# Repeated measure ANOVA vs independent 2-sample t-test

I have this data where I have a control and an intervention group. For both of these two groups, I have a continuous outcome measured at baseline $(y_0)$ and at 1 month $(y_1)$. To test for the difference between the control and intervention group, I can create an outcome by $y_1 - y_0$ and run a 2 sample independent t-test. However, I was suggested to use a repeated measure ANOVA instead. Could anybody tell me if there is an advantage using an RM-ANOVA in this case? Thank you in advance.

An Independent Samples t-Test and ANOVA are both part of the General Linear Model (GLM). For a t-test, the null and alternative hypotheses are that $H_0:\mu_1-\mu_2=0;H_1:\mu_1-\mu_2\ne0$. For an ANOVA, the null and alternative hpyotheses are $H_0:\mu_1=\mu_2;H_1:\mu_1\ne\mu_2$.
A t-Test is represented by the formula $\hat{Y}=\beta_0+\beta_1(X_1)+$ and the ANOVA is also represented by the formula $\hat{Y}=\beta_0+\beta_1(X_1)$, so they are essentially the same, and that is because they are both part of the GLM. However, in this case, you have a new and rich data point called 'time,' and time is a really neat concept. Thus, you don't have just a plain old ANOVA, you have an RM-ANOVA.
The formula for an RM-ANOVA includes the time as a predictor (independent variable): $\hat{Y}=\beta_0+\beta_1(Group)+\beta_2(Time)$. That means that each of these predictors could exhibit statistical significance and both yield a measure of effect size. Using standard ANOVA table, you would get an $\eta^2$ effect size for each and using multiple linear regression, you would get an $R^2$ effect size. However, you might even consider Hierarchical Linear Modelling where time is a level-1 predictor and group is a level-2 predictor, but this is normally done with more than two measurements.