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I have a situation where I have more than 50 samples in a given set of inputs and I cannot use the Shapiro-Wilk test as I don't have the numbers for the pyramid for $n>50$. I was then asked to use the Shapiro-Francia test as this would be acceptable in the field of industrial hygiene for what I am doing.

I implemented the algorithm and for example a small set of values: 

0.06, 0.1, 0.05, 0.1, 0.01, 0.09, 0.04, 0.2, 0.04, 
0.08, 0.08, 0.03, 0.09, 0.03, 0.07, 0.03

it gives me a p-value of 0.349115.

I am trying to find if this set is fit for a lognormal or a normal distribution. I know this is fit for a lognormal distribution, however I am not sure how to interpret this p-value.

For the Shapiro-Wilk test, I would see if the $p > 0.05$ and act upon it. However I cannot seem to find the critical value for a Shapiro-Francia test. I used an Excel spreadsheet made by a contractor and it seems the critical value hovers around 0.0305, but I would like to understand how this works.

Other parameters from my algorithm output:

Pearson Correlation (squared) = 0.94484..
mu = -3.116
sigma = 0.5649
Z' = 0.3877
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    $\begingroup$ p-values from goodness of fit tests are not a good way to select distributional models. $\endgroup$
    – Glen_b
    Commented Dec 13, 2018 at 1:49
  • $\begingroup$ I figured it out! It is a choice based on other factors like alpha and the user's choice. $\endgroup$
    – i_shoot_photos
    Commented Dec 13, 2018 at 13:31

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