Do groups differ on several numbers at once? (MANOVA)

In brief

Do teaching methods differ together in knowledge test, motivation and satisfaction? The MANOVA (multivariate analysis of variance) tests this for the combination of several numbers in one step. Statable then shows a one-way analysis of variance for each number.

How it works in Statable

1. "New analysis", then choose the card "Do groups differ on several numbers at once?".
2. "What was measured?": at least two number columns. "Which groups?": the column with the groups.
3. The result appears by itself. The main row is Pillai's trace; Wilks' Λ, the Hotelling-Lawley trace and Roy's largest root are shown beside it.

What the table looks like

One row per case, one column with the group and at least two columns with numbers (at most 10). Cases with a gap in one of the numbers drop out entirely; the number is shown in the result. Nothing is calculated if a group has only one case, if there are not more cases than numbers plus groups, or if a number is constant or can be calculated from the others.

Reading the result

• Four test statistics are in one table: Pillai's trace, Wilks' Λ, the Hotelling-Lawley trace and Roy's largest root, each with F, degrees of freedom and p. Statable takes Pillai's trace as the main line because it is the least sensitive to violated assumptions. Mostly all four say the same.
• Roy's value is an upper bound for F; its p is too small. The sentence is next to Roy.
• The note on interpretation: the result only says that the groups differ in the combination of the numbers. It does not say in which number or between which groups.
• The individual tests per number are not protected against multiple testing, and a significant overall result does not make them so.

Difference from SPSS

The four test statistics, F and the degrees of freedom are the same as in SPSS (GLM, multivariate), as are the individual tests per number.

Requirements and limits

• The calculation assumes equal covariances in the groups and a multivariate normal distribution. Statable does not check this with a test.
• If two numbers are very closely related (|r| above .9), one is almost the other. Statable points this out; often one of them is then enough.
• If you ask after a MANOVA which groups differ, it does not help: that takes comparisons between the groups with protection against multiple testing.

Reporting the result

Pillai's trace = 1.19, F(8, 290) = 53.47, p < .001

Typical examples

• Three teaching methods: do they differ at the same time in knowledge test, motivation and satisfaction?
• Two grade levels: do they differ together in several performance measures?

For specialists

R (stats): manova(Y ~ group) with summary(test = "Pillai", "Wilks", "Hotelling-Lawley", "Roy"); then anova(lm(Y[, j] ~ group)) per number. Checked on iris, also with unequal group sizes, against SPSS.