Chapter 11
Module 2For self-study: Running Tests in SPSS
Assignment 3.MANOVA
First answer the following question:
What is a good reason to run a MANOVA rather than a series of Univariate Analyses of Variance?
Assignment 11.2 introduced a study concerning some of the hypotheses generated by evolution theory. Open the file evolution.sav, and run through the variable view to familiarize yourself with the questions that were asked. Now let us focus on Picture 1. The students compiled a list with variables they considered indicative of evolutionary attractiveness. Using texts by theorists in the field they hypothesized that a female face with larger eyes and a wider mouth would be considered more friendly, more successful, more trustworthy, more satisfied, etc. The assignment is to run a MANOVA to see whether they were right. Enter the following variables as dependent variables in your analyses: “antisoc1”, “satis1”, “active1”, “intell1”, “crea1”, “friend1”, “succes1”, “excite1”, “access1”, “honest1”. For the purpose of this assignment, use “condition” as the independent variable and “gender” as a covariate. Make sure that you check all the necessary settings in this procedure and run the test.
Describe the results, cutting- and pasting the relevant parts of the output in a Word document, quoting the numbers from the tables in the appropriate way, and interpreting the data in terms of the students’ hypotheses.
The choice for a MANOVA should always be legitimized by your conceptual model: the items that are entered as dependent variables in the analyses are to be considered as different aspects of one and the same construct. In this case it could be argued that all the items listed in the assignment are aspects of evolutionary fitness.
The first step you should take is to open the dialogue box for MULTIVARIATE under the ANALYZE menu, and the submenu for GENERAL LINEAR MODEL. Following the instructions of the assignment, this is what you should see on your screen:
The assignment mentions that you should check other necessary settings before running the procedure. This means that you need to make sure that SPSS runs a test of homogeneity, produces descriptive statistics, and since you have three conditions, that you include a post hoc test.
You clicked on OPTIONS, and made sure you ticked the settings as seen in the figure above.After clicking on CONTINUE, you can run the test. This results in the following output (selection):
| Descriptive Statistics | ||||
|---|---|---|---|---|
| Condition (Which version of the pictures was shown?) | Mean | Std. Deviation | N | |
| Antisocial – Social look in picture 6 | Neutral | 3.16 | .958 | 19 |
| Evolutionary Unattractive | 3.52 | .814 | 21 | |
| Evolutionary Attractive | 3.11 | .937 | 19 | |
| Total | 3.27 | .906 | 59 | |
| Dissatisfied – Satisfied look in picture 1 | Neutral | 3.32 | .671 | 19 |
| Evolutionary Unattractive | 3.05 | .973 | 21 | |
| Evolutionary Attractive | 3.68 | .820 | 19 | |
| Total | 3.34 | .863 | 59 | |
| Lazy – Active look in picture 1 | Neutral | 3.42 | 1.017 | 19 |
| Evolutionary Unattractive | 3.76 | .889 | 21 | |
| Evolutionary Attractive | 3.74 | .933 | 19 | |
| Total | 3.64 | .943 | 59 | |
| Stupid – Intelligent look in picture 1 | Neutral | 3.79 | .631 | 19 |
| Evolutionary Unattractive | 3.76 | .831 | 21 | |
| Evolutionary Attractive | 3.89 | .658 | 19 | |
| Total | 3.81 | .706 | 59 | |
| Without fantasy – Creative look in picture 1 | Neutral | 3.68 | .946 | 19 |
| Evolutionary Unattractive | 3.62 | .740 | 21 | |
| Evolutionary Attractive | 3.95 | .780 | 19 | |
| Total | 3.75 | .822 | 59 | |
| Unfriendly – Friendly look in picture 1 | Neutral | 3.58 | .961 | 19 |
| Evolutionary Unattractive | 2.81 | .873 | 21 | |
| Evolutionary Attractive | 3.32 | .820 | 19 | |
| Total | 3.22 | .930 | 59 | |
| Unsuccessful – Successful look in picture 1 | Neutral | 3.47 | .612 | 19 |
| Evolutionary Unattractive | 3.14 | .727 | 21 | |
| Evolutionary Attractive | 3.32 | .582 | 19 | |
| Total | 3.31 | .650 | 59 | |
| Dull – Exciting look in picture 1 | Neutral | 3.42 | .961 | 19 |
| Evolutionary Unattractive | 3.43 | .926 | 21 | |
| Evolutionary Attractive | 3.53 | .905 | 19 | |
| Total | 3.46 | .916 | 59 | |
| Dishonest – Honest look in picture 1 | Neutral | 3.42 | .692 | 19 |
| Evolutionary Unattractive | 3.19 | .680 | 21 | |
| Evolutionary Attractive | 3.53 | .612 | 19 | |
| Total | 3.37 | .667 | 59 | |
As you can see in the listing of the descriptive statistics, we do not see a pattern for all the items that is consistent with the predictions. The students had expected higher scores to occur only in the Evolutionary Attractive condition and the lowest scores consistently in the Evolutionary Unattractive condition. Only on four of the ten variables do we see this pattern: for ‘satisfied’, ‘intelligent’, ‘creative’ and ‘honest’. Moreover, we should also note that the differences are rather small. We may conclude that the evidence here for evolutionary aesthetics is hardly convincing. Let us look further down the output to find out.
Box’s Test of Equality of Covariance Matrices a| Box’s M | 101.408 |
| F | .862 |
| df1 | 90 |
| df2 | 8445.778 |
| Sig. | .821 |
Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups.
a.Design: Intercept + gender + GROUP.
The Box’s Test tells us that we can reject the hypothesis that variances are unequal for the variables. This means that the data meet one of the criteria for running a MANOVA. Now look at the next table:
Multivariate Tests c| Effect | Value | F | Hypothesis df | Error df | Sig. | |
|---|---|---|---|---|---|---|
| Intercept | Pillai’s Trace | ,896 | 39,482 a | 10,000 | 46,000 | ,000 |
| Wilks’ Lambda | ,104 | 39,482 a | 10,000 | 46,000 | ,000 | |
| Hotelling’s Trace | 8,583 | 39,482 a | 10,000 | 46,000 | ,000 | |
| Roy’s Largest Root | 8,583 | 39,482 a | 10,000 | 46,000 | ,000 | |
| gender | Pillai’s Trace | ,219 | 1,288 a | 10,000 | 46,000 | ,265 |
| Wilks’ Lambda | ,781 | 1,288 a | 10,000 | 46,000 | ,265 | |
| Hotelling’s Trace | ,280 | 1,288 a | 10,000 | 46,000 | ,265 | |
| Roy’s Largest Root | ,280 | 1,288 a | 10,000 | 46,000 | ,265 | |
| GROUP | Pillai’s Trace | ,439 | 1,323 | 20,000 | 94,000 | ,184 |
| Wilks’ Lambda | ,604 | 1,320 a | 20,000 | 92,000 | ,187 | |
| Hotelling’s Trace | ,584 | 1,315 | 20,000 | 90,000 | ,191 | |
| Roy’s Largest Root | ,409 | 1,923 b | 10,000 | 47,000 | ,065 | |
Exact statistic.
b.The statistic is an upper bound on F that yields a lower bound on the significance level.
c.Design: Intercept + gender + GROUP.
As you can see, none of the MANOVA’s shows significant effects. Only Roy’s Largest Root test shows a tendency toward significance for GROUP. Nevertheless, we advise you to conclude that these results prohibit further interpretation of the output in favor of the hypothesis. We can conclude that the effect of the manipulation on the items as one construct did not occur. We already guessed so, since we did not detect a general pattern in the descriptive statistics. Nevertheless, let us look a bit further down to see what we find there. Maybe we will have enough reason to run separate Univariate ANOVA’s for some of the items. The next table shows us another test of homogeneity: again we can conclude that the data meet the criteria for running a MANOVA.
Levene’s Test of Equality of Error Variances a| F | df1 | df2 | Sig. | |
|---|---|---|---|---|
| Antisocial – Social look in picture 1 | ,079 | 2 | 56 | ,924 |
| Dissatisfied – Satisfied look in picture 1 | 2,628 | 2 | 56 | ,081 |
| Lazy – Active look in picture 1 | ,476 | 2 | 56 | ,624 |
| Stupid – Intelligent look in picture 1 | ,866 | 2 | 56 | ,426 |
| Without fantasy – Creative look in picture 1 | ,746 | 2 | 56 | ,479 |
| Unfriendly – Friendly look in picture 1 | ,379 | 2 | 56 | ,686 |
| Unsuccessful – Successful look in picture 1 | ,217 | 2 | 56 | ,806 |
| Dull – Exciting look in picture 1 | ,483 | 2 | 56 | ,620 |
| Inaccessible – Accessible look in picture 1 | ,757 | 2 | 56 | ,474 |
| Dishonest – Honest look in picture 1 | ,862 | 2 | 56 | ,428 |
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a.Design: Intercept + gender + GROUP.
None of the F values is significant. That means that we cannot reject the hypothesis that the variances are equal.
Above we inserted a part of the table you will find in the output. As you may have expected, gender does play a role (as covariate) in the effects, that is, for two of the ten variables: ‘satisfied’ (p = .032) and ‘exciting’ (p = .006). However, SPSS will take those effects into account when looking at the effects of condition (group). Interestingly, we do see strong effects there: for social (p < .001), satisfied (p < .029), and friendly (p < .021). It could be argued that the students now have sufficient reasons to explore the items individually by means of Univariate Analyses of Variance. They may also consider looking at the three items as one construct. Of course, they should mention the failure of finding significant effects for the first attempt, and argue in their report why they think responses for ‘social’, ‘satisfied’ and ‘friendly’ make one construct – this does not seem too problematic, considering their semantic resemblance.
Let us see exactly which of the differences are significant. For this you take a look at the table entitled “Pairwise comparison”. This table is the result of the Bonferroni post hoc test that you asked SPSS to produce. In the table below we print part of the table.
As you can see, the pattern is not very consistent, except in one respect: the evolutionary unattractive version of the female face is more antisocial, dissatisfied and unfriendly than the evolutionary attractive and/or neutral version of the face. This complies with the students’ predictions. In conclusion, they need to do more analyses before they can report their results.