March 30, 2005
Statistics term of the day: Kurtosis
Kudos to all of you who knew kurtosis was next on the list! Kurtosis is the fourth moment of the distribution, and is the peakedness (that's three syllables, not two) of the distribution. From the Risk Glossary we get these lovely graphs:
The distribution on the right has greater kurtosis - more peaked, less flat - but it's possible that it has about the same SD as the graph on the left, which is more spread out but is thinner at the tails. Normal distributions are likely have a skew of 0 and a kurtosis of 3.The graph on the right is more likely to be leptokurtic (defined as a kurtosis value of greater than 3), while the graph on the left is platykurtic (kurtosis value less than 3).
You now know the first four moments of the distribution (mean, SD, skew, and kurtosis), which come in very handy for describing a set of scores. If a test score distribution has a mean of 75, an SD of 5, zero skew, but a kurtosis of 4, it might look very much like the right graph above. This would suggest a test on which most examinees score very close to the mean, with some out on the fat tails, and no real floor or ceiling effect (i.e., examinees aren't bunching up on the high or low end).
This is the funniest graph I've found to help you remember lepto (peaked) vs. platy (flat) in kurtosis:
