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

2004
Views:

439

Pages:

23
Author:

Emilee Weeks

ANCOVA Lecture 9 Part 1 What is ANCOVA? Analysis of covariance ► an extension of ANOVA in which main effects and interactions are assessed on DV scores after the DV has been adjusted for by the DV’s relationship with one or more Covariates (CVs) ANCOVA ► In MR we saw this as the relationship between X1 and Y while controlling for other Xs y ' = β1 x1 + β 2 x2 + K + β j x j Basic requirements 1 DV (I, R) 1 IV (N, O) 1 CV (I, R) Basic requirements ► Minimum number of CVs that are uncorrelated with each other ► You want a lot of adjustment with minimum loss of degrees of freedom ► The change in sums of squares needs to greater than a change associated with a single degree of freedom lost for the CV Basic requirements ► CVs should also be uncorrelated with the IVs (e.g. the CV should be collected before treatment is given) in order to avoid diminishing the relationship between the IV(s) and DV. Covariate ►A covariate is a variable that is related to the DV, which you can’t manipulate, but you want to account for it in you relationship. Applications ►Three major applications Increase test sensitivity (main effects and interactions) by using the CV(s) to account for more of the error variance therefore making the error term smaller Applications ► Adjust DV scores to what they would be if everyone scored the same on the CV(s) This second application is used often in nonexperimental situations where subjects cannot be randomly assigned Applications Subjects cannot be made equal through random assignment so CVs are used to adjust scores and make subjects more similar than without the CV This second approach is often used as a way to improve on poor research designs. This should be seen as simple descriptive model building with no causality Applications Realize that using CVs can adjust DV scores and show a larger effect or the CV can eliminate the effect Applications ► The third application will be addressed later in MANOVA, but is the adjustment of a DV for other DVs taken as CVs. Assumptions Unequal sample sizes, missing data, and number of cases ► Missing data and unequal sample sizes can be two different entities or seen as the same idea If data was collected with equal samples sizes planned and there is data missing on the CV or DV then this can be seen as a missing data problem Unequal sample sizes, missing data, and number of cases ► If data is unequal because of some reason (e.g. larger population of certain type of subject) then this isn’t missing data and needs to be dealt with appropriately Unequal sample sizes, missing data, and number of cases ► The problem here is that with unequal samples it is unclear how to calculate the marginal mean. Is it the mean of the group means or the mean of the scores? ► Another problem is that the variances then start to overlap one another forcing the within plus between variances to be larger than the total variance. Unequal sample sizes, missing data, and number of cases ► Listwise deletion to balance cells is an option, but a bad one. You’ll lose too much data Unequal sample sizes, missing data, and number of cases ► Change the types of Sums of squares you use ► Type 3 sums of square (SSTYPE3 in GLM or method=unique in MANOVA) is the default in SPSS and assumes that the data was supposed to be complete and the difference in the number of subjects is not meaningful Acts like standard multiple regression. Each main effect and interaction is assessed after all other main effects, interactions and covariates are controlled for Treats all groups the same – small group is weighted equally as a large group (sometimes called the unweighted approach) Unequal sample sizes, missing data, and number of cases ► Type 1 sums of squares (SSTYPE1 in GLM or method = experimental in MANOVA) assumes that the difference in number of subjects is meaningful and gives more weight to the values from larger groups Unequal sample sizes, missing data, and number of cases ► Number of cases required depends on the number needed to reach appropriate level of power power Outliers ► No outliers – you need to test for univariate outliers on the DV and all of the CVs individually and for multivariate outliers in the combined DV and CVs space. No Multicollinearity/Singularity ► If a CV is highly related to another CV (at a correlation of .5 or more) than it will not adjust the DV over and above the other CV. ► One or the other should be removed since they are statistically redundant.

What is ANCOVA