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In answering a question about a confidence interval for a binomial proportion I pointed out the fact that the normal approximation is an unreliable method that is archaic. It should not be taught as a method, although there might be an argument that it be included as a part of a lesson about what makes an adequate method.

What are other 'standard' statistical approaches that have passed their use-by date and should be omitted from future editions of textbooks (thereby making space for useful ideas)?

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    $\begingroup$ Larry Wasserman asks the question and suggests some answers in his blog. See also the users comments. $\endgroup$ – JohnRos Mar 11 '13 at 9:25
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    $\begingroup$ Why is the normal approximation bad to teach? $\endgroup$ – Douglas Zare Mar 11 '13 at 14:08
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    $\begingroup$ I did suspect this question could yield some constructive answers but, after seeing the answers that have been posted so far (including deleted ones), I'm seriously doubting that, so I'm voting to close. $\endgroup$ – Macro Mar 11 '13 at 16:27
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    $\begingroup$ To answer my own comment, I think the idea is supposed to be that the normal approximation will tend to produce intervals which are too wide when the probability is close to $0$ or $1$ and/or the number of trials is small, and there are other techniques which produce tighter confidence intervals and work better with a small number of trials. Does this mean it's bad to cover the normal approximation? I don't think so. The normal approximation is simple and easy to remember. Slight modifications approximate the Wilson interval very well. So, include it and its domain of applicability. $\endgroup$ – Douglas Zare Mar 11 '13 at 17:05
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    $\begingroup$ I don't think that's a good argument against teaching it. People use what they understand and remember, and teaching only formulas with intricate typesetting means students won't build their intuitions as much or to be able to do simple examples by hand. If the drawbacks are important, teach about them, and people may remember why more complicated methods exist. If you don't teach the normal approximation, how could you say, "the Wilson interval is close to the normal approximation with Laplace smoothing with k=2?" This is sounding subjective and argumentative, so I'm voting to close. $\endgroup$ – Douglas Zare Mar 12 '13 at 14:57
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These three would probably rank somewhere in a list of deprecated exercises:

  1. looking for quantiles of the normal/F/t distribution in a table.
  2. Tests of normality.
  3. Tests of equality of variances before doing the two sample t-tests or anova.
  4. Classical (e.g. non robust) univariate parametric tests and confidence intervals.

Statistics has moved in the age of computers and large multivariate dataset. I don't expect this to be rolled back. By necessity, the approaches taught in more advanced courses have in some sense been influenced by Breiman's and Tukey's critics. The focus has, IMO, permanently shifted towards those approach that require fewer assumptions to be met in order to work. An introductory course should reflect that.

I think some of the elements could still be taught in a latter stage to students interested in the history of statistical thoughts.

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    $\begingroup$ Please provide evidence to support your answer. If this thread devolves into pure lists of stuff some people think are bad, it will have to be closed. $\endgroup$ – whuber Mar 11 '13 at 16:07
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    $\begingroup$ I would agree that using statistical tables is an absolutely obsolete computational technology. Tests of normality, however, do have their reasons. $\endgroup$ – StasK Mar 11 '13 at 16:12
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    $\begingroup$ @StasK Agreed about the tables (and normality tests); but since we appear to be discussing pedagogy, insofar as "textbooks" connote references to support teaching, I think a strong case can be made for teaching how to relate quantiles to areas under graphs of PDFs and to test that understanding by asking questions requiring manipulation (and therefore estimation) of those areas. Table lookups remain a convenient way to estimate areas, especially in tails. We just need to remember that the lookup (or calculation!) is purely an auxiliary computation and is not the point of the exercise. $\endgroup$ – whuber Mar 11 '13 at 17:50
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    $\begingroup$ I agree about tables, and not only for the reason that they are unnecessary. They also play to the notion that there is something special about the P-value associated with the critical values that they specify. That tends to obscure the use of P-values as indices of evidence. $\endgroup$ – Michael Lew Mar 12 '13 at 9:58
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    $\begingroup$ Normality tests might be omitted, but perhaps they should be complemented with exercises that show how little power they have to discriminate between distributions with the small sample sizes for which the normality actually matters! Perhaps exercises that show to what extent non-normality affects the properties of various tests and interval estimates would be better still. $\endgroup$ – Michael Lew Mar 12 '13 at 10:00

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