Skew

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Next, I want to talk about skewness, which is a handy way to quickly summarise the shape of a distribution or, in other words, what your scores tend to be doing. Here I’ve got three histograms on the screen. Now if you look in the middle, you see one that looks symmetrical. We say this has no skew. It looks like a bell curve. The bulk of the scores are right in the middle. So we say that has no skew. But look at the one to the left. The bulk of the squares have shifted off to the side a little bit, and there’s a long tail going off to the right. We say this is positive skew. Why positive skew?

Because the long tail is going in the positive direction. If I know a variable has a positive skew, it tells me most scores tend to be at the low end, but there’s a small number of people that trail off in the positive direction. So just by knowing a variable has a positive skew, I now have that information. Most scores tend to be at the low end. A large number of people trail off in the positive direction. So it’s a useful thing to know about a variable, just by knowing the skew. I can also go the other way. Look at the graph on the right.

Here we have the bulk of the scores on the right of the distribution, or at the upper end. And they trail off in the negative direction. So we say that is negative skew, a very handy way to describe the shape of a variable, and therefore know about what that variable is doing. Now briefly, I have something where I can quantify the skewness and it’s called the skewness statistic, or sk. It’s very intuitive. If there’s no skew, it’s symmetrical. Skew is zero. If there’s positive skew, or negative skew, the number is positive or negative. So if I’ve got negative skew, I’m going to have a negative number, a positive skew, a positive number.

You’ll get a chance to play with this in the labs. And you can see how different skewness levels translate into different numbers. But it is a handy way to summarise what your variable is doing. [LOGO MUSIC PLAYING]