# Superiority of linear regression compared to students t-test

I am looking for some literature about linear regression and students t-test to cite them in my discussion within my paper. In a nutshell: I would like to argue that I prefer using the results of a regression compared to t-tests of my individual variables. Is this an acceptable argument? Does someone know some paper about this?

My (simplyfied) Problem: I have two groups (group A and group B) solving an assessment to achieve points. Now, I would like to run a linear regression with the achieved points as dependent variable and group classification as independent variable, instead of using a t-test to compare the means of both groups.

Thanks in advance :)

Challenge

The approaches are the same...except for this little issue where the default form of t-testing in some software (I know in R, maybe in Python SciPy, etc) is the Welch t-test that makes an adjustment to the testing to account for possibly different variances of the two groups.

Welch testing is usually considered superior to the classical t-test, since it is unlikely that the groups have identical variance.

If, however, you want to compare regression to the classical t-test with equal variance assumed, they are exactly the same. The test of the group membership coefficient is the t-test of the equality of the group means.

• A related doubt: In such a case when independent variables (although here it would only be one) are all categorical, what would be the use of F-statistic? Would a significant F-statistic only convey that mean of dependent variable is not zero? Oct 24 '20 at 12:59
• Then please edit your original question with the additional details.
– Dave
Oct 24 '20 at 13:05
• @einervonwenigen Yeah, it seems to be different question then. In such case regression in fact has advantages, however Dave answer is adequate to what you described in this question.
– cure
Oct 24 '20 at 13:05
• Yeah...I said to edit the original question. I answered the original question, and it is correct. To keep Cross Validated clean, please post your clarification as a new question.
– Dave
Oct 24 '20 at 13:07
• Yeah I meant regression f-stat only. I was considering a case where all independent variables are categorical with dummy for each level (so without intercept). With intercept it is clear of course. Oct 24 '20 at 13:08