Discuss the below:
Q. Four experimenters investigated the number of items recalled in a study of short-term memory when comparing some 25 year-old participants (Y) with some 65 year-old participants (O). (Use a two-tailed test.) For this question you will be assigned data from one of these experiments on the basis of the first letter of your last name.
If your last name begins with the letters A-E use data from Experiment 1
If your last name begins with the letters F-K use data from Experiment 2
If your last name begins with the letters L-R use data from Experiment 3
If your last name begins with the letters S-Z use data from Experiment 4
Expt 1 Expt 2 Expt 3 Expt 4
Y O Y O Y O Y O
13 9 11 8 12 4 12 5
10 8 10 8 13 10 11 5
11 9 9 4 11 5 9 9
8 6 8 6 7 9 9 7
9 12 9 6 12 9 12 5
13 10 8 8 10 8 9 9
12 8 7 5 14 7 10 8
11 10 7 8 8 9 10 8
(a) Analyze the data as an independent samples design. On a standard answer sheet, state the null and alternative hypotheses in words, the critical value of t required to reject Ho, for a given value of alpha, and the appropriate degrees of freedom. Perform the calculations (using calculator or computer), and the calculations to the standard answer sheet. Make the appropriate statistical decisions, and indicate how this would be reported (include means and report effect sizes as r2). For example, "significantly more items were recalled by younger (mean=10.7) than older (mean=6.2) participants (t(14)=3.8, p<0.05, r2=0.239)".
(b) The researchers then realised that they had matched participants on sex and estimated intelligence. Analyze the same data set as a matched pairs design. On a standard answer sheet state the null and alternative hypotheses in words, the critical value of t required to reject Ho, for a given value of alpha, and the appropriate degrees of freedom. Perform the calculations (using calculator or computer), and attach the calculations to the standard answer sheet. Make the appropriate statistical decisions, and indicate how this would be reported (include means and report effect sizes as Cohen's d). For example, "there were no statistical differences in the numbers of items that were recalled by younger (mean=10.9) than older (mean=9.0) participants (t(7)=2.376, p<0.05, d=0.376)".