PSY 1950 Repeated-Measures ANOVA October 29, 2008

Partitioning of Sums of Squares Total variation Between subjectsWithin subjects Between conditionsError numeratordenominator

Partitioning of Sums of Squares Total variation Between conditionsWithin conditions Between subjectsError numerator denominator

Error as Interaction Why does the interaction between Subject and Condition equal the error? –Interaction reveals how much the treatment effect varies across subjects –Small interaction means that the treatment has a reliable effect –Big interaction means that the treatment has an unreliable effect

Assumptions Independence (of errors) –from scores from different sampling units, not of measurements Normality (of errors) Sphericity (  ) –AKA circularity –Equal dependency among conditions –Homogeneity of the variances of the differences between conditions –Only when > 2 levels of repeated measure

Sphericity Drug SubjectABCDE Mauchly’s test determines whether population variances differ significantly

John Mauchly ENAIC –The first Turing- complete purpose digital computer –Built to calculate artillery firing tables –A “giant brain” –5 million hand- soldered joints

Violations of Sphericity Correct degrees of freedom –Only to convert F to p, not to calculate MS Multiply numerator and denominator dfs by  Three different estimates of  –Lower-bound 1/(k - 1) ≤  ≤ 1 Always too conservative, never too liberal –Greenhouse-Geisser Too conservative when >.75 –Huynh-Feldt Too liberal when <.75

SPSS