Saad,

I agree with you completely that we need to deemphasize the teaching of the normal curve in the classroom. Or, at least, when we teach that curve, we need to mention the danger if the true distribution is not normal.

Peihua

Saad -

I saw that article, and there is a lot of truth to it.  "Normality" is often useful, perhaps especially because of the Central Limit Theorem, which often makes it useful for confidence intervals, and it is sometimes somewhat desirable when considering residuals in regression (or the estimated random factors of the estimated residuals, really), but even in these cases, it is often of little importance.  Hypothesis tests are often based on them, but they are overused and misused themselves.  I think the key problem, as in the case of the word "significance," is that "normality" is something of a misnomer.  The name itself, unwisely chosen, is naturally, highly misleading. 

In statistics (and I certainly suspect, in other disciplines), there are other examples of terminology which is misleading.  "Ignorable nonresponse" comes to mind.  In the area where I spent most of my career, official energy statistics, where industry populations have highly "skewed" data (that is, skewed distributions are 'normal'), and the use of regression through (to) the origin is very helpful, it may be a sign of very low data quality to ever want to use OLS ("ordinary least squares") regression, because that should not only not be "ordinary," theoretically, it should never happen.  Weighted least squares (WLS) regression would be "ordinary" for such applications.  Well, I should say that there should be substantial heteroscedasticity.  Actually, OLS is just a special case of WLS. 

So, in the case of "normal" distributions, I think that they are important, but are given greatly out-of-proportion emphasis, and this situation might have been substantially alleviate if we had just called them Gaussian, and left it at that. 

Should teaching the Gaussian distribution be deemphasized?  Well, it is important, but it should be put in proper perspective. 

Interestingly, the article you cite is in a magazine of a title (Significance) that greatly bothered me when it first came out.  Though I've learned to live with it, I'd like to see it changed.  In recent months I had a letter published in there where I noted the very important difference between a forecast, and prediction (for a finite population), as people often confuse prediction for a forecast.  I then suggested to the editor that there were terms such as "normality" and "significance" (the title of the magazine) that are misnomers, and at his urging for possible publication, I wrote a couple of drafts on that.  However, he lost interest and abruptly stopped writing to me.  (Hmmm??) 

Cheers - Jim

Dear Saad,

For me, teaching the normal curve is important in order to introduce assumption checking for parametric tests, many of which assume normally distributed data, but may work in other (non-normal) circumstances.

However, testing for normality is also tricky as I am told that the sensitivity of the standard tests (Shapiro Wilk and Kolmogorov Smirnov) depends on the sample size.