University:
California State University, Northridge
Course:
PSY 524/L | Multivariate Analysis Computer and Lab
Academic year:

2005
Views:

40

Pages:

20
Author:

Yareli Key

MANOVA Basics What is MANOVA Multivariate Analysis of Variance n n an extension of ANOVA in which main effects and interactions are assessed on a combination of DVs MANOVA tests whether mean differences among groups on a combination of DVs is likely to occur by chance MANOVA n A new DV is created that is a linear combination of the individual DVs that maximizes the difference between groups. n In factorial designs a different linear combination of the DVs is created for each main effect and interaction that maximizes the group difference separately. n Also when the IVs have more than one level the DVs can be recombined to maximize paired comparisons MANCOVA n n is the multivariate extension of ANCOVA where the linear combination of DVs is adjusted for by one or more continuous covariates. A covariate is a variable that is related to the DV, which you can’t manipulate, but you want to removes its (their) relationship from the DV before assessing differences on the IVs. Basic requirements n 2 or more DVs (I, R) n 1 or more categorical IVs (N, O) n for MANCOVA you also need 1 or more continuous CVs (I, R) MANOVA advantages over ANOVA n By measuring multiple DVs you increase your chances for finding a group difference n With a single DV you “put all of your eggs in one basket” n Multiple measures usually do not “cost” a great deal more and you are more likely to find a difference on at least one. MANOVA advantages over ANOVA n n Using multiple ANOVAs inflates type 1 error rates and MANOVA helps control for the inflation Under certain (rare) conditions MANOVA may find differences that do not show up under ANOVA n Under most circumstance the more complex an analysis becomes the less power there is Kinds of Research Questions asked by MANOVA n The questions are mostly the same as ANOVA just on the linearly combined DVs instead just one DV. Are there any main effects? n Holding all other effects constant, is a difference among groups greater than expected by chance? Are there any main effects? n Holding constant can mean: – Controlling for other effects by averaging over them in a factorial design – Holding extraneous variables constant or counterbalancing/randomizing their effects – Using covariates to adjust the composite DV in order to create a state of “pseudo equality” Are there any main effects? n Tests of main effects are orthogonal if they are completely crossed and equal samples in each cell, they are only linked by a common error term Are there any interactions among the IVs? n Does change in the linearly combined DV for one IV depend on the levels of another IV? n For example: Given three types of treatment, does one treatment work better for men and another work better for women? n If equal samples in each cell then one interaction is independent of main effects and other interactions. Which DVs are most important? n n If there are any significant main effects or interactions, on which individual DV is there the most change (difference), if any, “caused” by the levels of the IV? You can follow a significant MANOVA with individual ANOVAs in order to see on which DV is there large, medium, small or no effect. Which DVs are most important? n Another procedure is the Roy-Bargman step-down procedure which uses ANCOVA on each individual DV, with higher priority DVs as covariates. What are the parameter estimates? n Marginal means are the best population estimates for the main effects and cell mean are the best estimates of interactions n When the Roy-Bargman step procedure is used then the interpretation is the best estimates of adjusted population values n All parameters are accompanied by standard error and/or confidence intervals. Which levels of the IV are significantly different? n n If there are significant main effects on IVs with more than two levels than you need to test which levels are different from each other And if there are interactions the interactions need to be taken apart so that the specific causes of the interaction can be uncovered. How strong is the IV(s)/composite DV association? n n What is the proportion of the composite DV explained by each IV? You can also then pick out the strength of association between the IVs and each DV separately. Can MANOVA be used when assumptions are violated in repeated measure ANOVA? n n The test of sphericity in repeated measures ANOVA is often violated Corrections include: – adjustments of the degrees of freedom (e.g. Huynh-Feldt adjustment) – decomposing the test into multiple paired tests (e.g. trend analysis) or – treating the repeated levels as multiple DVs (e.g. profile analysis which we will talk about next)

MANOVA Basics. What is MANOVA