Skip to Main Content
The Library

MASH : Maths and Stats Help

Two-Way Mixed ANOVA

Introduction

A Two-Way Mixed ANOVA compares the difference between multiple sets of data comprising between-subjects and repeated-measures variables.

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)

This is one of the most advanced statistical tests that students may need to conduct for their analysis. 

 

Test Procedure

  1. Click Analyze > General Linear Model > Repeated Measures

  2. Within the "Repeated-Measures Define Factors" Window, create a name for your repeated-measures factor and specify the number of levels, in my example I have two levels. Click Add. Click Define.

  3. Within the "Repeated Measures" Window, select the dependent variables you are analysing and move them into the "Within-Subjects Variables" box. Then select the grouping variable and move it into the "Between-Subjects Factors" box.

  4. Click "Pst Hoc". Within the "Repeated Measures: Post Hoc Multiple Comparisons for Observed Means" window select your between-subjects factor and move it to the "PostHoc Tests for" window. Select "Bonferroni", click "Continue"

  5. Click "Options". Within the "Repeated Measures: Options" window select "Descriptive Statistics" and "Estimates of effect size".

  6. Select Continue à OK

 

Results

 

SPSS will generate a very large number of tables, to correctly report this test we need to select the correct pieces of information from each table. This can be very challenging.

Reporting the Results in APA Formatting

There was a significant main effect of Temperature on animal speeds, F(1,70)=6.10, p = .016, η=.08.  Average speeds were significantly higher on hot days (M = 51.71, SD = 14.54) than cold days (M = 49.67, SD = 8.15). There was a significant main effect of animal species on animal speed F(2,70) = 242.97, p < .001, η = .87.  Giraffes (M = 64.18, SD = 8.00) were faster than White Rhinos (M = 45.02, SD = 6.03) and African Elephants (M = 42.61, SD = 5.42). There was also a significant interaction effect between temperature and animal species  F(2,70) = 35.63, p < .001, η=.50.

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

The difference between Giraffes and White Rhinos, 19.16 95% CI [16.92, 21.40], was statistically significant (p < .001). The difference between White Rhinos and African Elephants, 2.41 95% CI [0.21, 4.61], was statistically significant (p = .032).The difference between Giraffes and African Elephants, 21.57 95% CI[19.47, 23.67], was also statistically significant (p < .001).