# Grouped data for factorial Anova

## Problem(Abstract)

I am trying to do a 2 * 2 factorial anova using SPSS. Unfortunately, I only have the grouped data (means, SD, N) . I thought that the following syntax should work to produce the results but I get an error message about not having enough SD's (standard deviations).

MATRIX DATA VARIABLES=gender group ROWTYPE_ posttest
/FACTORS gender group.
BEGIN DATA
1 1 MEAN 9.60
1 1 SD 4.461
1 1 N 65
2 1 MEAN 11.04
2 1 SD 3.427
2 1 N 114
1 2 MEAN 11.25
1 2 SD 4.14
1 2 N 121
2 2 MEAN 10.13
2 2 SD 4.23
2 2 N 122
END DATA.

MANOVA POSTTEST BY GENDER (1,2) GROUP (1,2)
/MATRIX=IN(*)
/DESIGN=gender group.

I've entered an SD for every group. Why is this not enough?

## Resolving the problem

When you run MANOVA with MATRIX input, it expects you to include the pooled SDs and intercorrelations among the dependent variables (DVs). Although you have only 1 DV and no covariates, MANOVA still demands that you enter the correlation of 1.0 for the single DV and the pooled within-cells SD.

You may not have the pooled within-cell SD. Here is an easy way to compute this. The group info is first read into MATRIX DATA as if for a 4-group ONEWAY (with single factor GENGROUP). This is followed by a ONEWAY command to get the pooled within-cell variance. The square root of the MSerror from the ONEWAY output becomes the pooled SD in the second run of the MATRIX DATA command. In this second run of MATRIX DATA, both factors are mentioned and the data is read for a 2x2 design as you had before. A row is added for the pooled SD and CORR. Periods are placed as values for gender and group to show that these are pooled values. I note that you had a main effects design in your MANOVA command. MANOVA does apply the group SDs correctly for the error term, rather than just plugging in the pooled SD, which was based on a full factorial design. If only full-factorial models are to be considered, then only the pooled SD need be provided to MANOVA.

Here is the corrected syntax. The pooled SD was the square root of the MSerror from the ONEWAY output.

* corrected version .

MATRIX DATA VARIABLES=gengroup ROWTYPE_ posttest
/FACTORS gengroup.
BEGIN DATA
1 MEAN 9.60
1 SD 4.461
1 N 65
2 MEAN 11.04
2 SD 3.427
2 N 114
3 MEAN 11.25
3 SD 4.14
3 N 121
4 MEAN 10.13
4 SD 4.23
4 N 122
END DATA.
ONEWAY posttest BY gengroup
/ MATRIX = IN (*) .

MATRIX DATA VARIABLES=gender group ROWTYPE_ posttest
/FACTORS gender group.
BEGIN DATA
1 1 MEAN 9.60
1 1 SD 4.461
1 1 N 65
2 1 MEAN 11.04
2 1 SD 3.427
2 1 N 114
1 2 MEAN 11.25
1 2 SD 4.14
1 2 N 121
2 2 MEAN 10.13
2 2 SD 4.23
2 2 N 122
. . SD 4.04003
. . CORR 1
END DATA.

MANOVA POSTTEST BY GENDER (1,2) GROUP (1,2)
/MATRIX=IN(*)
/DESIGN=gender group .

## Historical Number

36771

### Document information

More support for: SPSS Statistics

Software version: Not Applicable

Operating system(s): Platform Independent

Reference #: 1475358

Modified date: 07 September 2016