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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

    Screenshot of "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.

    Screenshot of Step 2 Instructions

  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"

    Screenshot of Step 4

  5. Select Continue or OK

 

Results

Screenshot of One-Way Between-Subjects ANOVA Output

 

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.

In addition, if your ANOVA is significant you must  also report your post-hoc results:

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).