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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 :)

einervonwenigen
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1 Answers1

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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.

Dave
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  • 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? – Dayne Oct 24 '20 at 12:59
  • Maybe I simplyfied my problem to much. As I have more independet variables in my regression. – einervonwenigen Oct 24 '20 at 13:02
  • My regression indicates that the membership to be either in group a or b have significant effects on the achieved points. However, the means of group a and b do not significantly differ from each other...That`s why I am looking for an argument to use the regression – einervonwenigen Oct 24 '20 at 13:03
  • @Dayne F-stat of what? The F-test in R’s summary compares the given model to the intercept-only model, so the conclusion to a significant F-test there would be that the predictors, all together, have some influence over the response variable. – Dave Oct 24 '20 at 13:03
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    Then please edit your original question with the additional details. – Dave Oct 24 '20 at 13:05
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    @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
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    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
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    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. – Dayne Oct 24 '20 at 13:08
  • @Dayne I don’t follow all of what you’re saying, but I think you’re asking an interesting question that warrants its own post, not a discussion in the comments of someone else’s question. – Dave Oct 24 '20 at 13:10
  • Thank you. I will post a new question. – einervonwenigen Oct 24 '20 at 13:12
  • Please find a clarified question here https://stats.stackexchange.com/questions/493459/explaining-different-results-of-linear-regression-compared-to-students-t-test @Dave maybe you are also able to help me with this question. – einervonwenigen Oct 24 '20 at 13:21