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