ANOVA repeated measures
ANOVA repeated measures design
What are ANOVA repeated measures statistical designs? In ANOVA repeated measures statistical designs subjects and given the treatments of the experiments more than once in succession. in these designs we have more than one score for each subject.Example A researcher that wants to test four different drugs for their possible effect on body temperature uses a single group of subjects rather than four groups. He will give them Drug 1, wait for a week, then give Drug 2, wait for a week, give Drug 3, wait for a week, then give Drug 4.The difference of repeated measures designs as compared to independent groups designs can be best illustrated by giving the layout of each.
The layout of independent groups ANOVA
Treatment1 | Treatment2 | Treatment3 | Treatment4 |
---|---|---|---|
Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 |
Subject 6 Subject 7 Subject 8 Subject 9 Subject 10 |
Subject 11 Subject 12 Subject 13 Subject 14 Subject 15 |
Subject 16 Subject 17 Subject 18 Subject 19 Subject 20 |
The layout of repeated measures ANOVA
Subj | Treatment1 | Treatment2 | Treatment3 | Treatment4 |
---|---|---|---|---|
1 2 3 4 5 6 7 8 9 10 |
X Subject 1 X Subject 2 X Subject 3 X Subject 4 X Subject 5 X Subject 6 X Subject 7 X Subject 8 X Subject 9 XSubject10 |
X Subject 1 X Subject 2 X Subject 3 X Subject 4 X Subject 5 X Subject 6 X Subject 7 X Subject 8 X Subject 9 XSubject10 |
X Subject 1 X Subject 2 X Subject 3 X Subject 4 X Subject 5 X Subject 6 X Subject 7 X Subject 8 X Subject 9 XSubjet10 |
X Subject1 X Subject2 X Subject3 X Subject4 X Subject5 X Subject6 X Subject7 X Subject8 X Subject9 XSubjct10 |
FORMAT OF REPEATED MEASURES ANOVA SUMMARY TABLE
SOURCE1 | SS | df | MS | F | p |
---|---|---|---|---|---|
Between Treatments | |||||
Between Rows | |||||
Error | |||||
Totalr |
ANOVA repeated measures - formula
The formula for Anova repeated measures experiments is the formula for variance The final step in the analysis of our data is the F ratio, which is variance of the data in particular ways. $$F={{MS_{between}} \over {MS_{within}}}$$ANOVA repeated measures- practice example
An experimenter wanted to test four new Drugs for their effect on body temperature. He randomly selected six subjects and gave them Drug 1. He waited for one hour and then he measured the temperature of each subject using a Celsius thermometer. He recorded the data. On week later he gave these subjects Drug 2. He waited for one hour and measured the temperature of each subject. A week later he gave these subjects Drug 3 One hour later he measured their temperature One week later he gave these same subjects Drug 4. He waited for one hour and then he measured their temperature. The data are presented in the table below.Subjects | Treatment 1 | Treatment 2 | Treatment 3 | Treatment 4 |
---|---|---|---|---|
1 2 3 4 5 6 |
36.5 36.8 35.4 35.6 36.5 36.4 |
36.2 36.4 36.6 36.4 36.3 36.2 |
36.9 36.8 37.7 37.3 37.9 37.1 |
36.9 37.8 37.7 37.5 37.9 37.6 |
REPEATED MEASURES ANOVA SUMMARY TABLE
SOURCE | SS | df | MS | F | p |
---|---|---|---|---|---|
Between Treatments | 8.2433 | 3 | 2.7478 | 15.84241 | <0.05 |
Between Rows | 3.2967 | 5 | 3.2967 | ||
Error | 2.6017 | 15 | 0.1734 | ||
Totalr | 23 |
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