Experimental Designs Week 4 Solution

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Experimental DesignsWeek 4 SolutionExperimental Designs2. Explain the difference between multiple independent variables and multiple levels of independentvariables. Which is better?Answer:The general purpose of multivariate analysis of variance (MANOVA) is to determinewhether multiple levels of independent variables on their own or in combination withone another have an effect on the dependent variables. MANOVA requires that thedependent variables meet parametric requirements.MANOVA is used under the same circumstances as ANOVA but whenthere are multiple dependent variables as well as independent variables within the modelwhich the researcher wishes to test. MANOVA is also considered a valid alternative tothe repeated measures ANOVA when sphericity is violated.Like an ANOVA, MANOVA examines the degree of variance within theindependent variables and determines whether it is smaller than the degree of variancebetween the independent variables. If the within subjects variance is smaller than the betw-een subjects variance it means the independent variable has had a significant effect on thedependent variables. There are two main differences between MANOVAs and ANOVAs.The first is that MANOVAs are able to take into account multiple independent and multipledependent variables within the same model, permitting greater complexity. Secondly,ratherthan using the F value as the indicator of significance a number of multivariate measures.MANOVAs the independent variables relevant to each main effect are weighted to givethem priority in the calculations performed. In interactions the independent variables areequally weighted to determine whether or not they have an additive effect in terms of thecombined variance they account for in the dependent variable/s.The main effects of the independent variables and of the interactions are examined withall else held constant. The effect of each of the independent variables is tested separately.Any multiple interactions are tested separately from one another and from any significantmain effects. Assuming there are equal sample sizes both in the main effects and the inter-actions, each test performed will be independent of the next or previous calculation (exce-pt for the error term which is calculated across the independent variables).

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