Interpreting MANOVA Output
Performing a MANOVA using interactive mode
You can use the interactive mode of SPSS to perform a MANOVA if all of your independent variables are manipulated between subjects.
To peform a MANOVA using the interactive mode in SPSS
• Choose Analyze thenGoto General Linear Model thenGoto Multivariate.
• Move the DVs you want to examine to the Dependent Variables box.
• Move any categorical IVs to the Fixed Factor(s) box.
• Move any continuous IVs to the Covariate(s) box.
• By default, SPSS will build a model including all interactions between the categorical independent variables, but no interactions with the continuous independent variables. To analyze a different model you must take the following steps.
o Click the Model button.
o Click the radio button next to Custom.
o Add all of main effects to your model by clicking the IVs in the box labeled Factors and Covariates, setting the pull-down menu to Main effects, and clicking the arrow button.
o Add each of the interaction terms to your model. You can do this one at a time by selecting the variables included in the interaction in the box labeled Factors and Covariates, setting the pull-down menu to Interaction, and then clicking the arrow button. You can also use the setting on the pull-down menu to tell SPSS to add all possible 2-way, 3-way, 4-way, or 5-way interactions that can be made between the selected variables to your model. You should be sure to center any continuous variables that you want to interact with other variables.
o Click the Continue button.
• You can ask SPSS to perform post-hoc contrasts by clicking the Contrasts button. SPSS reports the contrasts separately for each dependent variable but will not produce a multivariate contrast testing for a difference between two groups across all of the dependent variables. You can also ask SPSS to create new variables to hold the predicted values, residuals, or diagnostics from your model by clicking the Save button. If you ask SPSS to save one of these values, you will get a number of new variables in your data set equal to the total number of dependent variables in your model. These values will all be based on the univariate ANOVAs predicting the individual dependent variables from your independent variables.
• Click the Ok button when you are ready for SPSS to perform the analysis.
Performing a MANOVA using syntax
If you want to perform a MANOVA including one or more within-subjects factors (so that you measure each of your DVs under each combination of your within-subjects factors), you will need to conduct your analysis using SPSS syntax. You will need to have a variable in your data set for the measurement of each dependent variable at each combination of the within-subjects factors in your study. For example, if you had a within-subjects factor with two levels and three dependent variables, you should have six different response variables in your data set.
Below is an example of the code that would be used to analyze a design with one within-subject factor with two levels, one within-subject factor with three levels, and one between-subjects factor with two levels, and four dependent variables. In this case we need a total of 4 (DVs) X 2
(levels of wthn1) X 3 (levels of wthn2) = 24 different variables. We will assume that the variable names start with var1, var2, or var3, depending on which dependent measure it reflects. The variable names end with c11, c12, c13, c21, c22, or c23, indicating the condition in which the measurement was taken. This way, you can tell exactly what each variable measures just by looking at its name. We also have a variable called betwn coding the between-subjects condition for each case.
var1c11 var1c12 var1c13 var1c21 var1c22 var1c23 var2c11 var2c12 var2c13 var2c21 var2c22 var2c23 var3c11 var3c12 var3c13 var3c21 var3c22 var3c23 var4c11 var4c12 var4c13 var4c21 var4c22 var4c23
/WSFACTOR = wthn1 2 wthn2 3
/METHOD = SSTYPE(3)
/CRITERIA = ALPHA(.05)
/WSDESIGN = wthn1 wthn2 wthn1*wthn2
/DESIGN = betwn .
As you can see, MANOVA is performed using the GLM statement. The first thing you do is list out all of the variables that contain the measurements on your dependent variables at each combination of your within-subject factors. You must list out the variables in a very particular
way, so that SPSS knows what variables correspond to the same dependent variables, and which correspond to the same levels of your within-subject factors. As you can see in the example, the variables must first be grouped by the dependent variable. Within each dependent variable, you then group them by the levels of the first within-subject factor. Finally, within each level of the first within-subject factor, you organize the variables by the levels of the second within-subject factor. In this way, the dependent variable changes the slowest, the first within-subject factor changes the second slowest, and the second within-subject factor changes the fastest. This list is then followed by the word BY, which in turn is followed by a list between-subjects factors.
After the variable list, you issue the subcommand /WSFACTOR to identify the names and number of levels of your within-subject factors. /METHOD establishes which sums of squares you want to base your tests on, and /CRITERIA sets the experimentwide alpha level.
Following this you issue the /WSDESIGN subcommand where you list what main effects and interactions between your within-subject factors you want included in your model. The /DESIGN subcommand does the same thing, except for between-subjects factors. Your model will also include all the interactions between the terms you define in the /WSDESIGN and /DESIGN subcommands. In this example the model would also include the two-way interactions betwn*wthn1, betwn*wthn2, as well as the three-way interaction betwn*wthn1*wthn2.
Interpreting MANOVA output
Performing a MANOVA in SPSS will produce the following sections of output.
• Within-subject Factors. Describes how SPSS assigns the different variables to the different measures and within-subject conditions. You should always make sure that SPSS is interpreting your variables in the correct way if you have within-subject factors. It is very easy to make an error when listing out the variables in the first part of the GLM command, which would completely throw off your analyses.
• Between-Subjects Factors. Reports the between-subjects conditions in your design and the number of subjects in each of those cells.
• Multivariate Tests. Provides the results of the multivariate tests of each effect in your model. As mentioned above, MANOVA actually produces a matrix of results. However, these results are very difficult to interpret on their own, and so they are typically converted to an F statistic to make the determination of the p-value easier. There are four common methods of converting the results of a MANOVA to an F. SPSS reports all four values as well as the corresponding F statistics and degrees of freedom. The most commonly used and accepted statistic is Wilk.s Lambda. More recently statisticians have used the Pillai-Bartlett trace, since research has indicated that this statistic is somewhat more robust to violations of the model assumptions than Wilk.s lambda. It is therefore recommended that you base your conclusions on one of these two statistics. The decision is often moot, however, since the different statistics almost always produce similar F conversions. When you report your results in a paper, you typically state the method you used and provide the resulting F-statistic with its degrees of freedom and p-value.
• Mauchly’s Test of Sphericity. Tells you whether your various dependent variables meet the assumption for a repeated measures ANOVA. This table only appears if you have a within-subject factor in the design. You will see a sphericity test for each dependent
variable in the design. If a sphericity test is significant, it means that this assumption is violated, so you should NOT interpret the results of a repeated-measures analysis on that dependent variable without correction. This has nothing to do with the overall MANOVA
itself, but just the follow-up repeated measures analyses on the individual DVs.
• Multivariate. Reports the ability of your within-subject effects to account for variability in the average of your dependent variables in a multivariate analysis. This test will not be meaningful unless your measures are all on the same scale of measurement and coded in the same direction.
• Univariate Tests. Reports the ability of your within-subject effects to account for variability in each of your dependent variables individually in a repeated measures analysis. For more information on interpreting this table, refer to the Multifactor withinsubjects
ANOVA section of these notes.
• Tests of Within-Subjects Contrasts. Provides the results of polynomial contrasts among your within-subject main effects and interactions. These will have no meaning unless your levels have an ordinal relationship.
• Tests of Between-Subjects Effects. which reports the ability of each of your betweensubjects effects to account for variability in each of your dependent measures individually. For more information on this table, refer to the Multifactor betweensubjects ANOVA section of these notes.