Yes, I agree. I think that what has given "normality" a role bigger than it should have is largely due to its usefulness with regard to the Central Limit Theorem (CLT). It helps with making confidence intervals easier to handle, and applies to means through the CLT.

In regression, people often think that the variables need to be "normally" distributed, when it is the estimated residuals (better, consider the random factors of the estimated residuals in weighted least squares regression) for which it may be somewhat desirable to have distributed not too unlike normality.

The word "normal" itself is misleading, something of a misnomer, as is also the case to some extent with the words/terms "significance," and "ordinary" least squares.

Actually, simulations suggest that the problem of non-normality in the residuals is less of an issue than the commonly associated consequence of heterogeneity of variance. Studies suggesting robustness only hold under narrow sets of conditions, so be careful not to make general claims about robustness.

Michael E Young. Thanks for your response, Michael. Actually, I was referring to normality of the "raw" / original data, not normality of the residuals. (Sorry that I didn't make that explicit.) Do you think I'm still on safe ground in thinking that robustness of stats procedures is good despite nonnormality in the original data?

And I'd like your thoughts, if possible and if you feel inclined, about whether you think the presence of outliers should be of concern - and what to do about outliers if they are present.

Thanks again.

Non-normality of the raw is irrelevant unless it gives rise to non-normality in the residuals. So, robustness can’t be judged by only considering the distribution of the raw data. And, regarding “outliers”, the Issue is more complex than I can cover in a short reply. Apologies!

Michael E Young, thanks for getting back. I realise that outliers present a range of issues. I'm pretty much on top of them, but I thought you might have some insights / suggestions. Don't worry . . .

I'll repeat here what I wrote when we corresponded, Robert:

The approach we had at a statistical agency collecting official statistics seems like a good one: Suspected outliers were investigated to see if they might be outliers. Sometimes when the sources were contacted, they might say they provided data from the wrong file, or something like that. I tried to make it clear however that when the sources were contacted, they not be led to the results we expected to see. Sometimes a potential outlier may not actually be an outlier, but often one may find a reason that it is an outlier.

James R Knaub. Thanks, James. I guess you're posting this publicly so that others have the advantage of your contribution. All good.

As I indicated in our separate correspondence: Wow! It's interesting - well, a bit disconcerting - that the source(s) of information could be so unreliable. I think you might have been in the fortunate situation of being able to contact the sources of outliers. In research we're conducting, the responses are often obtained online and anonymously, so we don't have that opportunity.

When we encounter outliers, we'll just have to be as responsible as possible with what we do to the data.

Thanks again.

Various data issues in various applications may be more common than you think, but the example I gave might happen rarely compared to the volume of data.

If you suspect an outlier, I'm just saying it is best if you can explain its origin. Otherwise it may be too tempting to throw out data just because it is inconvenient. After all, for a 99% confidence interval or 99% prediction interval, we EXPECT 1% of the data to be outside of that range.

If you aren't certain, you could document what you did, and perhaps show the difference in results if you do and if you do not keep the questionable data. In survey statistics, at least, you then have the problem of what is the best imputation method to use, and what are the possible impacts including on variance, or survey weight adjustment might be used, depending upon your methodology.

Normality of raw data comes from skewness and kurtosis and both led to test of normality referred to as Jarque and Bera test - available

In Eviews, Mfit and Stata. If you have a negatively or positively skewed distributed data that will affect the interpretation given for the raw data. On the kurtosis, if the data are not mesokurtic, it will affect the interpretation of data because one has to at least explain why data are leptokurtic or platykurtic. Evidence that nonnormality can be inferred by JB test. A good writer would indicate why these are so. When the variable is then introduced into a model can affect the parameters. Of course, use of standardixed residual may help to identify the outlying observation and possibly leading to dummying

Anonymous data from the Internet sounds like you might be using nonprobability sampling, and without regression for 'prediction' either.  That would make inference problematic.

Here is an interesting and entertaining account of how we got where we are in survey statistics regarding inference:

Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,

(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.

http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm

But for more on nonprobability sampling, some of the best information would be authored or co-authored by Mike Brick:

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 "The Future of Survey Sampling"

 Article in Public Opinion Quarterly 75(5):872-888 · December 2011

Impact Factor: 2.25 · DOI: 10.2307/41345915

J. Michael Brick

 https://www.researchgate.net/publication/261967521_The_Future_of_Survey_Sampling

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"Beyond traditional survey taking: adapting to a changing world

Explorations in Non-Probability Sampling Using the Web"

Proceedings of Statistics Canada Symposium 2014

J. Michael Brick

http://www.statcan.gc.ca/sites/default/files/media/14252-eng.pdf

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"Summary Report of the AAPOR Task Force on Non-probability Sampling"

 Article · October 2013

Journal of Survey Statistics and Methodology

DOI: 10.1093/jssam/smt008

 https://www.researchgate.net/publication/273561892_Summary_Report_of_the_AAPOR_Task_Force_on_Non-probability_Sampling

Hope something above is helpful.

James R Knaub. Thanks, James, for your last post. I'll devour the references with keen interest.

I regard your input as an example of true collegiality.

If anonymous data from the Internet are used then statistical analysis would not apply. Who is respondent? Inference will be catastrophic. Of course, it is like using Wikipedia in research setting. Why not conduct a study where validity and reliability and sampling error are largely not an issue If this is indeed a journal article?