significant Shapiro-Wilk Test [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2017-07-30 17:36 (2433 d 23:20 ago) – Posting: # 17631
Views: 6,662

Hi Mohamed,

❝ What to do if Normality shapiro-wilk test on Ln transformed Auc and cmax are non normal?


Given the sample sizes commonly seen in BE, it is very (very!) unlikely that you will see a significant result. See this presentation (slides 5–6).
The problem with Shapiro-Wilk (and any other test for distributional assumptions like Kolmogorov–Smirnov, Anderson–Darling, …) is that they test against a reference probability distribution. If you run two concurrent tests (one against the normal and the other one against the log-normal) you may end up with two nonsignificant results (as in slide 6) – which is contradictory. These tests cannot support you in deciding which distribution fits the data “better”. Hence, you are left out in the rain. Theoretically you could assess the Kullback–Leibler divergence, but I have never seen that in practice.

❝ Can we proceed using parametric analysis test "Anova"?. As according to my knowledge, we can't use any parametric analysis tests on non normal data.


The t-test is pretty robust against deviations from normality. Howver, it is very sensitive against imbalance (hence, in crossovers always use the formula given there and not the simple σw2∕n; in parallel designs with unequal group sizes Sattertwaite’s approximation). However, only the model’s residuals have to be normally distributed. Even for IIDs (assumed in ANOVA) which are non-normal, their difference will be (central limit theorem).

❝ I want any references or guidelines regarding that?


A test for normality should not be performed. Justification of the multiplicative model is based on:Already stated 25 (‼) years ago in the FDA’s guidance (Section III).

Only in the Japanese Q&A-document (Feb 2012) something is stated:

Q-32  Is logarithmic transformation always necessary? Is it acceptable to carry out logarithmic transformation only if necessary?
(A)     Based on the principle of international harmonization, assessment should be made using logarithmically transformed values. However, when it is not appropriate to conduct an analysis with transformed data, assessment can be made with untransformed data. For example, the assessment can be made using untransformed data if the parameters are normally distributed or transformed data can be used with non-normally distributed data.


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