# Comparison of independent groups on an outcome

## Number of groups, scales of measurement, and meeting statistical assumptions

__are used when comparing independent groups on an outcome. Independent groups means that the groups are "different" or "independent" from each other according to some characteristic. With between-subjects designs, participants can only be part of one group (independence) and only observed once (independence of observations, IOO).__

**Between-subjects statistics**One chooses a between-subjects statistical test based on the following:

1. Number of

__being compared (one group, two groups, or three or more groups)__

**independent groups**2.

__of the outcome (categorical, ordinal, or continuous)__

**Scale of measurement**3. Meeting

__(independence of observations, normality, and homogeneity of variance)__

**statistical assumptions**Here is a list of between-subjects statistical tests and when they are utilized in applied quantitative research:

1.

__- One group, categorical outcome,__

**Chi-square Goodness-of-fit***a priori*hypothesis for dispersal of outcome

2.

__- One group, ordinal outcome,__

**One-sample median test***a priori*hypothesis for median value

3.

__- One group, continuous outcome, meet the assumption of IOO and normality, a priori hypothesis for mean value__

**One-sample t-test**4.

__- Two independent groups, categorical outcome, and chi-square assumption (more than five observations in each cell)__

**Chi-square**5.

__- Two independent groups, categorical outcome, and when the chi-square assumption is not met__

**Fisher's Exact test**6.

__- Two independent groups, ordinal outcome, and when the assumption of homogeneity of variance for independent samples t-test is violated__

**Mann-Whitney U**7.

__- Two independent groups, continuous outcome, meet the assumption of IOO, normality (skewness and kurtosis statistics), and homogeneity of variance (also known as homoscedasticity, tested with Levene's test)__

**Independent samples t-test**8.

__- Three or more independent groups, categorical outcome, chi-square assumption, choose a reference category and compare each independent group to the reference__

**Unadjusted odds ratio**9.

__- Three or more independent groups, ordinal outcome, and when the assumption of homogeneity of variance is violated__

**Kruskal-Wallis**10.

__- Three or more independent groups, continuous outcome, meet the assumption of IOO, normality, and homogeneity of variance__

**ANOVA**