Quality & Quantity 34: 217–222, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Statistics Curriculum Revisited: Sequencing
Presentation of Independent Groups and
Repeated-Measures Designs as to Reﬂect Both the
Effect Size and Statistical Signiﬁcance
DAVID J. KRUS
and JAMES M. WEBB
Arizona State University, Tempe, AZ, U.S.A.;
Kent State University, Kent, OH, U.S.A.
Abstract. Eigenstructure of the variance-covariance matrix associated with the repeated-measures
t-test is used to conceptualize standard components of variance within the sequential presentation of
independent-measures and repeated-measures experimental designs.
In a recently published textbook, Heiman (1992: 355–359) well illustrated some of
the problems associated with the estimation of the effect size within the repeated
measures t-test. Heiman’s discussion revolved around the following example of a
repeated-measures t-test. Therapy outcomes of ﬁve clients suffering from arachno-
phobia were evaluated by measuring their physiological reactions of fear to a
picture of a spider. These reactions were recorded in Table 1 as a variable Y .The
parent vector X indicates whether the measures were taken before (0) or after (1)
therapy. The coding vectors X
show that the same subjects were used
for both conditions of the experiment. The symbol σ
signiﬁes true variance, not
adjusted by the degrees of freedom.
This conceptualization of the repeated-measures t-test provides both the signif-
icance and strength of the measured relationship. Including the parent vector into
the stepwise regression analysis ﬁrst, the coefﬁcient of determination r
0.253. The coefﬁcient of multiple determination R
equals 0.878 of which 0.625
was accounted for by the coding vectors X
. The standard variance of
the residual component equals 0.122. The F ratio for the main effect (0.253/0.122)
4 equals 8.31 with the t ratio equal to 2.88.
Author for correspondence: Department of Measurement, Statistics, and Methodological
Studies, 325 Payne Hall, Arizona State University, Tempe, AZ 85287-0611, U.S.A.