Mohamed Yehia Junior Egypt, 20170729 20:47 Posting: # 17624 Views: 1,275 

Dear All, What to do if Normality shapirowilk 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, 20170729 21:13 @ Mohamed Yehia Posting: # 17625 Views: 891 

Hi Mohamed Yehia, » What to do if Normality shapirowilk 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 SWtest or similar. Any test for distributional departure will not have impact on the choice of method. — I could be wrong, but… Best regards, ElMaestro A potentially biased estimator may be a relevant estimator. The case of REML speaks volumes. 
Mohamed Yehia Junior Egypt, 20170729 22:12 @ ElMaestro Posting: # 17627 Views: 897 

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 Vienna, Austria, 20170730 15:36 @ Mohamed Yehia Posting: # 17631 Views: 870 

Hi Mohamed, » What to do if Normality shapirowilk 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 ShapiroWilk (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 lognormal) 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 ttest 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 σ_{w}√2∕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 nonnormal, 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:
Only in the Japanese Q&Adocument (Feb 2012) something is stated: Q32 Is logarithmic transformation always necessary? Is it acceptable to carry out logarithmic transformation only if necessary? — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro Hero Denmark, 20170730 21:27 @ Helmut Posting: # 17632 Views: 826 

Hi Helmut, » If you run two concurrent tests (one against the normal and the other one against the lognormal) you may end up with two nonsignificant results (as in slide 6) – which is contradictory. The absence of a low pvalue 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 A potentially biased estimator may be a relevant estimator. The case of REML speaks volumes. 
Helmut Hero Vienna, Austria, 20170731 12:52 @ ElMaestro Posting: # 17633 Views: 798 

Hi ElMaestro, » […] I don't think it is contradictory to have two unrejected mutually exclusive null hypotheses. Touché! You are absolutely right. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 