Rank biserial
Correlation between dichotomous and ordinal variables
The rank biserial correlation is used to assess the relationship between a dichotomous categorical variable and an ordinal variable. The rank biserial test is very similar to the non-parametric Mann-Whitney U test that is used to compare two independent groups on an ordinal variable. Mann-Whitney U tests are preferable to rank biserial correlations when comparing independent groups. Rank biserial correlations can only be used with dichotomous (two levels) categorical variables. Polychotomous (three ore more levels) categorical variables cannot be analyzed using rank biserial correlations.
The Venn diagram below depicts the correlation of a categorical and an ordinal variable. Rank biserial is the correlation test used when testing the relationship between a categorical and an ordinal variable.
The steps for conducting a rank 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 dichotomous categorical outcome variable to highlight it.
6. Click on the arrow to move the variable into the Variables: box.
7. Click on the ordinal 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 dichotomous categorical outcome variable to highlight it.
6. Click on the arrow to move the variable into the Variables: box.
7. Click on the ordinal 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 rank 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 variables.
If the p-value is MORE THAN .05, then researchers have evidence that there is not a statistically significant association between the two 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 variables.
If the p-value is MORE THAN .05, then researchers have evidence that there is not a statistically significant association between the two 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 rank 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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