One-Way Analysis of Covariance

1 / 15

# One-Way Analysis of Covariance - PowerPoint PPT Presentation

One-Way Analysis of Covariance. One-Way ANCOVA. ANCOVA. Allows you to compare mean differences in 1 or more groups with 2+ levels (just like a regular ANOVA), while removing variance from a 3 rd variable What does this mean?. ANCOVA. ANCOVA.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'One-Way Analysis of Covariance' - dyanne

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### One-Way Analysis of Covariance

One-Way ANCOVA

ANCOVA
• Allows you to compare mean differences in 1 or more groups with 2+ levels (just like a regular ANOVA), while removing variance from a 3rd variable
• What does this mean?
ANCOVA
• Removing variance that is unrelated to the IV/intervention = removing error variance
• Makes ANCOVA potentially a very powerful test (i.e. easier to find significant results than with ANOVA alone) by potentially reducing MSerror
• Generally, the more strongly related are covariate and DV, and unrelated the covariate and IV, the more useful (statistically) the covariate will be in reducing MSerror
ANCOVA
• Why would this be useful?
• Any longitudinal research design needs to control for T1 differences in the DV
• I.e. If assessing change in symptoms of social anxiety over time between 2 groups, we need to control for group differences in T1 social anxiety
• Even if random assignment is used, use of a covariate is a good idea – Random assignment doesn’t guarantee group equality
ANCOVA
• Why would this be useful?
• Any DV’s with poor discriminant validity
• I.e. SES and race are highly related – If we wanted to study the effects of SES, independent of race, on scholastic achievement we could use an ANCOVA using SES as the DV and race as a covariate
ANCOVA
• Why would this be useful?
• If you’re using 2+ DV’s (MANOVA) and want to isolate the effects of one of them
• ANCOVA with the DV of interest and all other DV’s used as covariates
• Note: In this case we’re specifically predicting that IV’s and covariates are related, it’s not ideal, but what can you do?
ANCOVA
• However, ANCOVA should not be used as a substitute for good research design
• If your groups are unequal on some 3rd variable, these differences are still a plausible rival hypothesis to your H1, with or without ANCOVA
• Controlling ≠ Equalizing
• Random assignment to groups still best way to ensure groups are equal on all variables
ANCOVA
• Also, covariates change the meaning of your DV
• I.e. We studying the effects of a tutoring intervention for student athletes – We find out our Tx group is younger than our control group – (Using age as a covariate)  (DV = class performance – age)
• What does this new DV mean??? Effects of Tx over and above age (???)
ANCOVA
• Also, covariates change the meaning of your DV
• For this reason, DO NOT just add covariates thinking it will help you find sig. results
• Adding a covariate highly correlated with a pre-existing covariate actually makes ANCOVA less powerful
• df decreases slightly with each covariate
• No increase in power since 2 covariates remove same variance due to high correlation
ANCOVA
• Assumptions:
• Normality
• Homoscedasticity
• Independence of Observations
• Relationship between covariate and DV
• Relationship between IV and covariate is linear
• Relationship between IV and covariate is equal across levels of IV
• AKA Homogeniety of Regression Slopes
• I.e. an interaction between IV and CV
ANCOVA
• Calculations
• Don’t worry about them, in fact, you can skip pp. 577-585 in the text
• Recall that in the one-way ANOVA we divided the total variance (SStotal) into variance attributable to our IV (SStreat) and not attributable to our IV (SSerror)
ANCOVA
• In ANCOVA, we just divide the variance once more (for the covariate)
• IV: Inferences are made re: its effects on the DV by systematically separating its variance from everything else
• Covariate: Inferences are made by separating its variance from everything else, however this separated variance is not investigated in-and-of itself