Psych 311 1nd Edition Lecture 17 Outline of Last Lecture I Independent Sample T Test Activity Outline of Current Lecture I Repeated Measures T Test II Repeated Measures T Test Example III When to Use Which Hypothesis Test Current Lecture I Repeated Measures T Test Repeated measures same group measured dependent variable twice once before we administer IV pretest measure and once after posttest measure This test allows us to see if the difference we see is due to our IV or SE we can see this difference in the scores from pretest to posttest if the difference we observe far exceeds the difference we see due to SE we can be confident that our IV had an effect Benefits of measuring same group twice can use fewer subjects sample serves as its own control group eliminates discrepancy between samples due to SE because you use one sample Because we use sample twice we compute a differences score for each participant Differences score D X2 X1 D posttest pretest if our D is a positive number than the scores increased from pre to posttest if our D is negative then our scores decreased from pre to posttest Example n 4 Participant X1 X2 D X2 X1 A 8 4 4 B 6 4 2 C 5 3 2 D 6 5 1 MD 2 25 When we average D we see an average of how much scores change from pre to posttest II Repeated Measures T Test Example A psychologish is interested in knowing whether relaxation training has an effect on stress levels The psychologist measured n 16 and gives them a stress test before and after training On average the stress test scores decreased by 6 points MD 6 00 ssD 960 from pre to posttest Possible explanations for 6 point decrease Ho due to SE H1 due to relaxation training IV Step 1 Ho D 0 H1 D 0 two tailed test 0 05 Step 2 df nD 1 df 15 critical region 2 131 Step 3 a Compute estimated standard error measure of SE S 2D ssD nD 1 SMD S 2D nD S 2D 960 15 SMD 64 16 S 2D 64 SMD 8 4 SMD 2 b Compute t t MD SMD t 6 2 t 3 00 Step 4 We reject our Ho in favor of H1 because our t 3 00 which is within our critical region Step 5 Cohen s d lMDl s d l 6l 8 d 6 8 d 0 75 large effect size III When to Use Which Hypothesis Test Test Stat Z test Use when We know and Ho M H1 2tailed M Observed SE dif numerator numerator M M Df Cohen s d Comparison Reference distribution NA lM l Standard error Sampling Distribution Use UNT 1tailed M or M Single Sample ttest Independen t Sample t When you find from theory and estimate from s use 1 sample M When we 1don t 2tailed M M n 1 lM l Estimated Standard Error 1tailed M or M 2tailed sM M1 M2 s M1 M2 t distribution use t table n1 1 n2 1 lM1 t distribution test know and 2 0 Compare 2 separate samples Repeated Measures ttest Don t know and compare same group twice 1 2 0 1tailed 1 2 0 or 1 2 0 D 0 2tailed D 0 1tailed D 0 or D 0 MD Estimated Standard Error df df1df2 M2l s use t table SMD nD 1 lMDl s t distribution Estimated Standard Error use t table Data nadd 8 nno add 4 Madd 50 Mno add 42 SSadd 108 SSno add 100 State Hypothesis two tailed H0 Madd Mnoadd 0 H1 Madd Mnoadd 0 Determine Critical Region two tailed 05 Critical region is 2 228 Calculate pooled variance s 2p ss1 ss2 df1 df2 s 2p 108 100 7 3 s 2p 208 10 s 2p 20 8 Calculate standard error s M1 M2 s 2p n1 s 2p n2 s M1 M2 20 8 8 20 8 4 s M1 M2 2 6 5 2 s M1 M2 7 8 s M1 M2 2 79 Calculate t t Madd Mnoadd s M1 M2 t 50 42 2 79 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute t 8 2 79 t 2 87 Make a decision We reject our Ho in favor of the H1 Calculate Cohen s d d lM1 M2l s 2p d l50 42l 20 8 d 8 4 56 d 1 75 Conclusion We should reject our Ho in favor of H1 and can conclude that the additional tests did make a statistically significant difference and had improved the adult s retention of high school algebra