1. Assignment for Chapter 11 (Related samples t-test) The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n = 8 participants before and after they receive the treatment. Participant Before 2. 3. 4. After 1 85 88 2 66 67 3 73 76 4 68 71 5 77 75 6 85 81 7 60 62 8 88 92 a. b. C. d. Calculate the difference scores and MD. Compute sample variance of the difference scores and the estimated standard error. Compute the repeated measures t-test. Report the degrees of freedom and the value of the t. Using a two-tailed test with α = .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) The stimulant, Ritalin, has been shown to increase attention span and improve academic performance in children with ADHD. To demonstrate the effectiveness of the drug, a researcher selects a sample of n = 12 children diagnosed with the disorder and measures each child's attention span of MD = 6 minutes with a variance of s² = 108 for the sample of difference scores. Compute the repeated measures t-test. Report the degrees of freedom and the value of the t. a. b. C. Using a one-tailed test with a = .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) Compute the 90% confidence interval for the mean change in attention span for the population. A sample of difference scores from a repeated-measures experiment has a mean of MD = 3.5 with a standard deviation of s = 8. a. b. Assume that n = 16. Compute the repeated measures t. Is a sample of n = 16 sufficient to reject the null hypothesis using a two-tailed test with α = .05? C. d. e. Assume that n = 25. Compute the repeated measures t. Is a sample of n = 25 sufficient to reject the null hypothesis using a two-tailed test with α = .05? Explain how the size of the sample influences the likelihood of finding a significant mean difference. Researchers were interested in determining if swearing affects the amount of pain you feel. In their study, participants were asked to place one hand in icy cold water for as long as they could bear the pain. Half of the participants were told to repeat a neutral word over and over for as long as their hands were in the water. For the remaining participants, participants were told to repeat a swear word over and over for as long as their hands were in the water. The data are listed below: (larger numbers indicate greater pain) Swear Word 9 Neutral Word 6 6 5 5 3 8 5 12 9 10 7 7 4 11 10 2 5. a. b. C. d. 7 Treat the data as if the scores are from an independent measures (between-subjects) study using two separate samples, each with n = 9 participants. Compute and report the pooled variance, the estimated standard error for the mean difference, and the independent-measures t-test. Using a two-tailed test with a = .05, would you reject the null or fail to reject the null? Now assume that the data are from a repeated-measures study using the same sample of n = 9 participants in both treatment conditions. Compute and report the variance for the sample of difference scores, the estimated standard error for the mean difference, and the repeated-measures t-test. Using a two-tailed test with a = .05, would you reject the null or fail to reject the null? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting the null hypothesis.) Gamification refers to the application of game design and development to social, industrial, and educational settings. A recent experiment on gamification in the workplace revealed that machinists' motivation to work improved when they were given feedback about their job performance through a game-like smartphone app. The data are below: Motivation before Motivation after 6 8 2 3 6 4 9 11 6 9 8 11 6 9 7 a. b. 3 Compute the repeated measures t-test. Report the degrees of freedom and the value of the t. Using a two-tailed test with a = .05, would you reject or fail to reject the null hypothesis? C. Compute Cohen's d to measure the size of the treatment effect.