Colorado State University — Pueblo; Fall 2015
Math 156: Introduction to Statistics
Applied Statistical Exegesis Example 2

Source

This is a blog post entitled What is the "Average" American Salary? from the COOLSTATSBLOG, posted on September 11, 2013, by Abbas Keshvani. It can be found at http://coolstatsblog.com/2013/09/11/what-is-the-average-american-salary/. The whole post is interesting, but one particularly interesting graphi is:

Explanation

It is important to read the whole article to realize what the individuals and variable are. The individuals were, in theory at least, all households in the US, in each year from 1980 to 2010. [In practice, the data comes from the US Census, which does not talk to every household.] The variable associated with these individuals was the annual household income. This is a quantitative variable.

From this data, the mean and median household income were computed for each year's worth of data. These were then displayed on a graph with the x-axis being the year and the y-axis being the household income in dollars. The means were shown in red and connected by red lines and the medians were shown in black and likewise connected by black lines. [Actually, this kind of plot with time on the x-axis and some other measurement on the y-axis is a kind of graph called a timeplot which was mentioned in Chapter 1 of our textbook but which we did not discuss in class.]

There is much discussion in the article which explains nicely the difference in general between a mean and a median, and what it is about in this particular dataset. In particular, it is interesting to notice that both the mean and median household incomes have fallen since the Great Recession of 2007, but the mean has fallen less quickly and in fact has recently turned around, while the median has fallen more precipitously and has not turned around. This tells us that the recent "economic recovery" has been mostly a matter of the mean, not the median. Therefore, the "recovery" was mostly a matter of the highest outliers (the most weatlhy people in America) becoming even more extreme recently.

Critique

The graph seems reasonable, all nicely and completely labelled, with sufficient resolution and detail.

It makes me a little nervous that the y-axis goes from 40,000 to 80,000, rather than starting at 0 and going to 80,000 or 100,000. Generally, starting an axis at some particular value other than 0 (or whatever the numerically natural "bottom" of the data could theoretically be) is a way to increase the visibility of variation. This is perhaps permissible in this case since the point of the plot is to see the variation of mean and median over time. It might have been worthwhile to plot the difference or the ration of the two values, though, in order to make that point clearer.

Putting the two timeplots on the same graph was a good way to see if the difference between the two has changed as time passed — so, to see if the shape of the income distribution has changed over the years or only shifted up and down in a largely unchanged manner. [The conclusion would be, by the way, that there have been some changes in the income distribtution over the years.]

Data from the US Census is considered quite reliable, although there is always a legal battle in Congress about how much statistical modelling the Census Bureau is allowed to do. So it could be argued that the lowest income households might not be correctly surveyed, since they are often not at home (they work longer hours than the richer households!) when the Census agents visit.