My dependent variable is cortical thickness. My independent variable is "group" (pts vs. controls). My covariates are sex, age, and intracranial volume.
I looked into Cohen's Fsq but read that that isn't appropriate for a categorical independent variable. Also considered omega-squared but read that that isn't appropriate if the covariates are "observed" and not "manipulated" (gender was specifically listed as an observed covariate).
Please let me know if there is any more information I can provide.
Thanks!
Usually, effect size of a predicting variable of interest in linear (OLS) regression is measured by
Cohen's f2 = (R2included - R2excluded) / (1 - R2included)
with included/excluded referring to the variance in your dependent variable that is explained by your model with/without the predicting variable of interest. f2 values of 0.02, 0.15, and 0.35 indicate small, medium, and large effect sizes, respectively.
You can also use and interpret the (unstandardized) coefficients of your regression model themselves as a measure of effect size. E.g., in your case, the coefficient for age indicates the amount of change in cortical thickness that is associated with an increase in age by one unit, holding all other predictors at their means. For group, the coefficient indicates the difference in the means of cortical thickness between pts and controls.
Usually, effect size of a predicting variable of interest in linear (OLS) regression is measured by
Cohen's f2 = (R2included - R2excluded) / (1 - R2included)
with included/excluded referring to the variance in your dependent variable that is explained by your model with/without the predicting variable of interest. f2 values of 0.02, 0.15, and 0.35 indicate small, medium, and large effect sizes, respectively.
You can also use and interpret the (unstandardized) coefficients of your regression model themselves as a measure of effect size. E.g., in your case, the coefficient for age indicates the amount of change in cortical thickness that is associated with an increase in age by one unit, holding all other predictors at their means. For group, the coefficient indicates the difference in the means of cortical thickness between pts and controls.
Thank you for the responses!
It seems that the Cohen's F^2 statistic gives us the effect size of the predictive variable of interest when controlling for the others. I'm more interested in the effect size between my two groups (pts vs controls) while controlling for variables. Do you think computing Cohen's d but with predicted values achieves that goal?
I suppose you are performing some kind of a RCT, with a comparison of the pts group with a control group with regard to cortical thickness at follow-up. In this case I would agree; Cohen’s d is frequently reported as an indicator of the effectiveness of a treatment in RCTs. Typically, this ‘standardized mean difference’ (SMD) would be measured as the (pure and unadjusted) difference in the treatment group means at follow-up, divided by the pooled standard deviation for your outcome (assuming that the size of your randomized groups is similar).
Assuming that you have pre-specified baseline characteristics (e.g., age, gender) to be strongly associated with your outcome I think you are also right to control for these covariates in a regression model and report Cohen’s d based on estimated (regressed) mean differences. Although, in this case I would use adjusted mean scores (or marginal means), i.e. predictions for the two groups at the mean of your covariates. Moreover, given that your groups have been appropriately randomized before baseline assessment, I would also calculate the “unadjusted” SMD as described above and compare it to your effect size derived from regression.
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