MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Zhou and Vohs (2009) published a study showing that handling money reduces the perception of pain. In the experiment, a group of college students was told that they were participating in a manual dexterity study. Half of the students were given a stack of money to count and the other half got a stack of blank pieces of paper. After the counting task, the participants were asked to dip their hands into bowls of very hot water (122° F) and rate how uncomfortable it was. The following data show ratings of pain similar to the results obtained in the study.
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Counting Money
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Counting Paper
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|---|---|
| 7 | 9 |
| 8 | 11 |
| 10 | 13 |
| 6 | 10 |
| 8 | 11 |
| 5 | 9 |
| 7 | 15 |
| 12 | 14 |
| 5 | 10 |
Convert the data from this problem into a form suitable for the point-biserial correlation (use Y = 1 for the money and 0 for the plain paper), and then compute the correlation.
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∑X
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∑Y
|
∑XY
|
SSXX
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SSYY
|
SP
|
r
|
|---|---|---|---|---|---|---|
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|
|
|
|
|
|
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Square the value of the point-biserial correlation to obtain r².
r² =
An independent-samples t test for the difference between the means of the two groups produced t = 3.573 with df = 16. Use the equation you learned for r² in connection with t tests to obtain r² directly from the t statistic and its df.
r² =
Within rounding error, this value of r² should be equal to the value obtained from the point-biserial correlation.
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