This question does not relate to JMP itself, but rather represents a basic question of interpretation. I understand that, due to the the phenomenon we call the CLT, sampling of a population will always strive towards a normal distribution of the resulting means with the overall mean and SD approaching the population mean and SD, irrespective of how the population data is distributed (skewed or normal), but provided a sufficient number of repeat samples are taken (≥30). Furthermore, as the size of each sample is increased, the precision of the estimated mean and SD increases. I also understand that, one does not need to perform such multiple sampling as the CLT is accomodated in parametric testing. What I'm trying to understand is whether there is a cut off point of sample size, above which normality can categorically be assumed without testing. Secondly, and perhaps unrelated, with the call by the The American Statistician journal to drop significance level thresholds (p<0.05) in favour of reporting of actual p-values and to refrain from the use of the term "statistically significant", how does one then determine the outcome in such matters as confirming normal distribution, for example through Shapiro-Wilk testing? Is there a grey line there too?
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