Lecture 17: March 21, 2017 (Chapter 11 within subjects ttest) III. Within subjects t (Also called Paired samples, related samples, or repeated measures ttest) CHAPTER 11 A. You use it when you have an IVDV design with 2 levels in the IV and a scale DV. B. You use it when your IV involves a within subjects comparison That is, each person is tested twice and you are comparing each person to themselves (hence the name repeated measures). C. Paired samples ttests can occur in either true experiments or quasiexperiments. (Notice that zs and onesample ts are always quasi because they involve a population mean). D. Paired samples ttests use almost EXACTLY the same procedures as the onesample ttest 1. The only difference is that there is a preliminary phase Where you calculate the DIFFERENCE column (abbreviated D) based on the difference in how each person performs in each condition. *After you have the Differences, you analyze the differences instead of the raw scores. *Notice.. This is a clever way of dealing with the fact that there are no population means given to you You only have one sample that you test twice.. You will never know the true value of the population means for these two conditions BUT you know that by the null hypothesis (Ho), the DIFFERENCE between conditions will be zero! t = M D m D sMD M Mean difference between conditions observed in the sample (when each person is compared to D : themselves) m expected difference between conditions in the population if Ho is true: m is always zero! D D sMD ESTIMATED standard error of the differences between conditions (comparing each person to themselves) 2. The Hypotheses are about DIFFERENCES in the population ( )*You need to define for D yourself what you mean by differences. (Generally it is easiest if you take the right column away from the left). Example IV Time of test (Condition) .Before Treatment .After treatment DV Depression test score (Beck Inventory) Difference (D) = After treatmentBefore treatment (depression test scores) *You can also define the difference BeforeAfter, and it will be fine ***AS LONG AS YOU ARE CONSISTENT WITH YOURSELF throughout the hypothesis testing process*** *Your hypotheses are about the differences that occurred across testings in the two conditions (test times) in each individual: D = (Before treatment Depression score) (After treatment Depression score).