Analytics For Social And Behavioral Sciences Homework 11

Homework # 11 (1) A researcher was interested in the environmental effects on handedness. He measured the handedness of twins raised apart, where a positive score indicates more righthandedness and a negative score indicates more left-handedness (a score of 0 means the subject is ambidextrous). He used matched pairs of identical twins as subjects to rule out any genetic contribution to handedness scores (identical twins are the same genetically). The scores for each pair of twins are listed below. Use these data to determine if the twins differ in handedness score (indicating that environment plays a role in handedness). Use alpha = .05. (Hint: A dependent-samples t-test is appropriate here.) Handedness Scores Pair 1 2 3 4 5 6 Pair 1 2 3 4 5 6 Twin A Twin B +10 +11 -8 +3 -11 +11 +15 +10 0 +8 -4 +7 1 10 -8 -11 15 0 -4 2 11 3 11 10 8 7 Diff(12) -1 -11 -22 5 -8 -11 Mean -8 Deviation scores 7 -3 -14 13 0 -3 Step 1: H0: μD = 0. H1: μD ≠ 0 Step 2: One-sample t-test will be used, a = .05, two-tailed, df = 6 – 1 = 5. tcri = T.INV(.975, 5) = 2.571. tcri = T.INV(.025, 5) = - 2.571. Step 3: tcri = ∓2.571 If tobs > 2.571, or tobs < -2.571, reject H0. Otherwise, fail to reject H0. Step 4: SSD = 432. D́=−8 Squared Deviations 49 9 196 169 0 9 SSD = 432. √ √ SD= SS D 432 =9.295 = n−1 5 D́−μ D́ D́ −8 = = =− 2.10>−2.571 SD́ S D 9.295/ √ 6 √n Step 5: Fail to reject. t obs= Conclusion: There does not appear to be a significant difference between twins in scores on the handedness scale. (2) Each of the following sets of sample statistics comes from a within-subjects (or dependent-samples) design. Set 1: n = 10, D̄ = +4.0, sD = 10; Set 2: n = 10, D̄ = +4.0, sD = 2 Which of the two sets is more likely to reject the H0 indicating that the D = 0? Why? For Set 1: t obs= For Set 2: t obs= D́−μ D́ D́ −4 = = =1.26 S D́ S D 10/ √ 10 √n D́−μ D́ D́ −4 =6.33 = = S D́ S D 2/ √ 10 √n The set with lower standard deviation of the difference scores is more likely to be rejected. When standard error is decreased, there is a corresponding increase in tobs.