Point Biserial Example

A researcher wishes to determine if a significant relationship exists between the gender of the worker and if they experience pain while performing an electronics assembly task.

One question asks “What is your gender?___ male ____ female”

The second question asks “How many years have you been performing the tasks? ____ years”

The data was as follows:

Case / Gender / Number of years
1 / M / 10
2 / M / 11
3 / M / 6
4 / M / 11
5 / F / 4
6 / F / 3
7 / M / 12
8 / F / 2
9 / F / 2
10 / F / 1

Step 1: Null and Alternative Hypotheses

Ho: There is no relationship between the number of years performing the tasks and the workers’ gender.

H1: There is a significant relationship between the number of years performing the tasks and the workers’ gender.

Step 1A: Determine dependent and independent variables and their formats.

Gender is dichotomous, independent

Years performing task is ratio, dependent

Step 2: Choose test statistic

Point Biserial

Step 3: Choose Alpha Level

Use Alpha level = .05

Interpreted as “There is a 5% chance that a significant relationship really does not exist although the results indicate one does (5% chance of committing a Type I error or stated as 5% chance of rejecting the Null hypothesis when in reality it is false).

Step 4: Determine the Critical Score

For the Point Biserial Coefficient, there is a two step process. Step one is to determine the correlation coefficient amd step 2 is to determine significance using the T-Test. The critical score is determined using a T-table Table. The first column is the Degrees of Freedom and the other columns are the Alpha levels.

The degrees of freedom for the T-test is equal to the (number of cases - 2). For example, if there are 10 cases, then the DF is (10-2) = 8

Step 5A: Run the Point Biserial Test

The Point Biserial should be set up as follows:

The value .87 is interpreted as a strong correlation. The next step is to determine if it is significant.

Step 5B: Run the T-test

Step 6: Compare your score to the critical score

To interpret the .87, compare the 5.11 to the critical score. If the obtained score is greater than the critical score, reject the Null and accept the alternative. The critical score from the t-table at .05 and DF = 8 is 2.31. (NOTE: On a T-table, use the .025 column since .025 at one end and .025 at the other end gives you .05).

Since 5.11 is greater than 2.31, Reject the Null Hypothesis and conclude there is a significant relationship between gender and the number of years working at the task..

Step 7: Conclusions

There is a significant relationship between the genders of the workers the number of years performing the task. Both males have been performing the task significantly longer than females.