# MASH : Maths and Stats Help

### 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 this example the variable Day (the repeated factor) has 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 Factor(s)" box.

4. Click "Post 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". (This Post Hoc test is only relevant if the between-subjects factor has 3 or more levels).

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

6. Click "Continue" and then "OK".

### Results

SPSS will generate a large number of tables, not all the information will be useful to you. To correctly report this test we need to select the correct pieces of information from each table and report them in a standardised format, this is usually in APA format (regardless of your usual referencing framework).

## Reporting the Results in APA Formatting

There was a significant main effect of temperature on animal speeds, (1,70) = 4.18, p = .045, η= .056.  Average speeds were significantly higher on hot days (M = 51.15, SD = 14.58) than cold days (M = 49.53, SD = 7.07). There was a significant main effect of animal species on animal speed F (2,70) = 310.05, p < .001, η= .90.  Giraffes (M = 64.60, SD = 7.29) were faster than White Rhinos (= 43.70, SD = 5.39) and African Elephants (M = 42.31, SD = 5.31). There was also a significant interaction effect between temperature and animal species  F (2,70) = 32.39, < .001, η= .48.

As there was a significant main effect of animal species, you must also report your post-hoc results. The statistics you need for this can be found in the “Pairwise Comparisons” table of the output.

The difference between Giraffes and White Rhinos, 20.90 95% CI [18.33, 23.46], was statistically significant (p < .001). The difference between Giraffes and African Elephants, 22.28 95% CI [19.89, 24.69], was also statistically significant (p < .001). The difference between White Rhinos and African Elephants, 1.39 95% CI [-1.14, 3.91], was not statistically significant (= .55).

If you have a significant interaction effect, a series of additional post hoc tests are required to examine this further. For the example shown above (temperature x species), a total of 9 post hoc tests are required. It is advised that you use an adjusted alpha when interpreting the results of these tests. One of the most common approaches is to make a Bonferroni adjustment. This can be made by dividing your original alpha by the number of tests being carried out (i.e., .05/9 = .006). ​Therefore any p-values from these post-hocs should be checked against this adjusted alpha (of .006) instead of our original alpha (of .05).

Three paired-sample t-tests are required to test for a difference in speed on hot and cold days, separately for each species. Followed by 6 between-subjects t-tests.

The steps to follow to carry out these additional post-hoc tests will be uploaded soon. If you require them in the meantime, please email lpearson@lincoln.ac.uk.