SAS HATCO MANOVA – HW Perform two MANOVA analyses, a 3-Group analysis and a Fact

Question

SAS HATCO MANOVA – HW

Perform two MANOVA analyses, a 3-Group analysis and a Factorial Design with 2-Independent variables as directed below on the HATCO dataset.

Include the following: USING SAS and SAS OUTPUTS!

1. Perform a brief exploratory data analysis of the data and evaluate the tenability of the multivariate data analysis assumptions and specifically those associated with MANOVA (Note: only need to assess univariate assumptions).

2. State ALL Null and Alternative Hypotheses. Use an alpha of 0.05 for all hypothesis testing and/or specify an alternative value as necessary.

3. 3-Group Model: X9 X10 = X14; including appropriate Multiple Means Comparisons Tests (e.g., Tukey and Scheffe)

4. Factorial Design Model: X9 X10 = X14 X13 X14*X13

5. Fully discuss and interpret all the analyses, results and conclusions.

Explanation / Answer

1) The two-way multivariate analysis of variance (two-way MANOVA) is often considered as an extension of the two-way ANOVA for situations where there is two or more dependent variables. The primary purpose of the two-way MANOVA is to understand if there is an interaction between the two independent variables on the two or more dependent variables.

2) For example, you could use a two-way MANOVA to understand whether there were differences in students' short-term and long-term recall of facts based on lecture duration and fact type (i.e., the two dependent variables are "short-term memory recall" and "long-term memory recall", whilst the two independent variables are "lecture duration", which has four groups – "30 minutes", "60 minutes", "90 minutes" and "120 minutes" – and "fact type", which has two groups: "quantitative (numerical) facts" and "qualitative (textual/contextual) facts"). Alternately, you could use a two-way MANOVA to understand whether there were differences in the effectiveness of male and female police officers in dealing with violent crimes and crimes of a sexual nature taking into account a citizen's gender (i.e., the two dependent variables are "perceived effectiveness in dealing with violent crimes" and "perceived effectiveness in dealing with sexual crimes", whilst the two independent variables are "police officer gender", which has two categories – "male police officers" and "female police offices" – and "citizen gender", which also has two categories: "male citizens" and "female citizens").

3} As mentioned earlier, a two-way MANOVA has generally one primary aim: to understand whether the effect of one independent variable on the dependent variables (collectively) is dependent on the value of the other independent variable. This is called an "interaction effect". However, if no interaction effect is present (usually assessed as whether the interaction effect is statistically significant), you would normally be interested in the "main effects" of each independent variable instead.

4) This is somewhat akin to assessing the effect that an independent variable has on the dependent variables collectively when "ignoring" the value of the other independent variable. On the other hand, if a statistically significant interaction is found, you need to consider an method of following up the result (i.e., what follow-up analyses you may want to run).

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