The point biserial correlation coefficient is used to correlate a dichotomous variable (with two possible outcomes, like correct/incorrect) with a continuous variable (like a test score). It measures the correlation between a nominal/dichotomous variable and an interval/ratio variable. The point biserial formula calculates the mean score on a test for people who got an item correct versus incorrect, along with the standard deviation and item difficulty. The document provides an example of calculating the point biserial correlation coefficient using scores from 20 students on a math test, where their sex is the dichotomous variable and test score is the continuous variable.

1. POINT BISERIAL
CORRELATION COEFFICIENT
Used
to correlate a dichotomous
variable with a continuous variable
In testing, used to correlate a person’s
performance on an item (correct,
incorrect) with their total test score
Used as an index of item discrimination

2. Point biserial correlation coefficient

denoted by rpb , is appropriate in
measuring the correlation between a real
nominal dichotomous variable and an interval
or ratio variable.

4. Point-biserial formula
Mean on the test for
people who got item
correct
Mean on the test for Standard
people who got item deviation
incorrect
for test
IF for
item
1 – IF for
item

5. Scores 0f 20 Students in a Comprehensive Math Test
STUDENT
SEX(X)
SCORE (Y)
1
1
15
2
0
21
3
0
16
4
1
17
5
0
18
6
0
14
7
0
32
8
1
22
9
0
23
10
1
20

6. STUDENT
SEX (X)
SCORE (Y)
11
0
18
12
1
26
13
0
25
14
0
28
15
1
29
16
1
26
17
0
34
18
1
30
19
1
35
20
0
29

8. ACTIVITY
Scores 0f 20 Students in a Comprehensive Math Test
STUDENT
SEX(X)
SCORE (Y)
1
1
13
2
0
16
3
0
17
4
1
20
5
0
22
6
0
38
7
0
25
8
1
32
9
0
23
10
1
19