udge 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.
udge 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 |
|
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|
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.
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