Solved – Using r, how might I check whether a collection of data points are normally distributed with skew

Question

I currently have a vector containing values which I wish to consider the distribution of. I am aware that when using a qqnorm() plot, it is possible to see that data is normally distributed if it closely approximates a straight line.

However, the qqnorm() plot for my data looks something like this:

My understanding of r, and of this function, is very limited. However, from searching online I suspect that this graph may tell me that my data is normally distributed with skew. How might I check whether this is indeed the case?

Answer 1

• The Q-Q plot indeed shows that your data are skewed; the values in the lower tail are larger (closer to the median) than expected from a Normal distribution (light left tail), while the values in the upper tail are also larger (but thus farther from the median) than expected (heavy right tail).
• There's not really any such thing (that I've ever heard) as "normally distributed with skew"; I would say these data are "skewed" or "right-skewed" (e.g. see here).

• If you want to get more of a feel for your data, it may help to draw a histogram; it's harder to detect subtle differences from Normality, but it's easier to understand what's going on, at least until you get the hang of reading Q-Q plots.

  

• you're asking whether you can "check whether this is indeed the case". It sounds like you're looking for a statistical test of skewness. While there are tests (such as the Jarque-Bera test, available for example in the tseries R package) that use skewness and kurtosis to test for deviation from Normality, I'm not aware off the top of my head about tests of skewness alone. That said, I would ask why you want to do such a statistical test: what question are you ultimately trying to answer? Many statisticians feel that statistical tests of Normality are mostly useless; similar arguments would apply to a test to reject the null hypothesis of symmetry (non-skewedness) ...