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Some while ago I attended a presentation of a case-control study for which enrolment was still in progress.

The lecturer, a PhD student with basic statistical education, mentioned that while in the treatment group, age was already normally distributed, the corresponding distribution in the control group was still far from normal, and therefore they were actively searching for people with the "right" age to get that nice Gaussian curve.

I have a strong feeling that proceeding in this fashion is at best problematic: Sampling this way is neither random nor independent, and age is normally distributed neither in the general population (from which the control group presumably is recruited) nor in patients with that disease (whose incidence is, of course, age-dependent).

On the other hand, maybe it is not problematic at all, as it could be seen as simply matching cases to controls.

I'm unsure of the implications for different analyses, in particular: Would one expect that inference on a treatment effect would be affected (age is a strong predictor of course of disease)?

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    $\begingroup$ I'm puzzled by the whole tale. Why on earth would he need age to be remotely normal in the first place? $\endgroup$
    – Glen_b
    Commented Apr 11, 2013 at 7:50
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    $\begingroup$ My guess is that the reasons are more psychological than statistical. The people conducting this study are MDs with very basic statistical expertise. I've observed several times that the normal distribution is the a priori "right distribution" for the statistically less adept. $\endgroup$
    – miura
    Commented Apr 11, 2013 at 7:53
  • $\begingroup$ I suppose there's some model for which he (or she) is assuming the independent variables need to be normal (which is certainly not the case for any model he's likely to want). $\endgroup$
    – Glen_b
    Commented Apr 11, 2013 at 8:09

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There is a common phenomenon among many statisticians and non-statisticians called leptokurtophobia:

The symptoms of leptokurtophobia are (1) routinely asking if your data are normally distributed and (2) transforming your data to make them appear to be less leptokurtic and more “mound shaped.

http://www.qualitydigest.com/inside/twitter-ed/do-you-have-leptokurtophobia.html#

I think this guy took it to the next level.

In some cases people assume normallity of the observations only because it simplifies their calculations in spite of clear evidence of departures from this assumption.

Besides possible misconceptions or other errors in the modelling, the immediate implications are:

  1. They are inducing a bias by selecting people in order to obtain data where they can use the models they "know". Ideally, statistics work the other way around: collecting data with a purpose in mind $\rightarrow$ statistical modelling.

  2. The conclusions drawn have to be changed to something like: if we sample in such a way that we obtain a normal sample, then ... Which may not be that useful.

There are many ways to modelling departures from normallity but specially non-statisticians are affraid of using them since they are typically more complicated.

Of course, there are cases where the Central Limit Theorem or some other (asymptotic) result make the assumption of normallity rather mild. However, we have to keep in mind that this is not always the case.

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    $\begingroup$ "Some people assume normallity simply because it simplifies their calculations"-- in a study where age is presumably a predictor (IV), what calculations could it simplify? $\endgroup$
    – Glen_b
    Commented Apr 11, 2013 at 8:07
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    $\begingroup$ @Glen_b As you wisely noticed, their problem is in the modelling. For this reason I included the sentence Besides possible misconceptions or other errors in the modelling. I am discussing the divinisation of the normallity assumption. I am in agreement with you, then it is not necessary to answer that question :) $\endgroup$
    – Macallan
    Commented Apr 11, 2013 at 8:09
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    $\begingroup$ Ah, I gather you intended "is perceived to simplify ..." or something along those lines, then. Okay. $\endgroup$
    – Glen_b
    Commented Apr 11, 2013 at 8:13
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    $\begingroup$ @Glen_b Sort of. I meant "In some cases people assume normallity of the observations only because it simplifies ..." Pardon my French!. $\endgroup$
    – Macallan
    Commented Apr 11, 2013 at 8:15

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