# Two-way analysis of variance

Command: | Statistics ANOVA Two-way analysis of variance |

## Description

The two-way analysis of variance is an extension to the one-way analysis of variance. There are two qualitative factors (A and B) on one dependent continuous variable Y.

Three null hypotheses are tested in this procedure:

- factor A does not influence variable Y
- factor B does not influence variable Y
- the effect of factor A on variable Y does not depend on factor B (i.e. there is no interaction of factors A and B).

Two-way analysis of variance requires that there are data for each combination of the two qualitative factors A and B.

## Required input

Select the (continuous) dependent variable (Y) and two discrete variables for the qualitative factors (A and B) suspected to influence the dependent variable. The qualitative factors A and B may either consist of numeric or alphanumeric data. One filter can also be defined in order to include only a selected subgroup of cases.

## Results

### Levene's test for equality of variances

Prior to the ANOVA test, Levene's test for equality of variances is performed. If the Levene test is positive (P<0.05) then the variances in the groups are different (the groups are not homogeneous), and therefore the assumptions for ANOVA are not met.

### Tests of Between-Subjects Effects

If the calculated P-values for the two main factors A and B, or for the 2-factor interaction is less than the conventional 0.05 (5%), then the corresponding null hypothesis is rejected, and you accept the alternative hypothesis that there is indeed a difference between groups.

When the 2-factor interaction is significant the effect of factor A is dependent on the level of factor B, and it is not recommended to interpret the means and differences between means (see below) of the main factors.

### Estimated marginal means

In the following tables, the means with standard error and 95% Confidence Interval are given for all levels of the two factors. Also, differences between groups, with Standard Error, and Bonferroni corrected P-value and 95% Confidence Interval of the difference are reported.

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
- Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical research. 4
^{th}ed. Blackwell Science. - Neter J, Kutner MH, Nachtsheim CJ, Wasserman W (1996) Applied linear statistical models. 4
^{th}ed. McGraw-Hill.