# Between-subjects statistics for three or more groups

## Between-subjects statistics can compare three or more independent groups on outcomes

Between-subjects statistics for three or more groups are used to compare several independent groups on an outcome.

For categorical outcomes and three or more groups, researchers calculate the odds ratio for having an outcome in comparison to a reference category.

With ordinal outcomes, researchers compare the medians and interquartile ranges of three or more independent groups to see if there is a statistically significant main effect.

When continuous outcomes are used with three or more groups, researchers have to meet the statistical assumptions of independence of observations, normality, and homogeneity of variance in order to compare the means and standard deviations between multiple groups.

If the statistical assumptions are not met for between-subjects statistics for three or more groups, then researchers can use non-parametric statistics to compare multiple independent groups on a continuous outcome.

In the event that statistically significant main effects are found for between-subjects statistics for three or more groups (significant main effect = significant difference among the multiple groups), then post hoc tests must be used to explain where the significant main effect comes from in between the groups (post hoc test = which of the groups are different from others).

**The choice of between-subjects statistical test for three or more groups depends upon meeting statistical assumptions and the scale of measurement of the outcome.**For categorical outcomes and three or more groups, researchers calculate the odds ratio for having an outcome in comparison to a reference category.

With ordinal outcomes, researchers compare the medians and interquartile ranges of three or more independent groups to see if there is a statistically significant main effect.

When continuous outcomes are used with three or more groups, researchers have to meet the statistical assumptions of independence of observations, normality, and homogeneity of variance in order to compare the means and standard deviations between multiple groups.

If the statistical assumptions are not met for between-subjects statistics for three or more groups, then researchers can use non-parametric statistics to compare multiple independent groups on a continuous outcome.

In the event that statistically significant main effects are found for between-subjects statistics for three or more groups (significant main effect = significant difference among the multiple groups), then post hoc tests must be used to explain where the significant main effect comes from in between the groups (post hoc test = which of the groups are different from others).

### What is the scale of measurement for the outcome in the between-subjects analysis?

The outcome represents

**numerical designations or categorical values**that describe events or group membership.The outcome variable is measured using an

**ordered numerical continuum**, such as a Likert scale.The outcome variable is an actual number that provides

**both a measure of distance and magnitude due to having a "true zero****."**## Hire A Statistician - Statistical Consulting for Professionals

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D. will provide statistical consulting for researchers, professionals, and organizations at $100/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics