Now we come to check if our data (sampling, collection) is good enough to apply statistics that are based on the Central Limit Theorem (eg. : Student test, t-test, z-test, anova,… are valid only when the data is reasonably ‘normally distributed’ or ‘bell shaped’). This is ‘type 0 error’ - where data ‘is’/’is not’ ‘normal’.

[Once upon a time, I looked at a few ‘class satisfaction’ measure statistics and learned that data samples are collected by or in presence of the teachers whose subjects are the objects of statistical measurement – that is a mouthful ;-) – so, data is ‘under influence’ or not independent and always too skewed to be valid for ‘95% confidence that such and such… How many decisions have been made with this skewed-up statistical measure? I don’t know. But we have had many specialist appointments because data skewness (from ‘normal’) was not checked.]

Type 3 errors usually come in to make the stats look ‘normal’. How often have this happened? Again, I don’t know. But I think those who validate ‘researches’ should first ‘validate’ data sampling and collection for normalcy, skewness and kurtosis before believing other [normal] statistical results.