It makes sense to compute a Pearson correlation between a binary (dichotomous) variable and a continuous variable. This is equal to a point-biserial correlation.

However, it doesn't make sense to compute a Pearson correlation between a polytomous nominal variable (such as your 3-category gender variable) and a continuous variable because the order of the categories is arbitrary and you would get a different result depending on the (arbitrary) coding of the 3 categories.

You could instead use eta-squared based on a one-way ANOVA as a measure of effect size (squared correlation) for that relationship. It would give you the proportion of variability in the continuous variable that is accounted for by group differences.

Christian Geiser That makes far more sense than what I was trying to do, thank you so much!! So a larger eta-squared value would suggest a higher relationship between my measure of gender and procrastination?

Going back to your initial point at the start if I recoded gender into 3 new dichotomous variables (Male:Female // Male:Non-Binary // Female:Non:Binary) and ran correlation analyses for procrastination using them would that also be an appropriate procedure?

Cormac Monaghan Yes, higher eta-squared means a stronger association. Like R-squared, eta-squared varies between 0 (no association) and 1 (100% variability accounted for).

Your proposed correlation procedure with 3 dichotomous variables may be fine, but it sounds somewhat tedious to me. Why not just compare the means across the 3 groups using ANOVA and reporting eta-squared (as well as Cohen's d values for pairwise comparisons of means) as standardized effect size measures?

Cormac,

Categorical Regression may be worth a try.

This is an example of SPSS v25 Syntax for regression of a continuous DV, with one categorical (nominal level of measure) IV.

Note that this is IBM SPSS syntax, but the concept is clear in the logic of the syntax. This could be done in R, STATA, or SAS.

* Encoding: UTF-8.

CATREG VARIABLES=CONTINUOUS_DV_NAME CATEGORICAL_IV_NAME

/ANALYSIS=CONTINUOUS_DV_NAME(LEVEL=SPORD,DEGREE=2,INKNOT=2) WITH CATEGORICAL_IV_NAME(LEVEL=NOMI)

/MISSING=CONTINUOUS_DV_NAME(LISTWISE) CATEGORICAL_IV_NAME(LISTWISE)

/MAXITER=100

/CRITITER=.00001

/PRINT=R COEFF ANOVA

/INITIAL=NUMERICAL

/PLOT=TRANS(CONTINUOUS_DV_NAME CATEGORICAL_IV_NAME)(20) RESID(CATEGORICAL_IV_NAME)(20)

/REGULARIZATION=NONE

/RESAMPLE=NONE.

If you consider that all regression models involve correlation, this may be a methods approach that gets to the same answer (i.e. is there any significant difference in the DV, based upon the variation present in one or all IVs?). If your IV were binary A or B) rather than trinary (A or B or C) if your data set met the assumptions of the Binary Logistic Regression models, then perhaps a BLR of Male (1 = Yes; 0 = No) as the DV instead of your current continuous DV (use the continuous variable to predict Male (or not) in a BLR.

On the other hand, categorical regression can yield some very fascinating and interesting results, as can ordinal regression when exploring data in search of an ideal predictive model.

I hope this helps,

Richard E. Gilder, MS RN-C

Bioinformatics Scientist

The Gilder Company

TTUHSC Adjunct Faculty

[email protected]