# MASH : Maths and Stats Help

### One-Way Between-Subjects ANCOVA

#### Introduction

The ANCOVA (Analysis of Covariance)  is an extension of an ANOVA, that is able to consider the effect of another variable(s) which correlates with the dependent variable.

A One-Way Between Subjects ANCOVA tests the difference between the means of two or more independent groups, such as comparing the difference between groups A, B and C, with the addition of one or more covariates.This ANCOVA compares differences between groups (levels) when accounting for the relationships between your dependent variable and the covariate(s).

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)

#### Test Procedure

1. Step 1: Click Analyze > General Linear Model > Univariate

2. Within the "Univariate" window, select the test variable or dependent variable you are analysing and move it to the "Dependent Variable" box. Then move your independent/grouping variable into the “Fixed factor(s)” box. Finally, move your covariate into the "Covariate(s)" box.

3. Click "Options". Within the "Univariate: Options" window select "Descriptive statistics", "Estimates of effect size", and "Homogeneity tests".

4. Click "EM means". Within the "Univariate: Estimated Marginal Means" move your grouping/independent variable into the "Display Means for" box. Click on "Compare main effects". Under the "Confidence interval adjustment" drop-down menu, select "Bonferroni".

5. Click "Continue" then "OK".

#### Results

SPSS will generate multiple tables, to correctly report this test we need three, the Descriptives, the ANOVA, and the Pairwise Comparisons:

##### Descriptives

Unlike an ANOVA without covariates, you want to report descriptive statistics from the "Estimates" table under "Estimated marginal means" instead of values from first table. This is because the values in the "Estimates" table are adjusted by the covariate.

##### Test of Between-subjects effects

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). You can also find effect sizes in this table (Partial Eta Squared).

In the "Pairwise comparisons" table, you can find the tests of difference for each possible pairing of groups (levels) from your independent variable, adjusted with a Bonferroni's correction, this is also known as Bonferroni post-hoc tests. The "Pairwise comparisons" table also provides you with mean difference values and confidence intervals.

## Reporting the Results in APA Formatting

Test scores of three groups (A, B, and C) were compared. A One-Way Between-Subjects ANCOVA, controlling for Related Scores, indicated there was a significant effect for test score, (2,62) = 20.04, p < .001, η2 = .393.

Some disciplines/journals encourage the reporting of the correlation between the dependent variable and the covariate. Please see our page on Pearson's 'r' correlation for guidance on how to conduct and report a correlation.