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# Tests and confidence intervals for mean values

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# Tests and confidence intervals for mean values

Mean known, Standard deviation known  — one sample, z-test. Tests if a sample comes from a Normal distribution with known variance and specified mean, against the alternative that it does not have that mean

Mean known, Standard deviation not known — one sample or paired-sample t-test. Tests if a sample comes from a Normal distribution with unknown variance and a specified mean, against the alternative that it does not have that mean

Two mean values to be compared, Standard deviations known — two-sample z-test

Two mean values to be compared, Standard deviations not known two-sample t-test. Tests if two independent samples come from Normal distributions with unknown but equal (or, optionally, unequal) variances and the same mean, against the alternative that the means are unequal.

Kruskal-Wallis — a hypothesis test of the equality of population medians for a one-way design (two or more populations). This test is a generalization of the procedure used by the Mann-Whitney test and, like Mood's median test, offers a nonparametric alternative to the one-way analysis of variance. The Kruskal-Wallis test looks for differences among the populations' medians. The Kruskal-Wallis test is more powerful (the confidence interval is narrower, on average) than Mood's median test for analyzing data from many distributions, including data from the Normal distribution, but is less robust against outliers

Friedman — a nonparametric analysis of a randomized block experiment and thus provides an alternative to the two-way analysis of variance. Randomized block experiments are a generalization of paired experiments. The Friedman test is a generalization of the paired sign test with a null hypothesis of treatments having no effect. This test requires exactly one observation per treatment-block combination

Mood's Median Test — a hypothesis test of the equality of population medians in a one-way design. Mood's median test, like the Kruskal-Wallis test, provides a nonparametric alternative to the usual one-way analysis of variance. Mood's median test is sometimes called a median test or sign scores test. The test is robust against outliers and errors in data, and is particularly appropriate in the preliminary stages of analysis. It is more robust against outliers than the Kruskal-Wallis test, but is less powerful (the confidence interval is wider, on the average) for analyzing data from many distributions, including data from the Normal distribution