# 4: Tests for One Measurement Variable

- Page ID
- 1733

- 4.1: One-Sample t-Test
- Use Student's t–test for one sample when you have one measurement variable and a theoretical expectation of what the mean should be under the null hypothesis. It tests whether the mean of the measurement variable is different from the null expectation.

- 4.2: Two-Sample t-Test
- To use Student's t-test for two samples when you have one measurement variable and one nominal variable, and the nominal variable has only two values. It tests whether the means of the measurement variable are different in the two groups.

- 4.3: Independence
- Most statistical tests assume that you have a sample of independent observations, meaning that the value of one observation does not affect the value of other observations. Non-independent observations can make your statistical test give too many false positives.

- 4.4: Normality
- Most tests for measurement variables assume that data are normally distributed (fit a bell-shaped curve). Here I explain how to check this and what to do if the data aren't normal.

- 4.5: Homoscedasticity and Heteroscedasticity
- Parametric tests assume that data are homoscedastic (have the same standard deviation in different groups). To learn how to check this and what to do if the data are heteroscedastic (have different standard deviations in different groups).

- 4.6: Data Transformations
- To learn how to use data transformation if a measurement variable does not fit a normal distribution or has greatly different standard deviations in different groups.

- 4.7: One-way Anova
- To learn to use one-way anova when you have one nominal variable and one measurement variable; the nominal variable divides the measurements into two or more groups. It tests whether the means of the measurement variable are the same for the different groups.

- 4.8: Kruskal–Wallis Test
- To learn to use the Kruskal–Wallis test when you have one nominal variable and one ranked variable. It tests whether the mean ranks are the same in all the groups.

- 4.9: Nested Anova
- Use nested anova when you have one measurement variable and more than one nominal variable, and the nominal variables are nested (form subgroups within groups). It tests whether there is significant variation in means among groups, among subgroups within groups, etc.

- 4.10: Two-way Anova
- To use two-way anova when you have one measurement variable and two nominal variables, and each value of one nominal variable is found in combination with each value of the other nominal variable. It tests three null hypotheses: that the means of the measurement variable are equal for different values of the first nominal variable; that the means are equal for different values of the second nominal variable; and that there is no interaction.

- 4.11: Paired t–Test
- To use the paired t–test when you have one measurement variable and two nominal variables, one of the nominal variables has only two values, and you only have one observation for each combination of the nominal variables; in other words, you have multiple pairs of observations. It tests whether the mean difference in the pairs is different from 0.

- 4.12: Wilcoxon Signed-Rank Test
- To use the Wilcoxon signed-rank test when you'd like to use the paired t–test, but the differences are severely non-normally distributed.

## Contributor

John H. McDonald (University of Delaware)