strong skewness (positive or negative), because Chauvenet’s criterion is excessively sensitive to such violations of normality.
Example 5: average state taxes per capita, by state.
What is the average amount of state taxes paid in the U.S.? One answer might come from simply dividing the total of all state tax income by the total U.S. population. Here is another, more informative approach.
Histograms of state taxes per capita, by state, are shown in Figures 7a and 7b. Although the two histograms show the same data, they emphasize slightly different features because of their different binning intervals. The coarser binning interval of Figure 7b makes the distribution look more normal, as is often the case for coarser binning (within reason). Finer binning (Figure 7a) makes the largest datum, per capita taxes of $2674 ($2.7K) in Alaska, look more anomalous. Both histograms are roughly bell-shaped but positively skewed (skewness=2.0). Thus it is worth trying a transform to logarithm of per capita taxes, but such a distribution is not shown because it accomplishes no improvement.
Chauvenet’s criterion shows that the value for Alaska taxes is far more than is likely by chance for a normal distribution. Recalculation of parametric statistics after omitting Alaska gives a more normal value of skewness, and permits us to exclude yet another state (Hawaii), but we will forgo that opportunity. It seems likely that Alaska and possible that Hawaii are anomalous in state taxes in comparison to other states, because costs are greater at remote locations.
