5. The Spearman correlation Aa Aa The rapid growth of video game popularity has

Question

5. The Spearman correlation Aa Aa The rapid growth of video game popularity has generated concern among practitioners, parents, scholars, and politicians," wrote researchers Hope M. Cummings and Elizabeth A. Vandewater. In their study, Cummings and Vandewater measured the time adolescents spent playing video games as well as time spent doing other activities, such as interacting with family and friends, reading or doing homework, or playing sports. [Source: Cummings, H., & Vandewater, E. (2007). Relation of adolescent video game play to time spent in other activities. Archives Pediatrics& Adolescent Medicine, 161(7), 684-689.] You decide to conduct a similar study among a sample of 9 teenage girls whom you have asked to keep a log of their activities for a day. You want to test whether the amount of time girls spend playing video games is correlated with the amount of time they interact with their parents. You decide to use a Spearman's correlation coefficient for rank data because some of the girls in your sample do not play video games at all, and thus your data will have many zeroes for the amount of time they play video games. The first thing you do is to convert the data to ranks. You convert the amount of time each girl plays video games by assigning the lowest rank to the five girls who don't play video games and the highest rank to those who play video games the most. The rank you assign to each of the five girls who don't play video games is 5 4.75 Hint: To deal with a tied score (such as a tie for third/fourth place), rather than arbitrarily a example, assigning one 3rd and one 4th), you divide the ranks between the tied scores sot of the scores (by assigning both a rank of 3.5) anks (for signed a mean

Explanation / Answer

The rank i assign to each of the five girls who dont play video games is (1 + 5)/2 = 3.

The rank Table

Sum Diffs

-2

1

2

-9

X Ranksrs = Cov (rx,ry)/ (XRa St. Dev. * YRa St. Dev.)

Mean: 5
Standard Dev: 2.5

Y Ranks
Mean: 5
Standard Dev: 2.73

Combined
Covariance = -23 / 8 = -2.88
R = -2.88 / (2.5 * 2.73) = -0.422

so rs = -0.4222

Video Games Parents Rank (Video Games) RV RV - M (RV) Rank (Parenets) RP RP - M(RP) d d^2

Sum Diffs

0 60 3 -2 1 -4 2 4 8 0 162 3 -2 6 1 -3 9

-2

0 221 3 -2 9 4 -6 36 -8 0 130 3 -2 4.5 -0.5 -1.5 2.25

1

0 215 3 -2 8 3 -5 25 -6 20 200 6 1 7 2 -1 1

2

33 130 7 2 4.5 -0.5 2.5 6.25 -1 82 65 8 3 2 -3 6 36

-9

126 85 9 4 3 -2 6 36 -8 sum 155.5 -23

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