Explanation Given: Noncontact Athletes Contact Athletes 10 7 8 4 7 9 9 3 13 7 7 6 6 10 12 2 Formula Used: r p b = ( M Y 1 − M Y 2 S Y ) ( p q ) Calculations: First we have to convert the given data into a form suitable for the point-biserial correlation. We will have two new variables Cognitive score showing up the cognitive score of varsity athletes and Athlete type with 1 denoting noncontact athletes and 0 denoting contact athletes. Cognitive score Athlete Type 10 1 8 1 7 1 9 1 13 1 7 1 6 1 12 1 7 0 4 0 9 0 3 0 7 0 6 0 10 0 2 0 Let's denote the Cognitive score by Y and the Athlete type by X . Now to compute the point-biserial correlation, we will use the below formula: r p b = ( M Y 1 − M Y 2 S Y ) ( p q ) Where: M Y 1 = average of cognitive scores for noncontact athletes . M Y 2 = average of cognitive scores for contact athletes . p = proportion of non contact athletes . q = proportion of contact athletes . S Y = standard deviation of cognitive scores . Now let's find each of these terms: M Y 1 = 10 + 8 + 7 + 9 + 13 + 7 + 6 + 12 8 = 72 8 = 9 M Y 2 = 7+4+9+3+7+6+10+2 8 = 48 8 = 6 p = 8 16 = 0.5 q = 8 16 = 0.5 S Y = ∑ ( Y − Y ¯ ) 2 n Y ¯ = ∑ Y i n = 10+8+7+9+13+7+6+12+7+4+9+3+7+6+10+2 16 = 120 16 = 7

Statistics for The Behavioral Sciences (MindTap Course List)

10th Edition

ISBN: 9781305504912

Author: Frederick J Gravetter, Larry B. Wallnau

Publisher: Cengage Learning

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Question

Chapter 15, Problem 22P

To determine

The conversion of the data from this problem into a form suitable for the point-biserial correlation (use 1 for the noncontact athletes and 0 for the contact athletes), and then compute the correlation.
Square the value of the point-biserial correlation to verify that you obtain the same r 2 value that was computed in Chapter 10 i.e. r 2 =0.265 .

Expert Solution & Answer

Chapter 15 Solutions

Statistics for The Behavioral Sciences (MindTap Course List)

Ch. 15 - What information is provided by the sign (+ or -)...Ch. 15 - What information is provided by the numerical...Ch. 15 - Calculate SP (the sum of products of deviations)...Ch. 15 - Calculate SP (the sum of products of deviations)...Ch. 15 - For the following scores, X Y 2 7 5 4 4 7 7 5 2 6...Ch. 15 - For the following scores, X Y 0 4 2 9 1 6 1 9 a....Ch. 15 - For the following scores, X Y 4 0 1 5 1 0 4 5 a....Ch. 15 - For the following scores, X Y 3 6 5 5 6 0 6 2 5 2...Ch. 15 - With a small sample, a single point can have a...Ch. 15 - For the following scores, X Y 4 5 6 5 3 2 9 4 6 5...

Ch. 15 - Correlation studies are often used to help...Ch. 15 - In the Chapter Preview we discussed a study by...Ch. 15 - The researchers cited in the previous problem also...Ch. 15 - 14. Identifying individuals with a high risk of...Ch. 15 - 15. For a two-tailed test with =.05 , use Table...Ch. 15 - 16. As we have noted in previous chapters, even a...Ch. 15 - 17. A researcher measures three variables, X, V,...Ch. 15 - A researcher records the annual number of serious...Ch. 15 - 19. A common concern for students (and teachers)...Ch. 15 - It appears that there is a significant...Ch. 15 - Prob. 21P Ch. 15 - Prob. 22P Ch. 15 - Prob. 23P Ch. 15 - Studies have shown people with high intelligence...

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Solution Summary: The author explains how to convert the data into a form suitable for the point-biserial correlation.

Chapter 15 Solutions