16. Gravetter/Wallnau/Forzano, Essentials - Chapter 14 - End-of-chapter question 16 Judge and Cable XXXXXXXXXXreport the results of a study demonstrating a negative relationship between weight and...

16. Gravetter/Wallnau/Forzano, Essentials - Chapter 14 - End-of-chapter question 16

Judge and Cable (2010) report the results of a study demonstrating a negative relationship between weight and income for a group of men. Following are data similar to those obtained in the study. To simplify the weight variable, the men are classified into five categories that measure actual weight relative to height, from 1 = thinnest to 5 = heaviest. Income figures are annual income (in thousands), rounded to the nearest $1,000.

Weight	Income
4	151
5	88
3	52
2	73
1	49
3	92
1	56
5	143

These data show a positive relationship between weight and income for a sample of men. However, weight was coded in five categories, which could be viewed as an ordinal scale rather than an interval or ratio scale. If so, a Spearman correlation is more appropriate than a Pearson correlation. Convert the weights and the incomes into ranks and complete the table that follows.

Ranks
X	Y	XY
	8
	7
	6
	5
	4
	3
	2
	1

Compute ∑X, ∑Y, ∑XY, SSXX, SSYY, SP, and the Spearman correlation for these ranks.

∑X	∑Y	∑XY	SSXX	SSYY	SP	rSS

Is this correlation statistically significant? Use a two-tailed test with α = .05.

Critical Values

df = n - 2	Level of Significance for One-Tailed Test
.05	.025	.01	.005
Level of Significance for Two-Tailed Test
.10	.05	.02	.01
1	.988	.997	.9995	.9999
2	.900	.950	.980	.990
3	.805	.878	.934	.959
4	.729	.811	.882	.917
5	.669	.754	.833	.874
6	.622	.707	.789	.834
7	.582	.666	.750	.798
8	.549	.632	.716	.765
9	.521	.602	.685	.735
10	.497	.576	.658	.708
11	.476	.553	.634	.684
12	.458	.532	.612	.661
13	.441	.514	.592	.641
14	.426	.497	.574	.623
15	.412	.482	.558	.606
16	.400	.468	.542	.590
17	.389	.456	.528	.575
18	.378	.444	.516	.561
19	.369	.433	.503	.549
20	.360	.423	.492	.537
21	.352	.413	.482	.526
22	.344	.404	.472	.515
23	.337	.396	.462	.505
24	.330	.388	.453	.496
25	.323	.381	.445	.487
26	.317	.374	.437	.479
27	.311	.367	.430	.471
28	.306	.361	.423	.463
29	.301	.355	.416	.456
30	.296	.349	.409	.449
35	.275	.325	.381	.418
40	.257	.304	.358	.393
45	.243	.288	.338	.372
50	.231	.273	.322	.354
60	.211	.250	.295	.325
70	.195	.232	.274	.302
80	.183	.217	.256	.283
90	.173	.205	.242	.267
100	.164	.195	.230	.254

Critical value of rSS =

. This relationship significant.

Jun 08, 2022

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16. Gravetter/Wallnau/Forzano, Essentials - Chapter 14 - End-of-chapter question 16 Judge and Cable XXXXXXXXXXreport the results of a study demonstrating a negative relationship between weight and...

16. Gravetter/Wallnau/Forzano, Essentials - Chapter 14 - End-of-chapter question 16

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