You decide to use the Spearman correlation for the data. The first thing you do

Question

You decide to use the Spearman correlation for the data. The first thing you do is convert the data to ranks. You convert the amount of time each girl plays video games by assigning the lowest rank to the seven 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 seven girls who don't play video games is ____. The following table consists of the data for the 11 girls in your study. The data are sorted in order of the amount of time the girls spent playing video games. Fill in the missing ranks for the time spent playing video games and the ranks for the time spent watching television. Note that the time spent watching television is not sorted in order. Using your completed table, you can calculate the Spearman correlation in two different ways. One way is to use the Pearson correlation formula on the ranks of the data. When you do this, you get r_s = 0.28. The second way to calculate the Spearman correlation is to use the following formula: r_s = 1 - 6 sigma D^2/n(n^2 - 1) In this formula, D represents the difference between ranks for each individual. Using this formula, you get r_a = 0.37. These two estimates of the Spearman correlation are different for the following reason: The Pearson correlation formula applied to the ranks loses accuracy when there are many ties. The formula that uses the differences (D) loses accuracy when there are many ties. The formula that uses the differences (D) is always only a rough estimate of r_s. You do not use pearson correlation formula when calculating the spearman correlation.

Explanation / Answer

(a)

The rank assigned to each of the 7 girls who dont play video games is: (1+2+3+4+5+6+7)/7 = 4

(b)

(c) The two estimates of the Spearman Rank Correlation are different for the following reason:

The pearson correlation formula applied to the ranks looses accuracy when there are many ties.

Time Spent Playing Video Games(Minutes/Day) Time Spent Watching Television (Minutes/Day) Rank of the Time Spent Playing Video Games Rank of Time Spent Watching Television 0 90 4 9 0 60 4 7 0 50 4 6 0 0 4 2   [(1+2+3)/3] 0 0 4 2   [(1+2+3)/3] 0 100 4 10 0 30 4 4 20 0 8 2 [(1+2+3)/3] 33 45 9 5 82 65 10 8 126 110 11 11

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