Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 15.5 | Alternatives to the Pearson Correlation 519
The Pearson correlation formula is then used with the converted data to compute the
phi-coefficient.
Because the assignment of numerical values is arbitrary (either category could be designated
0 or 1), the sign of the resulting correlation is meaningless. As with most correlations,
the strength of the relationship is best described by the value of r 2 , the coefficient of
determination, which measures how much of the variability in one variable is predicted or
determined by the association with the second variable.
We also should note that although the phi-coefficient can be used to assess the relationship
between two dichotomous variables, the more common statistical procedure is a chisquare
statistic, which is examined in Chapter 17.
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LEARNING CHECK
1. If the following scores are ranked, what rank is assigned to an individual with a
score of X = 7?
Scores: 1, 2, 2, 5, 6, 6, 6, 7, 10, 12
a. 5
b. 6
c. 7
d. 8
2. The Pearson and the Spearman correlations are both computed for the same set of
data. If the Spearman correlation is r S
= +1.00, then what can you conclude about
the Pearson correlation?
a. It will be positive
b. It will have a value of 1.00
c. It will be positive and have a value of 1.00
d. There is no predictable relationship between the Pearson and the Spearman
correlations
3. The effect size for the data from an independent-measures t test can be measured by
r 2 , which is the percentage of variance accounted for. The value for r 2 can also be
obtained by ____.
a. squaring the Spearman correlation for the same data
b. squaring the point-biserial correlation for the same data
c. squaring the Pearson correlation for the same data
d. None of the other options will produce r 2 .
4. In what situations can the phi-coefficient be used?
a. When an independent-measures t test would also be appropriate.
b. When both X and Y are ranks.
c. When a single-sample t test would also be appropriate.
d. When both X and Y are dichotomous.
ANSWERS
1. D, 2. A, 3. B, 4. D