Statistical Tests
Choosing the Appropriate Statistical Test
Which test should you use?
|# of groups OR |Type of design |Assumptions |Type of test to use |
|conditions | | | |
| | | | |
|1 sample |Single sample |1, 2, 4 & 5 are all met |Single sample z-test |
| | | | |
|1 sample |Single sample |1, 2, & 4 are all met |Single sample t-test |
| | | | |
|2 |Independent (Between) groups |1, 2 & 3 are met |Independent t-test |
| | | | |
|2 |Independent (Between) groups |At least 1 2, or 3 broken |Mann-Whitney U |
| | | | |
|2 |Dependent (Within) groups |1 and 2 are both met |Paired t-test (Correlated |
| | | |t-test) |
| | | | |
|2 |Dependent (Within) groups |At least 1 or 2 broken |Wilcoxon |
| | | | |
|2 |Dependent (Within) groups |Using binomial data |Sign Test |
| | | | |
|1 factor | |Using nominal data |Chi-Square |
| | | | |
|2 or more factors | |Using nominal data |Contingency Table |
| | | | |
|3 or more |Independent (Between) groups |1,2 & 3 are met |ANOVA |
| | | | |
|3 or more |Independent (Between) groups |At least 1, 2 or 3 broken |Kruskal-Wallis |
Have these assumptions been met?
1. The data must be interval or ratio.
2. The data are normally distributed, meaning a) the population raw scores are known to be normally distributed, or b) the sample size is > 30, or c) the skewness and kurtosis values are approximately between -1.0 and +1.0.
3. The variances are equal between the groups, called homogeneity of variance (HOV). The variances can be up to 4 times different from each other, but no more than that, and still be considered “equal.” To find HOV, you divide the larger variance by the smaller variance.
4. Known population mean
5. Known population standard deviation
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