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C82MST Lecture 9 - Overview of lecture What is ANCOVA...

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1 C82MST Statistical Methods 2 - Lecture 9 1 Overview of lecture What is ANCOVA? Partitioning Variability • Assumptions • Examples • Limitations C82MST Statistical Methods 2 - Lecture 9 2 Analysis of covariance Analysis of Covariance is used to achieve statistical control of error when experimental control of error is not possible. The Ancova adjusts the analysis in two ways:- • reducing the estimates of experimental error • adjusting treatment effects with respect to the covariate C82MST Statistical Methods 2 - Lecture 9 3 Analysis of covariance In most experiments the scores on the covariate are collected before the experimental treatment • eg. pretest scores, exam scores, IQ etc In some experiments the scores on the covariate are collected after the experimental treatment • e.g.anxiety, motivation, depression etc. It is important to be able to justify the decision to collect the covariate after the experimental treatment since it is assumed that the treatment and covariate are independent. C82MST Statistical Methods 2 - Lecture 9 4 Partitioning variability in ANOVA In analysis of variance the variability is divided into two components • Experimental effect • Error - experimental and individual differences Error Effect C82MST Statistical Methods 2 - Lecture 9 5 Partitioning variability in ANCOVA In ancova we partition variance into three basic components: • Effect • Error • Covariate Error Effect Covariate C82MST Statistical Methods 2 - Lecture 9 6 Estimating treatment effects When covariate scores are available we have information about differences between treatment groups that existed before the experiment was performed Ancova uses linear regression to estimate the size of treatment effects given the covariate information
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