 EZ Statistics is a web service with the goal of making statistical testing easy. It supports a range of the most commonly used parametric and non-parametric tests.

### - Check if there is a difference between the means of samples

There are several tests and which one to use depends on the properties of your data and the setup of your study:
• Independent or paired samples:
This depends on the setup of your study. Consider an example where you want to know if a Volvo is as comfortable as an Audi. You have 40 participants in your study. The independent approach is if you let 20 participants test the Volvo and fill in a questionnaire, and the other 20 participants test the Audi and fill in a questionnaire. The paired (dependent) approach is if all 40 participants first test the Volvo and fill in a questionnaire, then test the Audi and fill in a questionnaire. Another example of a dependent approach is if you measure the same variable several times (repeated measurements), for example the effect of a treatment is measured every month for a year.
• Equal or unequal variances:
If the variances of the samples differ significantly, you shall use a test for unequal variances. You can check if two samples have equal variances or not using the F-test for equal variances. If you have three or more samples, use the Bartlett's test for equal variances instead.
• Normally or not normally distributed samples:
Generally, parametric tests require that your samples are normally distributed. If one or more sample is not normally distributed, consider using a non-parametric test instead. Note that many parametric tests are fairly robust to not normally distributed samples, so unless the samples are severely non-normal you can still use the parametric tests. You can check if a sample is normally distributed using the Shapiro-Wilk Expanded test.
Use the following tables to find out which test to use:

Parametric tests
Requires that the samples are normally distributed
Number of samples Variance? Dependency? Use the following test
1 (and a specified mean) - - T-test (single sample)
2 Equal Independent T-test (independent, equal variances)
2 Unequal Independent T-test (independent, unequal variances)
2 - Dependent T-test (paired)
3 or more Equal Independent One-way ANOVA
3 or more Dependent Repeated Measures ANOVA

Non-parametric tests
Does not require that the samples are normally distributed
Number of samples Variance? Dependency? Use the following test
1 (and a specified mean) - - Wilcoxon Signed-Ranks (single sample)
2 - Independent Wilcoxon Rank-Sum test
2 - Dependent Wilcoxon Signed-Ranks test
3 or more - Independent Kruskal-Wallis test
3 or more Dependent Friedman test

### - Find outliers

• Find outliers using the Generalized Extreme Studentized (ESD) test.