x: [[One Sample T Tests]] # Repeated measure t tests Repeated measure t tests are usually done on one sample of participants in [[Types of Experimental Design#Within Subject Design|within subject design]] where the participants experience every treatment. However, they can also be done on multiple samples using [[Types of Experimental Design#Matched Pairs Design|Matched pairs design]] and [[Types of Experimental Design#^d670d2|counterbalancing]] to avoid order effects. While repeated measures t tests reduce the variability from individual differences, they have the caveat of creating possible [[Biases of Experimental Design#Order effects|Order effects.]] Here's an example: ![[Pasted image 20221003154057.png]] ### The power of repeated measures design Repeated measure t tests measure the variability between scores with each other. The effect of this can be seen with this r computation. The treated population was gotten by adding a random small value to every score. **This means every score in the treatment is greater than its untreated score.** One hypothesis test was done with a normal t test while the other was done with a repeated measure t test. You can see the difference in p-values. ![[Pasted image 20221005150238.png]] ## How is repeated measure t testing dif than one sample t tests? T testing for the repeated measure design is essentialy done the same way as a [[One Sample T Tests]] but we use the differences between scores rather than the scores themself. Thus the t statistic value equation looks like this instead: ![[Pasted image 20221003154320.png]] When doing [[Hypothesis Testing]] the null hypothesis is slightly different from usual as instead of saying the null hypothesis is the sample mean is different from the population mean we say the differences between sample mean and population mean is zero and the alternate hypothesis is that the differences are not zero. When calculating the standard deviation and finding sum of squares we call it the sum of squares of the deviations in scores. ### Equations ![[Pasted image 20221003155143.png]] ![[Pasted image 20221003155154.png]] ### Measuring effect size for repeated measures test #### Cohen's d ![[Pasted image 20221005144904.png]] For more information on Cohen's d see [[Effect size#What is Cohen's d]]. #### r^2 The equation is the same as a one sample t test but when we report r^2 we have to say that x percentage of variability in the scores is due to the treatment or to the passage of time. #### Confidence Intervals ![[Pasted image 20221005145447.png]] Related: ___ # Resources