H0 : The k treatments are not significantly different.If t1, t2, …, tk correspond to the k treatments, the null and alternative hypotheses used in the test are: This test has been extended to the case of incomplete blocks by Alvo and Cabilio (2005). Asymptotic method: The p-value is obtained using the asymptotic approximation of the distribution of the z statistics.To compute the p-values corresponding to the various statistics, XLSTAT offers two alternative methods: Where, for the alternative hypotheses, at least one inequality is strict. Monte Carlo method: The computation of the p-value is based on random resamplings.The reliability of the approximation depends on the number of treatments and on the number of blocks. The user must set the number of resamplings. A confidence interval on the p-value is provided. The more resamplings are performed, the better the estimation of the p-value. In order to avoid freezing Excel because of too long computations, it is possible with the two latter methods to set the maximum time that should be spent computing the p-value. If the p-value is such that the H0 hypothesis has to be rejected, then at least one treatment is different from another. To identify which treatment(s) is/are responsible for rejecting H0, a multiple comparison procedure can be used, XLSTAT allows using the procedure suggested by Cabilio and Peng (2008), with two alternative ways to compute the p-value of the paired comparisons. It can either use the normal approximation of a Monte Carlo based -pvalue.Two-sample t-tests compare the means of precisely two groups-no more and no less! Typically, you perform this test to determine whether two population means are different. For example, do students who learn using Method A have a different mean score than those who learn using Method B? This form of the test uses independent samples. In other words, each group contains a unique set of people or items. Statisticians consider differences between group means to be an unstandardized effect size because these values indicate the strength of the relationship using values that retain the natural units of the dependent variable. Cohen’s d is the corresponding standardized effect size and it’s appropriate to report in some cases. Effect sizes help you understand how important the findings are in a practical sense. The standard form tests the following hypotheses: To learn more about unstandardized and standardized effect sizes, read my post about Effect Sizes in Statistics. You’ll notice that Excel has two forms of the two-sample t-test. One that assumes equal variances and the other that assumes unequal variances. Variances and the closely related standard deviation are measures of variability. All t-tests assume you obtained data from normally distributed populations. However, the conventional t-test also assumes the standard deviations/variances for both groups are equal. Another form of the test, known as Welch’s t-test, does not assume equal variances.Īs an aside, thanks to the central limit theorem, you can safely use t-tests to analyze nonnormal data when have ~20 or more observations per group. Which One to Use?Īdvice for using either the equal or unequal variances form of the 2-sample t-test varies because this issue is more complicated than it first appears. Some analysts advise using an F-test to determine whether the variances are unequal. And, Excel does offer the F-test Two-Sample for Variances. However, using additional tests always increases the probability of both false positives and false negatives (a.k.a, Type I and Type II errors).Īdditionally, if you have a large sample size, the f-test has more statistical power. This condition can cause the test to identify an inconsequential difference as being statistically significant. That’s the difference between practical significance and statistical significance. #XLSTAT CALCULATE CONFIDENCE INTERVAL SERIES#Ĭonversely, small sample sizes can fail to detect a substantial difference between variances.
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