Advanced Statistics – Repeated Measures Designs
The Repeated Measures designs is one in which multiple measurements are carried out on the
same participants in an experiment. There are treatments which are used on each subject. This
allows us to control for variability between the experimental units so that experimental error
is reduced making us better able to detect the true differences between treatments. Repeated
Measures Designs are commonly used in experiments where there are few participants as
well as in clinical trials, education, and psychological research.
Key terms to note:
Carry-Over - effect can be defined as the effect that participation in one condition
may have on the performance under other conditions.
Fixed Factor - Factors which have levels that are set by the experimenter and remain
the same even if the experiment is repeated.
Random Factor - According to Skillings and Weber (1999), when the levels of a
factor are selected at random from a population, then the factor is a random factor.
The Repeated Measures Design is simply an experiment in which every treatment is applied
to every subject or participant at several points in time.
The Repeated Measures ANOVA tests the hypothesis that there are no differences between
the population means or that there is no treatment effect. The hypothesis statements are given
by: H0: µ1 = µ2 = … = µa where a represents the number of conditions being measured H1:
not all µ’s are equal.
Hypothesis statement for interaction:
H0: there is no significant interaction between factor A and factor B
H1: there is a significant interaction between factor A and factor B
Hypothesis statement for the Between-Subjects factor:
H0: µ1 = µ2 = … = µa where µ1 = … = µa are the means of the levels of the factor
H1: not all µ’s are equal
Hypothesis statement for the Within-Subjects factor:
H0: µ1 = µ2 = … = µb where µ1 = … = µb are the means of the levels of the factor
H1: not all µ’s are equal
The ANOVA output contains results used for analysing interaction and main effects of the
Between-Subjects and Within Subjects factors.
The Bartlett test statistic is designed to test for equality of variances across groups against
the alternative that variances are unequal for at least two groups.
The Repeated Measures designs is one in which multiple measurements are carried out on the
same participants in an experiment. There are treatments which are used on each subject. This
allows us to control for variability between the experimental units so that experimental error
is reduced making us better able to detect the true differences between treatments. Repeated
Measures Designs are commonly used in experiments where there are few participants as
well as in clinical trials, education, and psychological research.
Key terms to note:
Carry-Over - effect can be defined as the effect that participation in one condition
may have on the performance under other conditions.
Fixed Factor - Factors which have levels that are set by the experimenter and remain
the same even if the experiment is repeated.
Random Factor - According to Skillings and Weber (1999), when the levels of a
factor are selected at random from a population, then the factor is a random factor.
The Repeated Measures Design is simply an experiment in which every treatment is applied
to every subject or participant at several points in time.
The Repeated Measures ANOVA tests the hypothesis that there are no differences between
the population means or that there is no treatment effect. The hypothesis statements are given
by: H0: µ1 = µ2 = … = µa where a represents the number of conditions being measured H1:
not all µ’s are equal.
Hypothesis statement for interaction:
H0: there is no significant interaction between factor A and factor B
H1: there is a significant interaction between factor A and factor B
Hypothesis statement for the Between-Subjects factor:
H0: µ1 = µ2 = … = µa where µ1 = … = µa are the means of the levels of the factor
H1: not all µ’s are equal
Hypothesis statement for the Within-Subjects factor:
H0: µ1 = µ2 = … = µb where µ1 = … = µb are the means of the levels of the factor
H1: not all µ’s are equal
The ANOVA output contains results used for analysing interaction and main effects of the
Between-Subjects and Within Subjects factors.
The Bartlett test statistic is designed to test for equality of variances across groups against
the alternative that variances are unequal for at least two groups.
