A study demonstrated a negative relationship between weight and income for a gro
ID: 3045676 • Letter: A
Question
A study demonstrated a negative relationship between weight and income for a group of women professionals. Judge, T. A., & Cable, D. M. (2010). When it comes to pay, do the thin win? The effect of weight on pay for men and women. Journal of Applied Psychology, 96, 95-112. doi: 10.1037/a0020860] Following are data similar to those obtained in the study. Income figures are annual income (in thousands of dollars), rounded to the nearest $1,000. Ta simplify the weight variable, the women are classified into five categories that measure actual weight relative to height, from 1 thinnest to 5 heaviest. Treating these five categories as an interval scale yielded a Pearson correlation of-0.931 If the weight categories are viewed as an ordinal scale rather than an interval or ratio scale, however, a Spearman correlation is more appropriate than a Pearson correlation. Convert the weights and the incomes into ranks and compute the Spearman correlation for these scores. Ranked Ranked Weight Subject Weight Income Income 125 49 63 35 51 93 Use one decimal place for × and , three decimal places for r, and two for the other entries. SSx SSy SP rsExplanation / Answer
Answer:
weight
income
Ranked weight
Ranked income
di
di*di
1
125
1.5
10
-8.5
72.25
2
78
3.5
7
-3.5
12.25
4
49
7.5
4
3.5
12.25
3
63
5.5
6
-0.5
0.25
5
35
9.5
1
8.5
72.25
2
84
3.5
8
-4.5
20.25
5
38
9.5
2
7.5
56.25
3
51
5.5
5
0.5
0.25
1
93
1.5
9
-7.5
56.25
4
44
7.5
3
4.5
20.25
Total
322.5
Spearman correlation = 1-6 rac{sum d^2}{n(n^2 -1}
= 1-6*322.5/(10*(10^2-1))
= -0.9545
Critical value at n-2=8 df at 0.05 level =0.632
Calculated value of correlation is higher than critical value.
The correlation is significant.
weight
income
Ranked weight
Ranked income
di
di*di
1
125
1.5
10
-8.5
72.25
2
78
3.5
7
-3.5
12.25
4
49
7.5
4
3.5
12.25
3
63
5.5
6
-0.5
0.25
5
35
9.5
1
8.5
72.25
2
84
3.5
8
-4.5
20.25
5
38
9.5
2
7.5
56.25
3
51
5.5
5
0.5
0.25
1
93
1.5
9
-7.5
56.25
4
44
7.5
3
4.5
20.25
Total
322.5
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