- Thread starter tt13
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I think this view has changed in recent decades, but courses have not caught up with the new view.

You have been told twice that normality of the residuals is not a necessary requirement,

in addition you have been told that this is based on the central limit theorem (CLT).

What else do you need for coming to a conclusion?

Other assumptions are not affected by this discussion, of course.

With kind regards

Karabiner

in addition you have been told that this is based on the central limit theorem (CLT).

What else do you need for coming to a conclusion?

Other assumptions are not affected by this discussion, of course.

With kind regards

Karabiner

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for normality, while this is the most unimportant feature.

The most important assumptions (linear relationships, and equal

variance of errors i.e. homoscedascity) should be checked, and

whether there's multicollinearity.

With kind regards

Karabiner

Normality is part of the gaus markov assumptions which is why it is stressed. I guess no one considered the CLT.

@tt13 - you should look for heterogeneity. Even if you can address it via robust SEs, etc. - it is good to know your data and the underlying relationships, since this could also prompt you to opt to incorporate data transformations.

Should one use them by default (analogous to Welch t-test)?

With kind regards

Karabiner

With kind regards

Karabiner

I think it is good practice to test for heterogeneity and non-linearity regardless. I generally don't think there is much value in testing for Multicolinearity or normality unless you have very few cases.

Note that some say that high skew can distort regression results and that is a form of normality. I don't know if case size impacts this.

I don't know if it has any relevance, but I haven't mentioned it yet:

In the linear regression the mean values of Likert scales are used. For example:

Here are my results of heterogeneity and linearity test:

But what is that supposed to tell me in relation to my hypotheses? Are there some that should be better discarded?

Its beyond my expertise if you should evaluate your hypothesis based on it. I would look at the literature on likert variables and also run ordered logistic regression and see if the results agree. You won't have to worry about normality or hetero that way.