Point-biserial correlation coefficients |
James Dean Brown University of Hawai'i at Manoa |
[ p. 12 ]
Table 1. Types of Correlation Coefficients | |
Correlation Coefficient | Types of Scales |
Pearson product-moment | Both scales interval (or ratio) |
Spearman rank-order | Both scales ordinal |
Phi | Both scales are naturally dichotomous (nominal) |
Tetrachoric | Both scales are artificially dichotomous (nominal) |
Point-biserial | One scale naturally dichotomous (nominal), one scale interval (or ratio) |
Biserial | One scale artificially dichotomous (nominal), one scale interval (or ratio) |
Gamma | One scale nominal, one scale ordinal |
[ p. 13 ]
Table 2. Example Student Data | |||||
Student | Item 1 | Item 2 | Item 3 | Item 4, 5, 6... | Total Score |
Hachiko | 1 | 0 | 1 | . . . | 50 |
Kazuko | 1 | 0 | 1 | . . . | 45 |
Toshi | 1 | 0 | 1 | . . . | 45 |
Yoshi | 1 | 0 | 1 | . . . | 40 |
Tomoko | 0 | 1 | 1 | . . . | 35 |
Yasuhiro | 0 | 1 | 1 | . . . | 30 |
Yuichi | 0 | 1 | 1 | . . . | 30 |
Masa | 0 | 1 | 1 | . . . | 25 |
Mp | 45 | 30 | 37.5 | Total mean | 37.50 |
Mq | 30 | 45 | .00 | Standard Deviation | 8.29 |
p | .50 | .50 | 1.00 | ||
q | .50 | .50 | .50 | .00 | |
rpbi | .91 | -.91 | .00 |
[ p. 14 ]
Where:rpbi = | point-biserial correlation coefficient |
Mp = | whole-test mean for students answering item correctly (i.e., those coded as 1s) |
Mq = | whole-test mean for students answering item incorrectly (i.e., those coded as 0s) |
St = | standard deviation for whole test |
p = | proportion of students answering correctly (i.e., those coded as 1s) |
q = | proportion of students answering incorrectly (i.e., those coded as 0s) |
[ p. 15 ]
Table 3. Example Item Analysis (for 32 students) |
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Item # | IF | rpbi | * = p < .05 | |
1 | 0.930 | 0.153 | ||
2 | 0.656 | 0.295 | * | |
3 | 0.882 | 0.122 | ||
4 | 0.738 | 0.189 | ||
5 | 0.455 | 0.310 | * | |
6 | 0.838 | 0.394 | * | |
7 | 0.684 | 0.469 | * | |
8 | 0.552 | 0.231 | ||
9 | 0.581 | 0.375 | * | |
10 | 0.398 | 0.399 | * | |
11 | 0.926 | 0.468 | * | |
12 | 0.774 | 0.468 | * | |
13 | 0.663 | 0.414 | * | |
14 | 0.862 | 0.276 | ||
15 | 0.624 | 0.205 |
[ p. 16 ]