Question

**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:

H00 : μDD = 0

H11 : μDD ≠ 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 (MDD) | -0.8 |

Estimated population standard deviation of the differences (s) | 2.4 |

Estimated standard error of the mean differences (sMDMD) | 0.3000 |

Degrees of freedom (df) | 63 |

The t statistic | -2.67 |

The critical values of t when α = .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 α = .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 effect size.

Use r² to calculate the effect size. The r² is . This value of r² means that, on average,

% of the variability in the peripheral visual perception is explained by whether it was measured before or after playing the action video game. (Round to the nearest percent.)

Answer #1

Use Cohen’s d to calculate the effect size. The absolute value of the estimated d is 0.333 . Using Cohen’s criteria, this is a small effect size.

Use r² to calculate the effect size. The r² is 0.102 . 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

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