High Positive Kurtosis

Question

I'm looking at the distribution of income data examining the differences between two different surveys.

I've computed medians, means std etc.

Two other measures I've used are Kurtosis and Skewness.

For my Kurtosis value I've gotten 2112.81 and skewness 40.69.

I assume that my large kurtosis value would indicate that my data has a heavy tail and outliers?

And skewness value would be expected to be positive given income cannot be negative?

Any input about interpretations would be great.

I'm not particularly worried about values as I'm not hypothesis testing etc. but more examining the data.

Answer 1

Your interpretation is correct: High kurtosis indicates outliers. You have rare individuals in your data set with extreme income, as is typical for these type of data. I would suggest drawing a normal q-q plot to visualize the distribution more clearly. The histogram is also useful, but keep in mind that the outliers will distort the horizontal scale, making it difficult to see the actual shape of the distribution. So if you report the histogram, also report the histogram "zoomed in" so you can see how the distribution of the main body of the data looks.

Answer 2

When dealing with quantities like wealth and income, it is usual to analyse these on a logarithmic scale and describe the distribution of their logarithms (in this case, the log-income). Both wealth and income tend to accrue exponentially (e.g., accruing compound interest) and so they have extreme positive skewness and high kurtosis when put on an ordinary scale. I would suggest you start by making a density plot of data on a logarithmic scale (i.e., a density of the log-income data) and see what this looks like. If this is close to a normal distribution then the income follows a log-normal distribution. If it still has non-normal skewness or kurtosis then a different distribution may be in order, but I doubt it will be far from this.