# Distinguish between underlying Distribution and data shape in data transforming?

My question is not well worded, which is part of the problem. I’m specifically trying to apply this to my understanding of Six Sigma, but it probably applies everywhere.

I know that having a normal distribution in your sampling is preferable to a non-normal distribution, because of the wider range of statistical tests you can apply, their sensitivity, etc.

It seems to be that there are two reasons for non-normal distribution in your samples.

1. We either know in advance that the distribution is some other (Binomial, Poisson, etc.) or we discover it with a stat test after we collect the data.

2. Then we have skewness, bimodal, multimodal, and kurtosis. Not sure if these things mean the underlying distribution is not normal.

I’m struggling to understand the relationship between these seeming two types of nonnormality. I mean, a Poisson distribution looks “skewed” but that is really what we are getting at when we say skewed? Or is it?

I am taking a wild guess that the first type is due to the true structure of the underlying population, where the second type can result from poor sampling technique within a population that is actually normally distributed.

I hope I’ve expressed this well enough it’s hard to say correctly. In any case, try to interpret what I’m asking and answered several ways if you wish. There may be multiple perspectives on this.

And if you have the time, if you know that one set of “solutions” to cure distribution issues might be different from another set of solutions to cure skewedness, bimodality, etc., please let me know.