Chapter 13

Question 1

Compound symmetry

Answer 1

a condition that holds true when both the variances across conditions are equal (this is the same as the homogeneity of variance assumption) and the covariances between pairs of conditions are also equal.

Question 2

Greenhouse-Geisser correction

Answer 2

an estimate of the departure from sphericity. The maximum value is 1 (the data completely meet the assumption of sphericity) and minimum is the lower bound. Values below 1 indicate departures from sphericity and are used to correct the degrees of freedom associated with the corresponding F-ratios by multiplying them by the value of the estimate. Some say the Greenhouse-Geisser correction is too conservative (strict) and recommend the Huynh-Feldt correction instead.

Question 3

Huynh-Feldt correction

Answer 3

an estimate of the departure from sphericity. The maximum value is 1 (the data completely meet the assumption of sphericity). Values below this indicate departures from sphericity and are used to correct the degrees of freedom associated with the corresponding F-ratios by multiplying them by the value of the estimate. It is less conservative than the Greenhouse-Geisser estimate, but some say it is too liberal.

Question 4

Lower bound

Answer 4

the name given to the lowest possible value of the Greenhouse-Geisser estimate of sphericity. Its value is 1/k−1, in which k is the number of treatment conditions.

Question 5

Mauchly’s test

Answer 5

a test of the assumption of sphericity. If this test is significant then the assumption of sphericity has not been met and an appropriate correction must be applied to the degrees of freedom of the F-ratio in repeated-measures ANOVA. The test works by comparing the variance-covariance matrix of the data to an identity matrix; if the variance-covariance matrix is a scalar multiple of an identity matrix then sphericity is met.

Question 6

Repeated-measures ANOVA

Answer 6

an analysis of variance conducted on any design in which the independent variable (predictor) or variables (predictors) have all been measured using the same participants in all conditions.

Question 7

Sphericity

Answer 7

a less restrictive form of compound symmetry which assumes that the variances of the differences between data taken from the same participant (or other entity being tested) are equal. This assumption is most commonly found in repeated-measures ANOVA but applies only where there are more than two points of data from the same participant. (see also Greenhouse-Geisser correction, Huynh-Feldt correction).