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 81 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 0.31. After playing the action video game, the mean score was 0.35. The mean of the differences between each person’s pre- and post- scores was 0.04, with a standard deviation of the differences equal to 0.08. 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: H₀: μDD = 0 H₁: μDD ≠ 0 He uses a repeated-measures t test. Because the sample size is large, if the null hypothesis is true as an equality, the test statistic follows a t-distribution with n – 1 = 81 – 1 = 80 degrees of freedom. t Distribution Degrees of Freedom = 75 -4.0-3.0-2.0-1.00.01.02.03.04.0t This is a test. Use the Distributions tool to find the critical score(s) for the level of significance α = 0.05. The critical score(s) (the value(s) for t that separate(s) the tail(s) from the main body of the distribution, forming the critical region) is/are . To calculate the test statistic, you first need to calculate the estimated standard error under the assumption that the null hypothesis is true. The estimated standard error is . The test statistic is t = . Use the tool to evaluate the null hypothesis. (Note: You can place the purple line on your t statistic to tell whether it lies within or outside the critical region. It’s possible that this line may not rest exactly on the t statistic, but you will be able to tell whether it lies within or outside the critical region.) The t statistic in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is . The graduate student conclude that playing video games alters peripheral visual perception. The graduate student repeats his study with another random sample of the same size. This time, instead of the treatment being playing the combat simulation video game, the treatment is playing a soccer video game. Suppose the results are very similar. After playing a soccer video game, the mean score was still 0.04 higher, but this time the standard deviation of the difference was 0.10 (vs. the original standard deviation of 0.08). This means has the more consistent treatment effect. This difference in the standard deviation also means that a 95% confidence interval of the mean difference would be for the original study, when the treatment was playing the combat simulation video game, than the 95% confidence interval of the mean difference for the second study, when the treatment was playing a soccer video game. Finally, this difference in the standard deviation means that when the graduate student conducts a hypothesis test testing whether the mean difference is zero for the second study, he will be likely to reject the null hypothesis than he was for the hypothesis test you completed previously for the original study.

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 81 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 0.31. After playing the action video game, the mean score was 0.35. The mean of the differences between each person’s pre- and post- scores was 0.04, with a standard deviation of the differences equal to 0.08. 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: H₀: μDD = 0 H₁: μDD ≠ 0 He uses a repeated-measures t test. Because the sample size is large, if the null hypothesis is true as an equality, the test statistic follows a t-distribution with n – 1 = 81 – 1 = 80 degrees of freedom. t Distribution Degrees of Freedom = 75 -4.0-3.0-2.0-1.00.01.02.03.04.0t This is a test. Use the Distributions tool to find the critical score(s) for the level of significance α = 0.05. The critical score(s) (the value(s) for t that separate(s) the tail(s) from the main body of the distribution, forming the critical region) is/are . To calculate the test statistic, you first need to calculate the estimated standard error under the assumption that the null hypothesis is true. The estimated standard error is . The test statistic is t = . Use the tool to evaluate the null hypothesis. (Note: You can place the purple line on your t statistic to tell whether it lies within or outside the critical region. It’s possible that this line may not rest exactly on the t statistic, but you will be able to tell whether it lies within or outside the critical region.) The t statistic in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is . The graduate student conclude that playing video games alters peripheral visual perception. The graduate student repeats his study with another random sample of the same size. This time, instead of the treatment being playing the combat simulation video game, the treatment is playing a soccer video game. Suppose the results are very similar. After playing a soccer video game, the mean score was still 0.04 higher, but this time the standard deviation of the difference was 0.10 (vs. the original standard deviation of 0.08). This means has the more consistent treatment effect. This difference in the standard deviation also means that a 95% confidence interval of the mean difference would be for the original study, when the treatment was playing the combat simulation video game, than the 95% confidence interval of the mean difference for the second study, when the treatment was playing a soccer video game. Finally, this difference in the standard deviation means that when the graduate student conducts a hypothesis test testing whether the mean difference is zero for the second study, he will be likely to reject the null hypothesis than he was for the hypothesis test you completed previously for the original study.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5. A two-tailed hypothesis test for a repeated-measures research design

Before playing the action video game, the mean score in their accuracy on the spatial task was 0.31. After playing the action video game, the mean score was 0.35. The mean of the differences between each person’s pre- and post- scores was 0.04, with a standard deviation of the differences equal to 0.08.

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:

	H₀: μDD = 0
	H₁: μDD ≠ 0

He uses a repeated-measures t test. Because the sample size is large, if the null hypothesis is true as an equality, the test statistic follows a t-distribution with n – 1 = 81 – 1 = 80 degrees of freedom.

t Distribution

Degrees of Freedom = 75

-4.0-3.0-2.0-1.00.01.02.03.04.0t

This is a test. Use the Distributions tool to find the critical score(s) for the level of significance α = 0.05.

The critical score(s) (the value(s) for t that separate(s) the tail(s) from the main body of the distribution, forming the critical region) is/are .

To calculate the test statistic, you first need to calculate the estimated standard error under the assumption that the null hypothesis is true. The estimated standard error is .

The test statistic is t = .

Use the tool to evaluate the null hypothesis. (Note: You can place the purple line on your t statistic to tell whether it lies within or outside the critical region. It’s possible that this line may not rest exactly on the t statistic, but you will be able to tell whether it lies within or outside the critical region.) The t statistic in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is . The graduate student conclude that playing video games alters peripheral visual perception.

The graduate student repeats his study with another random sample of the same size. This time, instead of the treatment being playing the combat simulation video game, the treatment is playing a soccer video game. Suppose the results are very similar. After playing a soccer video game, the mean score was still 0.04 higher, but this time the standard deviation of the difference was 0.10 (vs. the original standard deviation of 0.08). This means has the more consistent treatment effect.

This difference in the standard deviation also means that a 95% confidence interval of the mean difference would be for the original study, when the treatment was playing the combat simulation video game, than the 95% confidence interval of the mean difference for the second study, when the treatment was playing a soccer video game.

Finally, this difference in the standard deviation means that when the graduate student conducts a hypothesis test testing whether the mean difference is zero for the second study, he will be likely to reject the null hypothesis than he was for the hypothesis test you completed previously for the original study.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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