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Back to the forum  Query: 2017-08-21 13:55 CEST (UTC+2h)
 
Mohamed Yehia
Junior

Egypt,
2017-07-29 20:47

Posting: # 17624
Views: 416
 

 Non Normal Shapiro-Wilk Test [General Sta­tis­tics]

Dear All,

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

I want any references or guidelines regarding that?.

Thanks.


Edit: Category changed; see also this post #1. [Helmut]
ElMaestro
Hero

Denmark,
2017-07-29 21:13

@ Mohamed Yehia
Posting: # 17625
Views: 354
 

 Non Normal Shapiro-Wilk Test

Hi Mohamed Yehia,

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

You don't have much choice in practice, generally.
BE data from human trials are always -as far as I know- analysed using parametric testing (linear model for the effects and residuals, derivation of 90% CI via the model residual, typically an ANOVA on top of all that). You are not even supposed to do a SW-test or similar. Any test for distributional departure will not have impact on the choice of method.

I could be wrong, but…


Best regards,
ElMaestro

- since June 2017 having an affair with the bootstrap.
Mohamed Yehia
Junior

Egypt,
2017-07-29 22:12

@ ElMaestro
Posting: # 17627
Views: 353
 

 Non Normal Shapiro-Wilk Test

Thanks a lot Elmaestro :)


Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5! [Helmut]
Helmut
Hero
Homepage
Vienna, Austria,
2017-07-30 15:36

@ Mohamed Yehia
Posting: # 17631
Views: 323
 

 significant Shapiro-Wilk Test

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:
  • The basic equation of PK (AUC = F·D∕CL) which – after taking logs – will be transformed into an additive model (as required in ANOVA).
    • Negative concentrations are not possible.
    • The distribution of raw data is skewed to the right (see slide 5).
  • Serial dilutions in bioanalytics lead to multiplicative errors.
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.


[image]All the best,
Helmut Schütz 
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The quality of responses received is directly proportional to the quality of the question asked. ☼
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ElMaestro
Hero

Denmark,
2017-07-30 21:27

@ Helmut
Posting: # 17632
Views: 281
 

 significant Shapiro-Wilk Test

Hi Helmut,

» 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.

The absence of a low p-value is not proof of the null being right. We can't prove which distribution the data follows but we can, so to say, test with some degree of power and with some alpha which distribution it doesn't follow.
What I am trying to say is I don't think it is contradictory to have two unrejected mutually exclusive null hypotheses.
:-):-):-)

I could be wrong, but…


Best regards,
ElMaestro

- since June 2017 having an affair with the bootstrap.
Helmut
Hero
Homepage
Vienna, Austria,
2017-07-31 12:52

@ ElMaestro
Posting: # 17633
Views: 254
 

 significant Shapiro-Wilk Test

Hi ElMaestro,

» […] I don't think it is contradictory to have two unrejected mutually exclusive null hypotheses.

Touché! You are absolutely right. :pirate:

[image]All the best,
Helmut Schütz 
[image]

The quality of responses received is directly proportional to the quality of the question asked. ☼
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