Monday, September 21, 2009

Mind the gap

News stories often give statistics on gaps, differences in achievement or performance between different groups. The comparisons are often based on gender or ethnicity but can look at anything. Over the last little while, articles on education in media often look at various gaps between boys and girls in school.

One thing to watch out for when looking at gaps is that there are different ways to look at a discrepancy between two groups. For example, if we have a group of people who make $20,000 a year and another group who make $100,000 a year, we clearly have a gap. One way of defining the gap is to say that the difference is $80,000 a year. Another way of defining the gap is to say that the second group makes five times what the first group does.

Why does it matter how the gap is defined? To answer, I will continue with my example. Suppose after a series of government programs intended to close the income gap between these two groups that the first group's income has been increased by 50% to $30,000. During the same time the second group's income increased by 20% to $120,000 a year. Let's look at the gap again.

If we look at the gap as an absolute we now see that the difference in income is $90,000 a year. The gap is getting bigger! Does that mean that the government programs were a waste of time and money? Maybe not. If we look at the ratio of incomes, the second group no longer makes five times the income of the first group, the ratio has been reduced to four to one. So one way of looking says the gap is getting worse, another way says that the gap is being reduced. Which one is correct? Well, like most things in life, the answer is "that depends".

And what it depends on is the context of the information. If we are looking at which group is going to be purchasing more luxury vacations, then maybe the straight difference of $90,000 is the more important figure. If we are looking at more basic purchases such as housing or food, the ratio might tell the story more accurately. And, to make things more complicated, there are lots of other factors that probably should be considered before we can accurately talk about the gap. What about taxes? The high income group does not get to keep all of its $20,000 a year gain but taxes will be lower for the other group. That will affect the difference and the ratio too.

The critical thing is to recognize that there are multiple ways of looking at any statistical information and to try and find the one that makes most sense. If you want to improve your knowledge of statistics, I listed some possible websites in the comments section of my blog entry We want everyone to be above average?

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