Point biserial
Correlation between continuous and categorical variables
The point biserial correlation is used to assess the relationship between a continuous variable and a categorical variable. The point biserial correlation is very similar to the independent samples t-test. Indeed, the p-value yielded from a point biserial correlation will be the exact same as the p-value for an independent samples t-test if the two tests are performed on the same sample. Categorical variables that have more than two levels (polychotomous) cannot be analyzed using a point biserial correlation. Only dichotomous (two levels) categorical variables can be analyzed using the point biserial correlation.
The Venn diagram below depicts the correlation of a categorical and a continuous variable. Point biserial is the correlation test used when testing the relationship between a categorical and a continuous variable.
The steps for conducting a point biserial correlation in SPSS
1. The data is entered in a within-subjects fashion.
2. Click Analyze.
3. Drag the cursor over the Correlate drop-down menu.
4. Click on Bivariate.
5. Click on the continuous outcome variable to highlight it.
6. Click on the arrow to move the variable into the Variables: box.
7. Click on the dichotomous categorical outcome variable to highlight it.
8. Click on the arrow to move the variable into the Variables: box.
9. Click OK.
2. Click Analyze.
3. Drag the cursor over the Correlate drop-down menu.
4. Click on Bivariate.
5. Click on the continuous outcome variable to highlight it.
6. Click on the arrow to move the variable into the Variables: box.
7. Click on the dichotomous categorical outcome variable to highlight it.
8. Click on the arrow to move the variable into the Variables: box.
9. Click OK.
The steps for interpreting the SPSS output for a point biserial correlation
1. In the Correlations table, match the row to the column between the two continuous variables. The Pearson Correlation is the actual correlation value that denotes magnitude and direction, the Sig. (2-tailed) is the p-value that is interpreted, and the N is the number of observations that were correlated.
If the p-value is LESS THAN .05, then researchers have evidence of a statistically significant bivariate association between the two continuous variables.
If the p-value is MORE THAN .05, then researchers have evidence that there is not a statistically significant association between the two continuous variables.
Higher coefficients denote a stronger magnitude of relationship between variables. Smaller coefficients denote weaker relationships.
Positive correlations denote a relationship that travels at the same trajectory. As one value goes up, then the other value goes up. Also, as one value goes down, then the other value goes down too.
Negative correlations denote a relationship that travels in different directions. As one value goes up, the other value goes down. Also, as one value goes down, then the other value goes up.
If the p-value is LESS THAN .05, then researchers have evidence of a statistically significant bivariate association between the two continuous variables.
If the p-value is MORE THAN .05, then researchers have evidence that there is not a statistically significant association between the two continuous variables.
Higher coefficients denote a stronger magnitude of relationship between variables. Smaller coefficients denote weaker relationships.
Positive correlations denote a relationship that travels at the same trajectory. As one value goes up, then the other value goes up. Also, as one value goes down, then the other value goes down too.
Negative correlations denote a relationship that travels in different directions. As one value goes up, the other value goes down. Also, as one value goes down, then the other value goes up.
Click on the Download Database and Download Data Dictionary buttons for a pre-configured database and data dictionary for point biserial. Click on the Adjusing for Multiple Comparisons button to learn more about Bonferroni, Tukey's HSD, and Scheffe's test. Click on the Validation of Statistical Findings button to learn more about bootstrap, split-group, and jack-knife validation methods.
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