133229DHS618 - MANOVA Example

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Trident University International *

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618

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Statistics

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Feb 20, 2024

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Uploaded by DoctorBraveryWalrus7988

Module 4 - Example MANOVA How to Perform MANOVA 1. In SPSS, select Analyze -> General Linear Model  Multivariate 2. Move dependent variable into box (i.e. useful, difficulty, importance). Move categorical independent variables into fixed factor box (i.e. group), as shown below. Covariate box should remain empty as there are no continuous control variables in this example.

3. Under options, mark descriptive statistics, estimates of effect size, and homogeneity tests. 4. Under PostHoc, move factors to the Post Hoc test box. Then mark the appropriate test (i.e. select Bonferroni for independent variables with four levels or fewer. Select Tukey for IVs with more than four levels). As group (independent variable) has three levels, Bonferroni test should be marked as shown below: 5. Select Continue and OK to obtain output below How to Interpret MANOVA 1. Are the assumptions met? To examine whether the assumptions of homoscedasticity are met, review the results of Box’s test and Levene’s test. The output for these tests are shown below. Box’s test (p>.05) indicated that the assumption of equality of covariance matrices was met. Levene’s test showed that the assumption of equality of error variance was met for difficulty and importance (p>.05), but not for useful. Please note that the Levene test is more robust in the face of non-normality than more traditional tests. Therefore, failure of the assumption is not fatal to MANOVA.

2. Are the combined DVs significantly different across three groups? The combined dependent variables were different across the three groups (Wilks' Lambda=.526, F(6,56)=3.538, p=.005, p<.01). The partial eta squared (estimate of effect size) was .275. Multivariate Tests c Effect Value F Hypothesis df Error df Sig. Partial Eta Squared Intercept Pillai's Trace .986 657.857 a 3.000 28.000 .000 .986 Wilks' Lambda .014 657.857 a 3.000 28.000 .000 .986 Hotelling's Trace 70.485 657.857 a 3.000 28.000 .000 .986 Roy's Largest Root 70.485 657.857 a 3.000 28.000 .000 .986 group Pillai's Trace .477 3.025 6.000 58.000 .012 .238 Wilks' Lambda .526 3.538 a 6.000 56.000 .005 .275 Hotelling's Trace .897 4.038 6.000 54.000 .002 .310 Roy's Largest Root .892 8.623 b 3.000 29.000 .000 .471 3. What is the effect of each independent variable on each DV?

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The main effect of group on each of the dependent variables (i.e. useful, difficulty, and importance) was not statistically significant (p>.05). Tests of Between-Subjects Effects Source Dependent Variable Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Corrected Model useful 52.924 a 2 26.462 2.701 .083 .153 difficulty 3.975 b 2 1.988 .472 .628 .031 importance 81.830 c 2 40.915 2.879 .072 .161 Intercept useful 8800.400 1 8800.400 898.106 .000 .968 difficulty 1077.878 1 1077.878 256.054 .000 .895 importance 1383.869 1 1383.869 97.371 .000 .764 group useful 52.924 2 26.462 2.701 .083 .153 difficulty 3.975 2 1.988 .472 .628 .031 importance 81.830 2 40.915 2.879 .072 .161 Error useful 293.965 30 9.799 difficulty 126.287 30 4.210 importance 426.371 30 14.212 Total useful 9147.290 33 difficulty 1208.140 33 importance 1892.070 33 Corrected Total useful 346.890 32 difficulty 130.262 32 importance 508.201 32 a. R Squared = .153 (Adjusted R Squared = .096) b. R Squared = .031 (Adjusted R Squared = -.034) c. R Squared = .161 (Adjusted R Squared = .105) 4. Are there significant differences between the DVs for any of the groups? If the multivariate and main effects are not statistically significant, you can disregard the results of the Post Hoc test. Follow-up multiple comparisons showed that the DVs were not significantly different between the groups.

Multiple Comparisons Bonferroni Dependent Variable (I) group (J) group Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound useful treatment control_1 2.5909 1.33477 .185 -.7937 5.9755 control_2 2.7727 1.33477 .139 -.6119 6.1574 control_1 treatment -2.5909 1.33477 .185 -5.9755 .7937 control_2 .1818 1.33477 1.000 -3.2028 3.5664 control_2 treatment -2.7727 1.33477 .139 -6.1574 .6119 control_1 -.1818 1.33477 1.000 -3.5664 3.2028 difficulty treatment control_1 .6091 .87486 1.000 -1.6093 2.8275 control_2 .8182 .87486 1.000 -1.4002 3.0366 control_1 treatment -.6091 .87486 1.000 -2.8275 1.6093 control_2 .2091 .87486 1.000 -2.0093 2.4275 control_2 treatment -.8182 .87486 1.000 -3.0366 1.4002 control_1 -.2091 .87486 1.000 -2.4275 2.0093 importance treatment control_1 3.5727 1.60750 .102 -.5035 7.6489 control_2 3.0455 1.60750 .203 -1.0308 7.1217 control_1 treatment -3.5727 1.60750 .102 -7.6489 .5035 control_2 -.5273 1.60750 1.000 -4.6035 3.5489 control_2 treatment -3.0455 1.60750 .203 -7.1217 1.0308 control_1 .5273 1.60750 1.000 -3.5489 4.6035 Based on observed means. The error term is Mean Square(Error) = 14.212. Please note that this example includes a very brief description of how to perform and interpret results of MANOVA. For your assignment, you should include more detail in your discussion of methods and results.