1 / 8

Test Statistics for MANOVA

Test Statistics for MANOVA. BMTRY 726 2/28/14. Univariate ANOVA. ANOVA valuates differences in mean response among multiple treatment groups Given a random sample We rewrite m l as the overall mean plus the treatment effect of treatment l

jadzia
Download Presentation

Test Statistics for MANOVA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Test Statistics for MANOVA BMTRY 726 2/28/14

  2. Univariate ANOVA ANOVA valuates differences in mean response among multiple treatment groups Given a random sample We rewrite ml as the overall mean plus the treatment effect of treatment l We test our hypothesis using the model Grand mean Treatment effect Error Sample mean Est. treatment effect Residual

  3. Univariate ANOVA • ANOVA does this by decomposing the variance of the sample into treatment and error components:

  4. F-Test ANOVA • Based on this decomposition, the resulting F test examines the ratio of MStrt to MSe: • We can rewrite this ratio as

  5. Extension to MANOVA • MANOVA is very similar but we are comparing treatment response of a vector of outcomes • We know then that out variance decomposition can be written in vector notation as:

  6. Extension to MANOVA • We can think about adapting our modified F-statistic from ANOVA for the MANOVA case (how would matrices make a difference?) • This then is the matrix analog to the statistic Awe discussed for ANOVA

  7. Extension to MANOVA • However, A is a matrix when we need a single statistic… • Early statisticians came up with several (4 in this case) statistics that all are based on • Wilk’s lambda • Pillai’s trace • Lawely-Hotellingtrace • Roy’s greatest root • All follow an exact or approximate F distribution • All are based on the eigenvalues of A = HE-1

  8. The 4 Statistics • All can be determined using the eigenvalues of A = HE-1 • 3 of the 4 can all be also calculated from H and E

More Related