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Week 9 Assignment Number 1: MANOVA in SPSS
LaShurn Hemphill
October 29, 2023
2
Multivariate Analysis of Variance (MANOVA)
Expanding on the fundamental One-Way ANOVA, Multivariate Analysis of Variance (MANOVA) examines the impact of an independent categorical variable on a dependent variable. The classic One-Way analysis gains additional dependent variables with the use of MANOVA. In this study, there are two continuous dependent variables and one categorical independent variable.
Using data from the General Social Survey, I examined: Does each respondent's highest year of school completed and their income in constant dollars change depending on their sex? Sex (male and female) is the independent variable. The dependent variables include the respondent's highest year of completion of school and their income in constant dollars. The study's participants ranged in age from 18 to 89 years old, with a mean age of 48. Box's M test evaluated if the variance/covariance matrices were homogeneous under different situations; it was found that there was a substantial violation in this regard: Box's M = 40.015,F (3, 18148409)
13.244, p<0.0001. Pillai's trace =.092, F (2, 306) = 15.428, p <.001 indicated that the multivariate test for the overall MANOVA was significant. The associated effect size, η2 =.092, was a small effect size. We used the Bonferroni test for all pairwise comparisons. This table shows that, while respondent highest year of school completed (F (1, 307) = 3.414; p =.066; partial η2 =.011) is not statistically significant to respondent sex, it does have a statistically significant influence on respondent income in constant dollars (F (1, 307) = 16.742; p <.001; partial η2 =.052). It is crucial to remember that, to account for running numerous ANOVAs, you should apply an alpha correction. I chose to use the Bonferroni adjustment. Using
α =.05 in this instance, I discovered that the Respondent Income in Constant Dollars for men was
3
much greater than that of women. There was no statistical significance found in the other paired comparison.
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References
.
Walden University (Producer). (n.d.). General Social Survey B [
Data set
]. Baltimore, MD: Author
Warner, R. M. (2013).
Applied statistics: From bivariate through multivariate
techniques
(2nd ed., pp.645-687). Thousand Oaks, CA: SAGE Publications.
5
Appendix
LM conrinc educ BY sex
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/POSTHOC=sex(BONFERRONI)
/PLOT=PROFILE(sex) TYPE=LINE ERRORBAR=NO MEANREFERENCE=NO
YAXIS=AUTO
/EMMEANS=TABLES(sex) COMPARE ADJ(BONFERRONI)
/PRINT=DESCRIPTIVE ETASQ HOMOGENEITY
/CRITERIA=ALPHA(.05)
/DESIGN= sex.
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