11872:
11870:
11867:
11866:
11864:
11862:
11858:
11852:
11849:
11847:
11844:
11842:
11838:
11835:
11833:
11830:
11829:
11827:
11825:
11824:Biostatistics
11821:
11817:
11813:
11808:
11804:
11786:
11785:Log-rank test
11783:
11782:
11780:
11776:
11770:
11767:
11766:
11764:
11762:
11758:
11752:
11749:
11747:
11744:
11742:
11739:
11737:
11734:
11733:
11731:
11729:
11725:
11722:
11720:
11716:
11706:
11703:
11701:
11698:
11696:
11693:
11691:
11688:
11686:
11683:
11682:
11680:
11678:
11674:
11668:
11665:
11663:
11660:
11658:
11656:(BoxâJenkins)
11652:
11650:
11647:
11645:
11642:
11638:
11635:
11634:
11633:
11630:
11629:
11627:
11625:
11621:
11615:
11612:
11610:
11609:DurbinâWatson
11607:
11605:
11599:
11597:
11594:
11592:
11591:DickeyâFuller
11589:
11588:
11586:
11582:
11576:
11573:
11571:
11568:
11566:
11565:Cointegration
11563:
11561:
11558:
11556:
11553:
11551:
11548:
11546:
11543:
11541:
11540:Decomposition
11538:
11537:
11535:
11531:
11528:
11526:
11522:
11512:
11509:
11508:
11507:
11504:
11503:
11502:
11499:
11495:
11492:
11491:
11490:
11487:
11485:
11482:
11480:
11477:
11475:
11472:
11470:
11467:
11465:
11462:
11460:
11457:
11455:
11452:
11451:
11449:
11447:
11443:
11437:
11434:
11432:
11429:
11427:
11424:
11422:
11419:
11417:
11414:
11412:
11411:Cohen's kappa
11409:
11408:
11406:
11404:
11400:
11396:
11392:
11388:
11384:
11380:
11375:
11371:
11357:
11354:
11352:
11349:
11347:
11344:
11342:
11339:
11338:
11336:
11334:
11330:
11324:
11320:
11316:
11310:
11308:
11305:
11304:
11302:
11300:
11296:
11290:
11287:
11285:
11282:
11280:
11277:
11275:
11272:
11270:
11267:
11265:
11264:Nonparametric
11262:
11260:
11257:
11256:
11254:
11250:
11244:
11241:
11239:
11236:
11234:
11231:
11229:
11226:
11225:
11223:
11221:
11217:
11211:
11208:
11206:
11203:
11201:
11198:
11196:
11193:
11191:
11188:
11187:
11185:
11183:
11179:
11173:
11170:
11168:
11165:
11163:
11160:
11158:
11155:
11154:
11152:
11150:
11146:
11142:
11135:
11132:
11130:
11127:
11126:
11122:
11118:
11102:
11099:
11098:
11097:
11094:
11092:
11089:
11087:
11084:
11080:
11077:
11075:
11072:
11071:
11070:
11067:
11066:
11064:
11062:
11058:
11048:
11045:
11041:
11035:
11033:
11027:
11025:
11019:
11018:
11017:
11014:
11013:Nonparametric
11011:
11009:
11003:
10999:
10996:
10995:
10994:
10988:
10984:
10983:Sample median
10981:
10980:
10979:
10976:
10975:
10973:
10971:
10967:
10959:
10956:
10954:
10951:
10949:
10946:
10945:
10944:
10941:
10939:
10936:
10934:
10928:
10926:
10923:
10921:
10918:
10916:
10913:
10911:
10908:
10906:
10904:
10900:
10898:
10895:
10894:
10892:
10890:
10886:
10880:
10878:
10874:
10872:
10870:
10865:
10863:
10858:
10854:
10853:
10850:
10847:
10845:
10841:
10831:
10828:
10826:
10823:
10821:
10818:
10817:
10815:
10813:
10809:
10803:
10800:
10796:
10793:
10792:
10791:
10788:
10784:
10781:
10780:
10779:
10776:
10774:
10771:
10770:
10768:
10766:
10762:
10754:
10751:
10749:
10746:
10745:
10744:
10741:
10739:
10736:
10734:
10731:
10729:
10726:
10724:
10721:
10719:
10716:
10715:
10713:
10711:
10707:
10701:
10698:
10694:
10691:
10687:
10684:
10682:
10679:
10678:
10677:
10674:
10673:
10672:
10669:
10665:
10662:
10660:
10657:
10655:
10652:
10650:
10647:
10646:
10645:
10642:
10641:
10639:
10637:
10633:
10630:
10628:
10624:
10618:
10615:
10613:
10610:
10606:
10603:
10602:
10601:
10598:
10596:
10593:
10589:
10588:loss function
10586:
10585:
10584:
10581:
10577:
10574:
10572:
10569:
10567:
10564:
10563:
10562:
10559:
10557:
10554:
10552:
10549:
10545:
10542:
10540:
10537:
10535:
10529:
10526:
10525:
10524:
10521:
10517:
10514:
10512:
10509:
10507:
10504:
10503:
10502:
10499:
10495:
10492:
10490:
10487:
10486:
10485:
10482:
10478:
10475:
10474:
10473:
10470:
10466:
10463:
10462:
10461:
10458:
10456:
10453:
10451:
10448:
10446:
10443:
10442:
10440:
10438:
10434:
10430:
10426:
10421:
10417:
10403:
10400:
10398:
10395:
10393:
10390:
10388:
10385:
10384:
10382:
10380:
10376:
10370:
10367:
10365:
10362:
10360:
10357:
10356:
10354:
10350:
10344:
10341:
10339:
10336:
10334:
10331:
10329:
10326:
10324:
10321:
10319:
10316:
10314:
10311:
10310:
10308:
10306:
10302:
10296:
10293:
10291:
10290:Questionnaire
10288:
10286:
10283:
10279:
10276:
10274:
10271:
10270:
10269:
10266:
10265:
10263:
10261:
10257:
10251:
10248:
10246:
10243:
10241:
10238:
10236:
10233:
10231:
10228:
10226:
10223:
10221:
10218:
10216:
10213:
10212:
10210:
10208:
10204:
10200:
10196:
10191:
10187:
10173:
10170:
10168:
10165:
10163:
10160:
10158:
10155:
10153:
10150:
10148:
10145:
10143:
10140:
10138:
10135:
10133:
10130:
10128:
10125:
10123:
10120:
10118:
10117:Control chart
10115:
10113:
10110:
10108:
10105:
10103:
10100:
10099:
10097:
10095:
10091:
10085:
10082:
10078:
10075:
10073:
10070:
10069:
10068:
10065:
10063:
10060:
10058:
10055:
10054:
10052:
10050:
10046:
10040:
10037:
10035:
10032:
10030:
10027:
10026:
10024:
10020:
10014:
10011:
10010:
10008:
10006:
10002:
9990:
9987:
9985:
9982:
9980:
9977:
9976:
9975:
9972:
9970:
9967:
9966:
9964:
9962:
9958:
9952:
9949:
9947:
9944:
9942:
9939:
9937:
9934:
9932:
9929:
9927:
9924:
9922:
9919:
9918:
9916:
9914:
9910:
9904:
9901:
9899:
9896:
9892:
9889:
9887:
9884:
9882:
9879:
9877:
9874:
9872:
9869:
9867:
9864:
9862:
9859:
9857:
9854:
9852:
9849:
9847:
9844:
9843:
9842:
9839:
9838:
9836:
9834:
9830:
9827:
9825:
9821:
9817:
9813:
9808:
9804:
9798:
9795:
9793:
9790:
9789:
9786:
9782:
9775:
9770:
9768:
9763:
9761:
9756:
9755:
9752:
9746:
9742:
9738:
9733:
9731:, conjoint.ly
9730:
9726:
9722:
9718:
9714:
9713:
9708:
9704:
9703:
9693:
9689:
9685:
9681:
9677:
9672:
9668:
9664:
9660:
9656:
9652:
9648:
9644:
9639:
9638:
9627:
9625:0-521-43108-5
9621:
9617:
9613:
9609:
9608:
9602:
9598:
9592:
9588:
9584:
9579:
9578:
9563:
9558:
9554:
9550:
9543:
9536:
9528:
9524:
9519:
9514:
9510:
9506:
9502:
9498:
9494:
9492:
9483:
9475:
9471:
9467:
9463:
9459:
9455:
9451:
9444:
9436:
9432:
9428:
9424:
9420:
9416:
9409:
9401:
9397:
9393:
9389:
9385:
9378:
9376:
9366:
9361:
9354:
9346:
9342:
9338:
9334:
9330:
9326:
9322:
9315:
9301:
9297:
9291:
9283:
9277:
9273:
9272:
9264:
9256:
9252:
9248:
9244:
9240:
9236:
9232:
9228:
9221:
9213:
9209:
9205:
9201:
9197:
9193:
9186:
9178:
9174:
9170:
9166:
9161:
9156:
9152:
9148:
9144:
9140:
9133:
9131:
9129:
9127:
9118:
9114:
9110:
9106:
9102:
9098:
9094:
9087:
9079:
9075:
9073:
9064:
9056:
9049:
9041:
9039:9781451130300
9035:
9031:
9024:
9016:
9010:
9006:
9005:
9000:
8994:
8986:
8982:
8978:
8974:
8970:
8966:
8962:
8958:
8957:
8949:
8941:
8937:
8933:
8931:81-7758-404-9
8927:
8923:
8916:
8908:
8904:
8900:
8896:
8892:
8888:
8881:
8873:
8867:
8852:
8848:
8844:
8840:
8836:
8832:
8831:
8823:
8816:
8814:
8804:
8799:
8795:
8791:
8787:
8783:
8779:
8772:
8764:
8760:
8756:
8752:
8748:
8744:
8741:(1): 73â104.
8740:
8736:
8729:
8721:
8717:
8713:
8709:
8705:
8701:
8697:
8690:
8682:
8678:
8674:
8670:
8666:
8663:(in German).
8662:
8658:
8651:
8643:
8639:
8635:
8631:
8627:
8624:(in German).
8623:
8619:
8612:
8604:
8600:
8596:
8592:
8588:
8584:
8580:
8577:(in German).
8576:
8569:
8561:
8555:
8547:
8541:
8537:
8533:
8529:
8522:
8514:
8508:
8504:
8503:
8496:
8492:
8481:
8478:
8475:
8473:
8468:
8465:
8463:
8458:
8455:
8453:
8450:MannâWhitney
8448:
8445:
8443:
8439:
8433:
8431:
8426:
8423:
8421:
8416:
8413:
8411:
8407:
8405:
8402:
8401:
8397:
8391:
8386:
8375:
8372:
8367:
8365:
8362:
8361:
8358:
8355:
8350:
8348:
8345:
8344:
8341:
8338:
8333:
8331:
8328:
8327:
8324:
8321:
8316:
8314:
8311:
8310:
8307:
8304:
8299:
8297:
8294:
8293:
8290:
8287:
8282:
8280:
8277:
8276:
8273:
8270:
8265:
8263:
8260:
8259:
8256:
8253:
8249:
8245:
8241:
8236:
8234:
8231:
8230:
8227:
8224:
8219:
8217:
8216:Google Sheets
8214:
8213:
8210:
8207:
8203:
8198:
8196:
8193:
8192:
8189:
8186:
8181:
8179:
8178:Apple Numbers
8176:
8175:
8172:
8169:
8165:
8161:
8157:
8153:
8148:
8145:
8142:
8141:
8138:
8135:
8131:
8127:
8123:
8119:
8114:
8111:
8108:
8107:
8103:
8100:
8097:
8096:
8093:
8091:
8087:
8083:
8079:
8075:
8071:
8067:
8063:
8059:
8055:
8051:
8047:
8043:
8039:
8035:
8031:
8021:
8019:
8015:
8011:
8007:
8003:
7999:
7995:
7990:
7988:
7980:
7976:
7972:
7969:
7966:
7962:
7961:
7960:
7958:
7953:
7951:
7946:
7940:
7936:
7933:
7932:
7931:
7923:
7920:
7917:
7914:
7911:
7910:
7906:
7903:
7900:
7897:
7894:
7893:
7889:
7886:
7883:
7880:
7877:
7876:
7873:
7812:
7802:
7799:
7796:
7793:
7792:
7791:
7739:
7733:
7613:
7603:
7593:
7590:
7587:
7586:
7582:
7579:
7576:
7575:
7571:
7568:
7565:
7564:
7560:
7557:
7554:
7553:
7549:
7546:
7543:
7542:
7538:
7535:
7532:
7531:
7527:
7524:
7521:
7520:
7517:
7514:
7512:
7507:
7503:
7501:
7497:
7489:
7469:
7465:
7459:
7440:
7435:
7415:
7409:
7406:
7386:
7382:
7376:
7357:
7352:
7332:
7322:
7318:
7314:
7309:
7305:
7297:
7293:
7287:
7283:
7276:
7271:
7267:
7259:
7258:
7257:
7255:
7254:
7244:
7237:
7231:
7229:
7225:
7221:
7215:
7208:
7201:
7175:
7164:
7142:
7139:
7126:
7116:
7105:
7085:
7082:
7077:
7073:
7065:
7064:
7063:
7061:
7060:
7050:
7044:
7038:
7036:
7032:
7028:
7024:
7020:
7016:
7015:
7010:
7006:
7002:
6998:
6994:
6992:
6986:
6980:
6970:
6968:
6957:
6955:
6951:
6946:
6944:
6940:
6937:-test is the
6936:
6932:
6928:
6926:
6923:MannâWhitney
6920:
6916:
6912:
6907:
6904:
6900:
6896:
6892:
6888:
6884:
6879:
6877:
6873:
6868:
6866:
6864:
6859:
6855:
6851:
6849:
6843:
6835:
6824:
6822:
6803:
6800:
6788:
6787:
6786:
6769:
6766:
6761:
6757:
6749:
6748:
6747:
6739:
6737:
6718:
6715:
6703:
6702:
6701:
6684:
6681:
6672:
6668:
6662:
6657:
6653:
6647:
6640:
6636:
6630:
6625:
6621:
6609:
6608:
6607:
6599:
6597:
6592:
6573:
6570:
6565:
6555:
6548:
6543:
6533:
6522:
6521:
6520:
6516:
6511:
6504:
6502:
6497:
6477:
6471:
6468:
6462:
6459:
6453:
6450:
6444:
6441:
6435:
6432:
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6421:
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6409:
6408:
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6401:
6378:
6372:
6369:
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6360:
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6327:
6322:
6318:
6310:
6309:
6308:
6302:
6290:
6287:
6278:
6272:
6270:
6265:This article
6263:
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6230:
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4318:
4314:
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4288:
4286:
4276:
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4270:
4251:
4242:
4239:
4234:
4230:
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4212:
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4203:
4197:
4192:
4188:
4178:
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4160:
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4127:
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4060:
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3993:
3972:
3959:
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3879:
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3866:
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3709:
3703:
3701:
3687:
3683:
3675:
3671:
3663:
3659:
3651:
3647:
3641:
3634:
3631: +
3627:
3620:
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3608:
3585:
3582:
3577:
3573:
3569:
3564:
3560:
3552:
3545:
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3498:
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3398:
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3371:
3367:
3359:
3349:
3342:
3337:
3327:
3317:
3314:
3307:
3306:
3305:
3302:
3296:
3290:
3283:
3279:
3261:
3257:
3245:
3241:
3215:
3212:
3205:
3199:
3194:
3192:
3187:
3182:
3171:
3164:
3152:
3145:
3136:
3129:
3125:
3120:
3115:
3092:
3086:
3080:
3073:
3069:
3064:
3060:
3055:
3048:
3044:
3039:
3031:
3026:
3022:
3014:
3013:
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2995:
2986:
2983:
2975:
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2963:
2953:
2946:
2941:
2931:
2921:
2918:
2911:
2910:
2909:
2906:
2900:
2894:
2891:
2890:
2889:
2878:
2872:
2866:
2846:
2838:
2828:
2821:
2816:
2807:
2796:
2788:
2785:
2780:
2771:
2763:
2762:
2761:
2755:
2746:
2740:
2738:
2734:
2715:
2707:
2703:
2699:
2696:
2689:
2686:
2683:
2678:
2672:
2663:
2655:
2654:
2653:
2647:
2627:
2617:
2603:
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2592:
2588:
2579:
2574:
2571:
2568:
2564:
2558:
2555:
2552:
2543:
2540:
2537:
2527:
2523:
2519:
2510:
2498:
2489:
2481:
2480:
2479:
2473:
2449:
2441:
2436:
2429:
2419:
2408:
2403:
2400:
2397:
2393:
2389:
2387:
2373:
2365:
2357:
2349:
2345:
2335:
2329:
2320:
2311:
2306:
2302:
2298:
2293:
2283:
2276:
2271:
2267:
2263:
2261:
2254:
2244:
2229:
2228:
2227:
2204:
2190:
2184:
2179:
2175:
2166:
2161:
2158:
2155:
2151:
2141:
2131:
2121:
2114:
2109:
2105:
2096:
2091:
2088:
2085:
2081:
2074:
2071:
2068:
2064:
2055:
2045:
2039:
2035:
2028:
2027:
2026:
2024:
2018:
2013:
1992:
1989:
1986:
1974:
1961:
1955:
1951:
1944:
1940:
1936:
1927:
1918:
1909:
1901:
1900:
1899:
1878:
1870:
1868:
1856:
1850:
1846:
1843:
1833:
1827:
1823:
1816:
1808:
1806:
1795:
1789:
1780:
1766:
1765:
1764:
1761:
1758:
1752:
1743:
1737:
1731:
1725:
1719:
1715:are unknown,
1713:
1707:
1701:
1681:
1678:
1675:
1672:
1669:
1666:
1663:
1660:
1657:
1650:
1649:
1648:
1640:
1638:
1634:
1630:
1629:-distribution
1628:
1622:
1620:
1615:
1610:
1608:
1604:
1600:
1596:
1568:
1565:
1562:
1556:
1551:
1547:
1541:
1534:
1531:
1522:
1511:
1503:
1496:
1493:
1475:
1471:
1465:
1461:
1455:
1451:
1443:
1440:
1419:
1415:
1411:
1408:
1402:
1397:
1393:
1386:
1383:
1374:
1363:
1354:
1353:
1352:
1338:
1330:
1325:
1323:
1318:
1316:
1312:
1308:
1306:
1301:
1297:
1293:
1289:
1284:
1282:
1274:
1270:
1266:
1261:
1258:
1256:
1250:
1246:
1242:
1238:
1234:
1233:Levene's test
1230:
1228:
1223:
1219:
1216:
1212:
1208:
1207:
1206:
1204:
1196:
1191:
1185:
1181:
1178:
1173:
1168:
1163:
1158:
1155:
1148:
1144:
1140:
1136:
1132:
1128:
1124:and variance
1122:
1115:
1110:
1109:
1108:
1106:
1101:
1099:
1094:
1089:
1069:
1055:
1049:
1044:
1040:
1031:
1027:
1020:
1017:
1014:
1010:
1003:
994:
983:
978:
972:
965:
961:
954:
947:
942:
920:
894:
886:
880:
870:
862:
859:
850:
841:
836:
833:
828:
825:
818:
817:
816:
814:
809:
806:
801:
796:
790:
785:
782:
776:
770:
766:
762:
756:
749:
747:
743:
738:
736:
731:
728:
721:
715:
698:
689:
685:
680:
678:
674:
670:
667:
662:
652:
650:
645:
641:
631:
629:
625:
621:
617:
613:
609:
605:
601:
597:
592:
590:
586:
583:
579:
575:
573:
567:
563:
561:
555:
551:
543:
538:
531:
526:
519:
513:
496:
493:
490:
460:
452:
447:
427:
414:
409:
404:
399:
394:
371:
345:
337:
331:
327:
320:
316:
312:
303:
294:
291:
284:
283:
282:
276:
271:
267:
266:location test
263:
261:
251:
242:
235:
226:
224:
220:
215:
213:
212:
207:
203:
199:
194:
192:
188:
187:Ronald Fisher
184:
180:
176:
172:
168:
164:
160:
156:
155:-distribution
154:
148:
144:
140:
136:
132:
128:
124:
120:
116:
108:
104:
100:
96:
87:
85:
81:
77:
73:
69:
65:
61:
57:
53:
49:
48:-distribution
47:
41:
38:in which the
37:
33:
29:
25:
23:
13234:
13222:
13210:
13179:Radium Girls
13174:Typhoid Mary
12861:Microbiology
12731:
12723:
12721:
12607:Epidemiology
12505:Organization
12456:Oral hygiene
12446:Hand washing
12424:Healthy diet
12354:Right to sit
12247:Labor rights
12062:
12050:
12031:
12024:
11936:Econometrics
11886: /
11869:Chemometrics
11846:Epidemiology
11839: /
11812:Applications
11654:ARIMA model
11601:Q-statistic
11550:Stationarity
11446:Multivariate
11389: /
11385: /
11383:Multivariate
11381: /
11321: /
11317: /
11091:Bayes factor
10990:Signed rank
10902:
10876:
10868:
10866:
10856:
10551:Completeness
10387:Cohort study
10285:Opinion poll
10220:Missing data
10207:Study design
10162:Scatter plot
10084:Scatter plot
10077:Spearman's Ď
10039:Grouped data
9728:
9710:
9683:
9679:
9675:
9653:(1): 49â64.
9650:
9646:
9642:
9606:
9596:0-82477337-3
9582:
9552:
9548:
9535:
9500:
9496:
9490:
9482:
9457:
9453:
9449:
9443:
9421:(1): 55â68.
9418:
9414:
9408:
9391:
9387:
9383:
9353:
9328:
9324:
9314:
9303:. Retrieved
9299:
9290:
9270:
9263:
9230:
9226:
9220:
9195:
9191:
9185:
9150:
9146:
9139:Diehr, Paula
9100:
9096:
9092:
9086:
9077:
9071:
9063:
9054:
9048:
9029:
9023:
9003:
8993:
8960:
8954:
8948:
8921:
8915:
8890:
8886:
8880:
8866:
8854:. Retrieved
8834:
8828:
8785:
8781:
8771:
8738:
8734:
8728:
8703:
8699:
8695:
8689:
8664:
8660:
8650:
8625:
8621:
8611:
8578:
8574:
8568:
8527:
8521:
8501:
8495:
8471:
8461:
8451:
8441:
8429:
8419:
8409:
8247:
8243:
8239:
8201:
8163:
8159:
8155:
8151:
8129:
8125:
8121:
8117:
8089:
8027:
8017:
8001:
7993:
7991:
7986:
7984:
7978:
7974:
7964:
7956:
7954:
7947:
7944:
7929:
7871:
7806:
7789:
7731:
7730:Perform the
7729:
7599:
7528:word.recall
7515:
7508:
7504:
7495:
7493:
7487:
7252:
7242:
7235:
7232:
7223:
7219:
7213:
7206:
7199:
7196:
7058:
7057:Hotelling's
7048:
7042:
7039:
7034:
7030:
7026:
7022:
7018:
7012:
7005:Type I error
7000:
6990:
6989:Hotelling's
6984:
6982:
6966:
6963:
6953:
6947:
6942:
6934:
6930:
6924:
6914:
6908:
6899:type-1 error
6894:
6886:
6880:
6871:
6869:
6862:
6857:
6853:
6847:
6841:
6839:
6833:
6820:
6818:
6784:
6745:
6735:
6733:
6699:
6605:
6595:
6588:
6514:
6509:
6505:
6498:
6495:
6399:
6396:
6300:
6297:
6282:
6267:may need to
6266:
6074:
6067:
6058:
5991:
5895:
5888:
5882:
5150:
4867:
4656:
4654:separately.
4363:
4360:
4303:
4299:
4295:
4289:
4282:
4266:
4009:
3957:
3951:
3942:
3925:
3922:
3811:
3712:
3707:
3705:
3699:
3685:
3681:
3673:
3669:
3661:
3657:
3649:
3645:
3632:
3625:
3615:
3604:
3438:
3300:
3297:
3288:
3281:
3277:
3273:
3259:
3255:
3243:
3239:
3210:
3203:
3195:
3185:
3169:
3162:
3150:
3143:
3134:
3127:
3123:
3110:
3107:
3010:
2904:
2901:
2898:
2887:
2876:
2864:
2861:
2758:score, slope
2753:
2744:
2741:
2732:
2730:
2645:
2642:
2478:is given by
2471:
2468:
2225:
2016:
2011:
2009:
1897:
1762:
1756:
1750:
1741:
1735:
1729:
1723:
1717:
1711:
1705:
1699:
1696:
1646:
1632:
1626:
1618:
1613:
1611:
1598:
1594:
1592:
1589:Calculations
1326:
1321:
1319:
1307:distribution
1304:
1299:
1295:
1291:
1285:
1280:
1278:
1272:
1268:
1264:
1254:
1248:
1226:
1221:
1202:
1200:
1189:
1183:
1171:
1161:
1157:distribution
1153:
1146:
1142:
1138:
1130:
1126:
1120:
1113:
1104:
1102:
1092:
976:
970:
963:
959:
952:
945:
909:
812:
810:
804:
794:
788:
786:
780:
774:
768:
764:
760:
757:
755:
745:
741:
739:
734:
732:
726:
719:
713:
696:
687:
683:
681:
676:
668:
664:
648:
639:
637:
619:
603:
595:
593:
584:
581:
577:
571:
559:
557:
549:
547:
541:
529:
517:
448:
412:
402:
392:
360:
274:
259:
257:
255:
249:
219:Karl Pearson
216:
209:
205:
197:
195:
190:
182:
152:
146:
143:Karl Pearson
134:
118:
114:
112:
109:of "Student"
102:
83:
75:
71:
60:scaling term
45:
21:
19:
18:
13236:WikiProject
12976:and history
12856:Engineering
12569:Vaccination
12441:Food safety
12064:WikiProject
11979:Cartography
11941:Jurimetrics
11893:Reliability
11624:Time domain
11603:(LjungâBox)
11525:Time-series
11403:Categorical
11387:Time-series
11379:Categorical
11314:(Bernoulli)
11149:Correlation
11129:Correlation
10925:JarqueâBera
10897:Chi-squared
10659:M-estimator
10612:Asymptotics
10556:Sufficiency
10323:Interaction
10235:Replication
10215:Effect size
10172:Violin plot
10152:Radar chart
10132:Forest plot
10122:Correlogram
10072:Kendall's Ď
9103:(1): 9â12.
9070:"Student's
8837:(1): 1â25.
8788:: 343â414.
8418:Noncentral
8279:Mathematica
8030:spreadsheet
7878:Coefficient
7831:word.recall
7764:word.recall
7736:var.equal=T
7680:word.recall
7037:statistic.
6589:The sample
2801:score,slope
1490:as per the
1437:as per the
1351:increases:
1195:independent
941:sample mean
752:Assumptions
594:Two-sample
516:Two-sample
248:One-sample
125:in 1876 by
13254:Categories
12989:Caribbean
12866:Processing
12800:Quarantine
12722:Student's
12522:Sanitation
12156:History of
11931:Demography
11649:ARMA model
11454:Regression
11031:(Friedman)
10992:(Wilcoxon)
10930:Normality
10920:Lilliefors
10867:Student's
10743:Resampling
10617:Robustness
10605:divergence
10595:Efficiency
10533:(monotone)
10528:Likelihood
10445:Population
10278:Stratified
10230:Population
10049:Dependence
10005:Count data
9936:Percentile
9913:Dispersion
9846:Arithmetic
9781:Statistics
9745:Mark Thoma
9725:The T-Test
9614:. p.
9365:2210.16473
9305:2024-05-17
8956:Pediatrics
8830:Biometrika
8700:Biometrika
8487:References
8432:-statistic
8428:Student's
8318:PROC TTEST
7912:drug.dose
7895:Intercept
7884:Std. Error
7626:data.frame
5881:Dependent
4292:exact test
1703:is known,
1294:-test and
1150:follows a
968:, of size
616:confounder
602:. Paired
558:Student's
550:two-sample
211:Biometrika
163:Biometrika
151:Student's
113:The term "
50:under the
44:Student's
42:follows a
20:Student's
13169:John Snow
13096:Education
13086:Full list
12974:education
12898:ISO 22000
12851:Chemistry
12764:Epidemics
12717:ROC curve
12527:Emergency
12307:Radiation
12287:Pollution
12271:Ministers
12168:Euthenics
11312:Logistic
11079:posterior
11005:Rank sum
10753:Jackknife
10748:Bootstrap
10566:Bootstrap
10501:Parameter
10450:Statistic
10245:Statistic
10157:Run chart
10142:Pie chart
10137:Histogram
10127:Fan chart
10102:Bar chart
9984:L-moments
9871:Geometric
9717:EMS Press
9587:CRC Press
9435:0022-0973
9345:2148-7456
9169:0163-7525
8940:818811849
8872:"T Table"
8763:121241599
8755:0003-9519
8595:0340-2061
8554:cite book
7963:From the
7924:0.000805
7837:drug.dose
7776:var.equal
7770:drug.dose
7632:drug.dose
7604:with the
7525:drug.dose
7453:¯
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7429:¯
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2339:^
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2324:^
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1990:−
1975:∼
1965:^
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1860:^
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1535:μ
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1239:, or the
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995:σ
924:¯
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871:σ
863:μ
860:−
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566:variances
431:¯
375:¯
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313:−
307:¯
167:pen names
107:pseudonym
13212:Category
12911:sciences
12846:Additive
12517:Safe sex
12488:Medicine
12402:Theories
12173:Genomics
12151:Eugenics
12141:Deviance
12121:Auxology
12026:Category
11719:Survival
11596:Johansen
11319:Binomial
11274:Isotonic
10861:(normal)
10506:location
10313:Blocking
10268:Sampling
10147:QâQ plot
10112:Box plot
10094:Graphics
9989:Skewness
9979:Kurtosis
9951:Variance
9881:Heronian
9876:Harmonic
9719:. 2001 .
9667:13802482
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8470:Welch's
8382:See also
8112:pre 2010
8101:Function
8020:-tests.
8010:variance
7907:0.02572
7890:P-value
7881:Estimate
7387:′
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6948:One-way
6846:Welch's
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6231:Mitchell
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3179:are the
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608:blocking
578:unpaired
570:Welch's
193:-test".
13224:Commons
13137:History
13034:Canada
13009:Europe
12493:Nursing
12473:Hygiene
12436:Hygiene
12161:Liberal
12114:General
12052:Commons
11999:Kriging
11884:Process
11841:studies
11700:Wavelet
11533:General
10700:Plug-in
10494:L space
10273:Cluster
9974:Moments
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9574:Sources
9518:2857732
9474:1164905
9212:2684360
9117:2684684
8887:Science
8856:24 July
8790:Bibcode
8720:1766040
8669:Bibcode
8630:Bibcode
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8092:-test.
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7918:0.8165
7901:0.5774
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7522:Patient
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6770:0.08399
6685:0.04849
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651:-test.
449:By the
396:is the
179:Ireland
127:Helmert
90:History
13024:India
12999:China
12871:Safety
12552:Worker
11921:Census
11511:Normal
11459:Manova
11279:Robust
11029:2-way
11021:1-way
10859:-test
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10107:Biplot
9898:Median
9891:Lehmer
9833:Center
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8233:Python
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8122:array2
8118:array1
8116:TTEST(
8104:Notes
8082:MATLAB
8070:Python
7977:-test
7938:means.
7921:4.899
7904:3.464
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3141:, and
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2010:has a
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1177:i.i.d.
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175:Dublin
133:. The
131:LĂźroth
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12297:Water
11545:Trend
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10905:-test
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10778:Power
10723:Pivot
10516:shape
10511:scale
9961:Shape
9941:Range
9886:Heinz
9861:Cubic
9797:Index
9545:(PDF)
9470:JSTOR
9360:arXiv
9251:S2CID
9208:JSTOR
9113:JSTOR
8981:S2CID
8825:(PDF)
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8599:S2CID
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8464:-test
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8364:Stata
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8160:tails
8126:tails
8062:gretl
8054:Stata
8028:Many
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7014:alpha
6865:-test
6850:-test
6501:means
6478:29.98
6469:30.02
6460:29.98
6451:29.72
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6037:s
6014:D
6004:X
5977:,
5969:n
5963:/
5957:D
5953:s
5945:0
5932:D
5922:X
5912:=
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5837:1
5831:n
5828:(
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5792:=
5789:i
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5670:=
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4968:n
4962:/
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4456:[
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4424:]
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3460:=
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3399:+
3392:1
3388:n
3384:1
3372:p
3368:s
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3350:X
3338:1
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3318:=
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3301:t
3292:2
3289:n
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3282:n
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3260:X
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3252:/
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3093:.
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3081:2
3074:2
3070:X
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3040:s
3032:=
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2996:,
2987:n
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2976:p
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2964:2
2954:X
2942:1
2932:X
2922:=
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2839:2
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2781:=
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2754:t
2745:t
2733:r
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2708:2
2704:r
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2684:n
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2628:.
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2593:i
2589:x
2585:(
2580:n
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2572:=
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2559:R
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2538:n
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2110:i
2106:y
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2097:n
2092:1
2089:=
2086:i
2075:2
2069:n
2065:1
2056:=
2040:E
2036:S
2017:n
2012:t
1993:2
1987:n
1981:T
1956:E
1952:S
1945:0
1919:=
1910:t
1879:.
1871:=
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1847:S
1844:,
1828:E
1824:S
1817:,
1809:=
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1757:y
1751:x
1745:0
1742:β
1736:β
1730:Y
1724:Ď
1718:Îľ
1712:β
1706:Îą
1700:x
1682:,
1676:+
1673:x
1667:+
1661:=
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1619:p
1614:t
1599:t
1595:t
1584:.
1572:)
1569:1
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1563:0
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1557:N
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1390:)
1375:X
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1227:F
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1203:t
1197:.
1190:s
1184:Z
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1162:n
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1147:Ď
1143:n
1141:(
1139:s
1134:.
1131:n
1129:/
1127:Ď
1121:Îź
1114:X
1105:t
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1070:2
1066:)
1056:X
1045:i
1041:X
1037:(
1032:i
1021:1
1015:n
1011:1
1004:=
977:s
971:n
964:n
960:X
956:2
953:X
949:1
946:X
921:X
895:,
887:n
881:/
851:X
842:=
837:s
834:Z
829:=
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813:t
805:t
795:s
789:Z
781:s
775:Z
769:s
767:/
765:Z
761:t
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735:t
727:n
720:n
714:n
704:2
701:/
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688:t
684:t
677:t
669:t
649:t
640:t
620:t
604:t
596:t
585:t
572:t
560:t
542:t
530:t
518:t
500:)
497:1
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491:0
488:(
483:N
461:t
428:x
413:n
403:n
393:s
372:x
346:,
338:n
332:/
328:s
321:0
304:x
295:=
292:t
278:0
275:Îź
260:t
250:t
206:t
198:t
191:t
183:t
153:t
147:t
135:t
119:t
115:t
103:t
84:t
76:t
72:t
46:t
22:t
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