Repeat-measures Designs
Definition
In repeat-measures designs each subject is measured
before and one or several times after an intervention.

Examples:
In Studies of pharmacokinetics of drugs subjects may be
measured three hourly for one or more days.
In evaluating treatments for the relief of asthma FEV1
may be measured before and after intervention.

Advantages and Disadvantages of
Repeat-measures Designs
 Disadvantages
Advantages
Carry-over effect occurs when a
Each subject serves as
treatment is administered
own control so that the
before the effects of previous
variability between
treatment has worn off.
subjects gets isolated.
Avoided by allowing
Analysis can focus more
sufficient time between
treatments.
precisely on treatment
Latent effect occurs when a
effects.
treatment can activate the
Repeat-measure designs
dormant effects of a previous
are more economical
treatment.
since each subject is
Learning effect occurs in
own control and so fewer
situations where response
subjects are needed.
improves each time a person

takes a test.
Terminology



Crossover Factor. When an intervention has more than
one level and a subject gets measured on each of these
levels the intervention factor is called a crossover factor.
Crossover factors are time dependent.
Nest Factor. When subjects are in two groups and each
group is measured on just one level of the treatment
the intervention factor is called a nest factor. Nest
factors are time independent.
If research interest is focused on individual subjects the
subject factor is fixed. If subjects have been drawn
from a larger population that is the focus of interest the
subject factor is random.
Principles of Analysis - 1

Repeated-measures analysis is a generalization
of paired ‘t’ test. The only difference is that
measurements are made on the same individuals.
These are likely to be correlated, and analysis
must take such correlations into account.
Principles of Analysis

The variability between subjects is partitioned
into between subjects / within subjects.
Next the within subjects variability is partitioned
into explained by treatment / residual
(unexplained) variability.
Assumptions in Repeated-measures
Designs




Normality – Each set of data has a Normal
distribution.
Random Selection – Selection of subjects has
been random from the population of interest.
Homogeneity of variance – Different sets of
measurements have homogeneous variances.
Sphericity – Differences in measurements
between any two variables are similar to
differences between any other two.
Analysis of Co-variance (ANCOVA)
Continuous variables that are not part of the
intervention but have an influence on the
outcome variable are called covariates.
In ANOVA we assess significance by comparing
total variability against variability explained by
the intervention. In ANCOVA we try to explain
part of the “unexplained” variability in terms of
covariates.
Principles of Analysis - 2
Total Variation
Between Subject
Variation
Within Subject
variation
Between Treatment
variation
Residual
Variation
Example of Repeat-measures
analysis
A lecturer assesses teaching by means of pre-test
and post–test. The participants comprise a
mixed group of residents and research fellows.
Analysis of the data is demonstrated in the slides
that follow.
Mean Scores Pre and Post
70
75
70
65
POST_TEST
PRETEST
60
50
40
60
55
50
45
40
35
30
30
1
2
GROUP
1
2
GROUP
In general, the scores have improved for both
groups. For Group 1 from mean score of 45 to 57
and for Group 2 from mean score of 43 to 59.
Correlation between pre-test and
post-test
Scatterplot of post-test against pre-test
POST _T EST = 31.6923 + 0.654709 PRET EST
S = 5.26648
R-Sq = 60.4 %
R-Sq(adj) = 58.3 %
POST_TEST
70
60
50
30
40
50
60
70
PRETEST
There is strong correlation between pre and post tests at 0.77
Analysis of Covariance - 1
Analysis using Pre-test as covariate
Source
P
PRETEST
0.000
GROUP
0.010
Error
Total
DF
1
Seq SS
802.83
1
166.82
18
20
360.16
1329.81
Adj SS
Adj MS
F
894.91
894.91
44.73
166.82
360.16
166.82
20.01
Total sum of squares is 1329.81. Error term (unexplained) sum of
squares is 360.16p value for Group is significant at 0.01
8.34
Analysis of Covariance - 2
Analysis not using Pre-test as covariate
Source
P
GROUP
1.13
Error
Total
DF
1
0.301
19
20
Seq SS
Adj SS
74.73
74.73
1255.08
1329.81
1255.08
Adj MS
F
74.73
66.06
Total sum of squares is 1329.81. Error (unexplained) sum of squares is now
1255.08. But P value for Group is not significant