Lecture 5 - repeated measures ANOVA Flashcards
When do you use a single factor repeated measures ANOVA?
When you have one independent variable with two or more levels, each produced by same group of people
Want to know if the means are really different or if the differences can be explained by error variability
Why do we need to treat our between subjects data differently from our repeated measures data?
The amount of error we would expect to find in the data is affected by whether we are testing the same repeatedly or different groups of people and need to take this into account when calculating our error term
What error term do we use for repeated measures?
Residual error
What error term do we use for between subjects?
Within treatments variance
In addition to random variation, what error variability does a between subjects ANOVA take into account?
Individual differences
Because of this we expect more error
What is the f ratio in a between subjects design?
Treatment effects + (experimental error + individual differences) Divided by (experimental error + individual differences)
What is the between treatment variance in a repeated measures design?
Treatment effects + experimental error only
What is the f ratio for a repeated measures ANOVA?
Experimental error divided by experimental error and individual differences
Why is a repeated measures ANOVA unbalanced?
It overestimates the total error variance. We need to subtract an estimate of the individual differences from the denominator
How do we calculate error in a repeated measures ANOVA?
Calculate within treatment variance
Find an estimate of individual differences and minus this out (subjects variance = individual differences only)
(Residual error = experimental error only)
How do you work out residual error SS?
Within treatments SS - subjects SS
How do you work out the residual error df?
Within treatments df - subjects df
How do you work out Residual error MS?
Residual error SS divided by Residual Error df
What is the f ratio for repeated measures?
Between treatments MS divided by residual error MS
Between treatment variance can be found where?
Treatment effects + error variability
Residual error variance can be found where?
Error variability
How do you hypothesis test in a repeated measures ANOVA?
Work out variability between the means predicted by the null hypothesis - how much expected if null is true measured by residual error
Compare obtained variability with this variability expected due to error
If this is 5% or less we reject null and support experimental
What is the f ratio for a between subjects ANOVA?
Between treatment variability divided by within treatment variability
How do you work out a repeated measures ANOVA f ratio?
Between treatment variability divided by residual error variability
How do you work out the between treatments variance in a within subjects ANOVA?
MSbtw = SSbtw (sum of squares btw) divided by df btw (degrees of freedom btw)
How do you work out the residual error variance in a within subjects ANOVA?
MSres = SSres (sum of squares residual error) divided by DFres (degrees of freedom residual error)
Why are repeated measures ANOVA’s considered more powerful?
Because they eliminate a large source of variability - smaller error term than between subjects test
What does the term between treatment mean?
That is our observed variance
What does within treatment variability in a between subjects ANOVA mean?
It is the error term and includes error variance due to individual differences
What does residual error variability mean in a repeated measures ANOVA?
It is an error term with experimental error only. Found by “minusing out” individual difference error (subject variability)
