It’s All Relative

It’s easy to quote someone out of context to impart a false impression. A movie critic might write a review saying, “This film is a delight compared to a colonoscopy” only to be quoted as saying, “This film is a delight.” Likewise, data presented without context may be misleading if they are related to other factors important to an analysis.

Hi, I’m from the government and I’m here to eat your tuna.

In analyzing data, some quantities are absolute in the sense that they mean the same thing under most conditions while others are relative to other influencing factors. Take a person’s age. If you are analyzing healthy six-year-old subjects, you would expect certain characteristics and behaviors that might vary within some typical range, but would be quite different from, say, sixty-year-old subjects. However, if your six-year-old subjects came from different cultures and geographies, you might find that their characteristics and behaviors are substantially different. In some societies, six-year-olds are protected innocents while in others they are hunters-in-training.

The Incredible Shrinking Government

Consider this example. How many times have you heard political pundits rant about the unbridled growth of the U.S. federal government? Is that really true? Sure, the government spends more dollars and has more employees than fifty years ago. But that’s to be expected because the country’s economy and population are both growing. It’s like a family that pays more for groceries to feed their hungry teenagers than they did when they were young children. So the government is indeed growing along with the rest of the country, but like children fueling an increase in grocery expenditures, the growth of the government is fueled by the growth of the economy and the population. If you want to examine the growth of the federal government, you have to compensate for the growth of the economy and the population. That’s what this chart does using data from a variety of federal websites.

Between 1960 and today, annual federal expenditures have been a fairly constant 20% of the country’s gross domestic product (GDP). The percentage was a bit less in the 1960s and 1970s, and a bit more in the 1980s. There have been two blips in the otherwise flat data trend—one in 1976 when the government changed its fiscal year, and one in 2009 attributable to the Troubled Asset Relief Program of 2008 (TARP, the Bailout) and the American Recovery and Reinvestment Act of 2009 (ARRA, the Stimulus). Overall, though, the amount the government spends is growing at about the same rate as the economy.

What about the federal workforce? The U.S. government is the largest employer in the world and it’s growing, but again, the growth is in response to the country’s growth in population. In fact, the chart shows that the number of full-time equivalent positions (FTEs) per thousand of population has decreased from 11 in 1960 to about 6 in 2009. The jump of half a percentage point in 2010 is attributable to the people the government hired for the 2010 Census, and more importantly, the people hired to administer TARP and ARRA. This data is for the Executive Branch of the government only and does not include Post Office Employees. The Office of Management and Budget has estimated that with Post Office FTEs, the ratio was 13.3 in 1962 and about 8.4 in 2010, but the trend is still downward.

Another popular rant of the political pundits is that Democrats grow the government and Republicans shrink the government. In the chart, the red lines represent Republican control of the government and the blue lines represent Democratic control of the government. Democrats have controlled the Presidency and both Houses of Congress five times in the past fifty years. The number of federal employees per the country’s population decreased substantially under Clinton, decreased slightly under Kennedy and Carter, remained about the same under Johnson, and increased under Obama. Republicans have controlled the Presidency and both Houses of Congress only once since 1960. The number of federal employees per the population remained about the same under G. W. Bush. So, it doesn’t matter who is in office, the government grows in line with the growth of the economy and the population. Don’t let those political pundits tell you differently.

Around the World in FTE Haze

Here’s another example along the same lines using data from http://www.numberof.net/number-of-government-employees-in-the-world/ and http://en.wikipedia.org/wiki/List_of_countries_by_population.

This table shows that the U.S. has a relatively large number of federal employees for its population and would top the list if the USPS employees were included. About a third of the countries have one government employee or less per 1,000 population. China with its huge population has the lowest ratio. The U.S. government may be getting smaller but it’s still way bigger than any other government in the world. Right? Maybe, but before you go all libertarian, consider this.

The data used in the table are frankendata—data collected by different people at different times and locations, analyzed with different procedures and equipment, and reported in different ways (http://statswithcats.wordpress.com/2010/10/31/resurrecting-the-unplanned/). The Employment data were collected between 2002 and 2010, each by a different source. Some are rounded to thousands and some are rounded to millions. Some represent FTEs and some are all employees. And perhaps most importantly, each country has a different government structure and defines civil service in different ways. Maybe there’s a grain of truth in it and maybe it’s just an illusion produced by a messy data set.

Putting Data in Perspective

If you are generating your own data, you can develop a sampling plan that will help ensure that your data are comparable and representative of the population you are investigating. Sometimes, though, you have no alternative except to use whatever data you can get. In that case, you can try three approaches:

  • Filter the data you will analyze by selecting from a much larger dataset only those data that are comparable to each other. For example, you might use only the environmental data that were collected at about the same time.
  • Index the data by some relevant factor, such as in the first example in which FTE counts over time were divided by population counts over time. The Consumer Price Index, used to adjust dollars to a constant point in time, is another example of indexing.
  • Transform the data so that they all have an entirely new common basis. The example of the chemical concentrations in groundwater that appears in the Stats with Cats blog Resurrecting the Unplanned is an example.

You may never have to resort to these measures to create a set of comparable data to analyze. Nevertheless, you should be aware of the problem and recognize it when you see relative data misused in an analysis. This is important … relatively.

Read more about using statistics at the Stats with Cats blog. Join other fans at the Stats with Cats Facebook group and the Stats with Cats Facebook page. Order Stats with Cats: The Domesticated Guide to Statistics, Models, Graphs, and Other Breeds of Data Analysis at Wheatmark, amazon.combarnesandnoble.com, or other online booksellers.

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About statswithcats

Charlie Kufs has been crunching numbers for over thirty years. He currently works as a statistician.
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7 Responses to It’s All Relative

  1. fxj says:

    the numbers for germany are wrong. wikipedia (http://de.wikipedia.org/wiki/%C3%96ffentlicher_Dienst) says: 4.576.000 working for the government, while the article says 2.000.000 which is more than a factor of 2.

    • I can’t argue with you since I don’t speak German, but I wouldn’t be surprised. The number you cited would put Germany on par with Italy. I don’t know if that makes sense or not because I don’t know enough about their governments, societies, and so on. The point is that you have to make your data comparable, which the data in that table definitely isn’t.

  2. Pingback: Be Data Informed » Archive » Just Learnt: frankendata

  3. babbo says:

    All the numbers should be per 100, not per 1,000. The US should have 6.8 workers per 100 (or 68 per 1,000)

  4. Pingback: It’s All Relative | Pets

  5. Pingback: The Best Super Power of All | Stats With Cats Blog

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