# MASH : Maths and Stats Help

### One-Way Between-Subjects ANOVA

#### Introduction

A One-Way Between Subjects ANOVA compares the means between more than two independent groups, such as comparing the difference between groups A, B and C. If your data only has two groups such as Male/Female or Present/Absent you should consider the Independent-Samples t-Test.

It is considered a parametric test and is only suitable for parametric data. To check if your data is parametric, please check out the dedicated guide: Parametric or Not Guide (PDF)

If your data is non-parametric you should consider using a Kruskal-Wallis Test

#### Test Procedure

1. Step 1: Click Analyze > Compare Means > One-Way ANOVA 2. Within the "One-Way ANOVA" Window, select the test variable or dependent variable you are analysing and move it to the "Dependent List" box. Then move your independent/grouping variable into the “Factor” box. 3. Click "Options". Within the "One-Way ANOVA: Options" window select "Descriptive", "Fixed and random effects","Homogeneity of variance test", and "Means plot" 4. Click "Post Hoc". Within the "One-Way ANOVA: Post Hoc Multiple Comparison" window select "Bonferroni" 5. Select Continue or OK

#### Results  SPSS will generate multiple tables, to correctly report this test we need three, the Descriptives, the ANOVA, and the ANOVA Effect Sizes:

##### Descriptives

This table shows a selection of descriptive statistics: the sample size of each group (N), the mean of each group (Mean), and the standard deviation of each group (Std. Deviation), best practice is to report them all.

##### ANOVA

This table shows the specific test results including the F-statistic (F), the degrees of freedom (df) the two-tailed significance or p-value (Sig).

##### ANOVA Effect Sizes

This table shows the eta-squared effect size of the ANOVA and its 95% confidence interval.

## Reporting the Results in APA Formatting

Test scores of three groups (A, B, and C) were compared. A One-Way Between-Subjects ANOVA indicated there was a significant effect for test score, F(2,70) = 4.39, p = .016, n2p = .112.

On average, Group A (Mean = 49.67, SD = 6.70) scored higher than Group B (Mean = 48.12, SD = 5.21), but lower than Group C (Mean = 54.14, SD = 8.44).

Post hoc comparisons were conducted using the Bonferroni method.

The difference between Group A and Group B, 1.25 95% CI [-3.45,5.97], was not statistically significant (p = .999).

The difference between Group B and Group C, 5.79 95% CI [.76,10.98], was considered statistically significant (p = .018).

The difference between Group A and Group C, 4.47 95% CI [-.36,9.30], was not statistically significant (p = .079).