# What method can I use to account for differences in group means?

Let's say the mean income in New Jersey (group 1) and Florida (group 2) is $80,000 and$55,000 respectively. Using a dataset of relevant predictor variables, I'd like to attempt to explain this gap (i.e. $25,000). My question is what method I'd use to do so. For example, would I take the difference of the means and estimate a regression with it as my DV? Thanks in advance! ## 1 Answer Assuming you are using continuous independent variables to explain the difference, you can use a linear regression of the form: $$y\sim\beta_1 + \beta_2 x + z_1(\beta_3+\beta_4 x)$$, where y is your income,$z_1$is an indicator variable for whether a subject is in group 2, and$x$is your covariate independent variable. When you fit this model, significance of$\beta_3$will tell you if there is a difference in the two group's intercept, and significance of$\beta_4$will tell you if your covariate contribute to the observed difference in group incomes. • Okay. So there's no need to regress the differences in mean income (i.e. I should just regress the income variable as a whole)? Feb 10, 2018 at 1:05 • Also, what are B3 and B4 in this case? Other IVs? Feb 10, 2018 at 1:08 • A regression is equivalent to conducting a t-test or ANOVA. To see this, suppose you want to see how an IV$x$affect the income -- you would be checking if the mean income differ for the different levels of$x$(if it's categorical). In that case the regression would be $$y\sim \beta_1+\beta_2 x$$. – Asy Feb 10, 2018 at 6:02 • If your IV is continuous, you would be conducting an ANCOVA. And that is what my original equation represents. In that case,$\beta_4$would tell you if the effect of$x$for your second group is different from that of your first/control group. – Asy Feb 10, 2018 at 6:04 • I suggest using the regression because the coefficient$\beta_2$in the categorical case, and$\beta_2$,$\beta_4\$ in the ANCOVA case gives you a quantitative estimate of your IV's effect. Also see this post about the equivalence between regression and t-test/ANOVA
– Asy
Feb 10, 2018 at 6:06