# 17.4.1.7 Interpreting Results of ANOVA

## Descriptive Statistics

The descriptive statistics table is useful in determining the nature of variables (magnitude, missing values, etc). Inspection of means and SDs can reveal univariate/variance difference between the groups.

## ANOVA

### Overall ANOVA

The Overall ANOVA table shows the statistics used to test whether the groups in the main effect (or two-way interactions, three-way interactions) are different.

If the P Value is less than 0.05, the null hypothesis is rejected. We can say overall the groups are different, and can go on to look at the Means Plot, and even the Mean Comparison table for more detailed analyses.

Please note that if the variables are related, results reported to the table are not reliable. This univariate perspective does not account for any share variance(correlation) among the variables.

### Mean Comparison

Multiple comparison procedures are commonly used in ANOVA analysis after obtaining a significant omnibus test result. The significant ANOVA result suggests that the global null hypothesis, H0, is rejected. The H0 hypothesis states that the means are the same across the groups being compared. We can use multiple comparison to determine which means are different.

For selecting different methods for means comparison, view the introduction page

The Mean Comparison table provides statistics of post-hoc tests, to compare means for each pair of groups.

 For interaction of two-way and three-way ANOVA, use a data filter to display only levels you are interested in, for instance, comparing the same level between different groups. To start with Click the triangle button next to the Interactions table and choose Create Copy as New Sheet from the context menu Activate the new sheet with interactions results, select a column and click the Add/Remove Data Filter button to add a data filter to the column. Click the Filter icon on the column header, then choose Custom Filter. In the dialog that opens, select the Advanced check box and add a desired condition such as col(a)$==col(d)$

### Test for Equal Variance/Homogeneity Tests

The table produces tests of the homogeneity of variance for each dependent variable across all level combinations of the between-subjects factors.

If the assumption is not satisfied, there are several options to consider including elimination of outliers and data transformation. However, ANOVA is robust to the violation of this assumption. You may still continue the study if the group size is equal.

### Power Analysis

The power analysis procedure calculates the actual power for the sample data, which let you know the probability of detecting differences in the population means. It also helps you to calculate the hypothetical power if additional sample sizes are specified.

## Plots

### Means Plot

The means plot is available in one-way and three-way ANOVA. It helps to detect whether means vary between groups.

### Means Comparison Plot

The means comparison plot is only available in the one-way ANOVA tool. It supplements other means comparison methods, allowing for visual inspection of the mean difference between groups.