IYH Dear Bruce Ira Gaynes

Yes, conducting linear regression with t-scores as the dependent variable is appropriate if you want to model the relationship btw t-scores and various demographic variables. This approach assumes that the errors in the regression model follow a normal distribution and that there is a linear relationship btw the independent variables and the dependent variable. It's always a good idea to check the residuals of the regression model to ensure that they are normally distributed and homoscedastic. Additionally, collinearity among the predictors should be checked and addressed: scrutinizing multicollinearity amongst predictors prevents misleading findings resulting from overinflated variances.

Lastl (h/t https://www.researchgate.net/profile/Jos-Feys) if you find your dependent variable is skewed and your analysis involves reaction times distribution this article by Robert Helan may help:

https://www.whelanlabtcd.org/wp-content/uploads/2018/10/Effective-analysis-of-reaction-time-data2008.pdf

Glossary of terms:

Linearity: Linear regression assumes a linear relationship between the dependent variable (t-scores) and the independent variable(s) (demographic variables). Ensure that a linear relationship exists between these variables by inspecting scatter plots or conducting regression diagnostics.

Independence: The observations should be independent from one another. Each data point should represent a unique participant or sample without any dependencies or clustering effects.

Normality of Residuals: Linear regression assumes that the residuals (the differences between the observed and predicted values) are normally distributed. Assess the normality assumption by examining residual plots or performing a test of normality.

Homoscedasticity: Homoscedasticity implies that the variability of the residuals is constant across all levels of the independent variables. Check for patterns in the residuals to ensure that there is no dis-proportional spread of errors across the range of t-scores.

No Multicollinearity: Verify that the independent variables do not exhibit high levels of multicollinearity, meaning they are not highly correlated with each other. High multicollinearity can lead to inflated standard errors and affect the interpretation of regression coefficients.