## 7. Measures of Effect Size for the Repeated-Measures tPrevious studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of the screen (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For his study, he selects a random sample of 64 adults. The subjects complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-person combat simulation) for 1 hour a day over 10 days, they complete the difficult perception task for a second time.Before playing the action video game, the mean score in their accuracy on the spatial task was 0.42. After playing the action video game, the mean score was 0.8 lower.The graduate student has no presupposed assumptions about whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone, so he formulates the null and alternative hypotheses as:- Null Hypothesis (\(H_0\)): \(\mu_D = 0\)- Alternative Hypothesis (\(H_1\)): \(\mu_D \neq 0\)Assume that the data satisfy all of the required assumptions for a repeated-measures t test. The graduate student calculates the following statistics for his hypothesis test:- **Mean difference (\(M_D\))**: -0.8- **Estimated population standard deviation of the differences (\(s\))**: 2.4- **Estimated standard error of the mean differences (\(S_{M_D}\))**: 0.300- **Degrees of freedom (df)**: 63- **The t statistic**: -2.67- **The critical values of t when \(\alpha = .05\)**: \(\pm1.998\)### Explanation of the Graph/TableThe table provided gives key statistical outcomes from a repeated-measures t test. It highlights the observed mean difference in scores before and after playing the video game, estimates of variability in these differences, and the resulting t statistic, which is compared against critical values to determine significance. Notice that since the t statistic (-2.67) is in the critical region (\(t < -1.998\) or \(t **Hypothesis Testing with a Repeated-Measures t Test**In this example, a graduate student is conducting a repeated-measures t test to determine the significance of their hypothesis. The hypotheses are as follows:- \( H_0: \mu_D = 0 \)- \( H_1: \mu_D \neq 0 \)**Assumptions:**The data satisfy all required assumptions for a repeated-measures t test. The following statistics are calculated:- **Mean Difference (\( M_D \)):** -0.8- **Estimated Population Standard Deviation of the Differences (\( s \)):** 2.4- **Estimated Standard Error of the Mean Differences (\( S_{MD} \)):** 0.3000- **Degrees of Freedom (df):** 53- **t Statistic:** -2.67- **Critical Values of t when \( \alpha = 0.05 \):** ±1.998**Analysis:**Since the t statistic (-2.67) falls within the critical region (t < -1.998 or t > 1.998), the hypothesis test is significant at \( \alpha = 0.05 \).**Tasks:**1. **95% Confidence Interval for the Mean Difference:** - Calculate and provide the interval.2. **Effect Size Calculation:** - **Cohen’s d:** - Calculate the absolute value of estimated d. - Determine and describe the effect size using Cohen’s criteria. - **r² (r-squared):** - Calculate r². - Explain that this value represents the percentage of variability in peripheral visual perception explained by whether it was measured before or after playing the action video game. Round to the nearest percent.

Solution: Given information: Mean difference = MD = -0.8Standard deviation of the difference = sD=2.4Standard error of the mean diffrence = SMD= 0.30Degrees of freedom =df = 63Test statistic t= -2.67Critical value =tc = ±1.998 The 95% confidence interval for the mean difference is MD±tc×SMD( -0.8±1.998×0.30)(- 0.8±0.5994)(-0.8- 0.5994, -0.8+0.5994)(-1.3994, - 0.2006) The 95% confidence interval for the mean difference is ( -1.3994, -0.2006) To find the effect size d d = MDsDd =-0.82.4d = -0.3333d=0.3333 The absolute value of the effect size is 0.3333 This is a small effect size. To find r2 r2= t2t2+df r2= (-2.67)2(-2.67)2+63r2= 7.12897.1289+63r2= 7.128970.1289r2= 0.101654r2= 0.10 The value of r2 is 0.10. This value of r2 means that on average 10% of the variability in the peripheral visual perception is explained by whether it was measured before or after playing the action video game.

Math

Statistics

7. Measures of effect size for the repeated-measures t Previous studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of the screen (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For his study, he selects a random sample of 64 adults. The subjects complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-person combat simulation) for 1 hour a day over 10 days, they complete the difficult perception task for a second time. Before playing the action video game, the mean score in their accuracy on the spatial task was 0.42. After playing the action video game, the mean score was 0.8 lower. The graduate student has no presupposed assumptions about whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone, so he formulates the null and alternative hypotheses as: Ho : Pp = 0 H: Pp * 0 Assume that the data satisfy all of the required assumptions for a repeated-measures t test. The graduate student calculates the following statistics for his hypothesis test: Mean difference (Mp) -0.8 Estimated population standard deviation of the differences (s) 2.4 Estimated standard error of the mean differences (SMp) 0.3000 Degrees of freedom (df) 63 The t statistic -2.67 The critical values of t when a = ,05 +1.998 Notice that since the t statistic (-2.67) is in the critical region (t < -1.998 or t > 1.998), the hypothesis test is significant when a = .05. A 95% confidence interval for the mean difference is Use Cohen's d to calculate the effect size. The absolute value of the estimated d is Using Cohen's criteria, this is a v effect size. Use r2 to calculate the effect size. The r2 is This value of r? means that, on average, % of the variability in the peripheral visual