Fun With Statistics

So, we all know that the economy has struggled in recent years. This is relatively undeniable, although I will admit that most people I know personally seem to be doing pretty ok. But one of the more distressing things I’ve been reading about is how even getting a college degree doesn’t seem to benefit people anymore, at least in the way that it used to. Even women, who relative to men have seen their incomes increase during the recession, seem to be struggling. Here’s data on the changes in median income (inflation adjusted) for women over 24. The data is for women who were defined as working full-time and by education level. It’s taken from the US census.

Less than 9th grade -3.7%

9th-12th but didn’t finish -6.7%

High school graduate -3.3%

Some college but no degree -3.7%

Associate’s degree -10.0%

Bachelor’s degree or more -2.7%

That’s pretty bleak, right? Women’s incomes have decreased at every level regardless of their level of education. It seems particularly alarming that the trend isn’t positive even for those with the most education. Even women with bachelor’s degrees earned less in 2012 than in 2000. And those with associate’s degrees faired especially poorly, earning a whopping 10% less.

Ok, so that doesn’t look good. But what would your guess be of what the total average change in women’s income was over the time period, across all groups? There’s not really enough information here to form more than an educated guess, but I’d imagine most people would surmise that it’s somewhere between the -2.7% and -10.0% thresholds given here. It only makes sense that the average would lie somewhere between the valley of -2.7% and the peak of -10.0%, right?

Except that it doesn’t. The average change across all groups turns out to be roughly 2.8%. That’s positive 2.8%. Not negative.

The reason is that the populations across groups aren’t constant. Many more women had college degrees in 2012 than in 2000. How many more? About 37% more – 41.8% of all female workers vs. 30.5% in 2000. Since so many more women were in the highest paying category (bachelor’s degree or more) it results in an average increase in the income of all women – even though women at each level perform worse than in the past. So median incomes for women actually increased from 2000 to 2012, despite what the numbers above imply.

I love these kinds of counterintuitive facts, because it shows just how elusive facts can be. A newspaper could insert the first numbers I pasted in here and have a perfectly believable story about how women’s incomes are falling at every level. The newspaper wouldn’t be reporting the numbers inaccurately even. It’s true, women’s incomes are falling at every education level. But that’s at least partially because the make-up of each education level is changing – the women with only an associate’s degrees today aren’t the same women that only had an associate’s degree even 12 years ago. The world has already changed in those 12 years and how the various levels of education are valued has also changed.

Bright people are very attracted to statistics because statistics feel factual. I suppose that, if done correctly, they are factual. But the reality is facts can be misleading. Sometimes it’s easy to stand behind your “facts” without realizing how fragile the interpretation of those facts may be. I think it’s a good idea to remain skeptical of any statistics you hear reported and not discount your instincts. Those instincts may be full of their own biases, but they can be pretty smart too, even if they haven’t calculated the numbers.

Hat tip to Russ Roberts at <a class="link" href="http://cafehayek.com/&quot; rel="

nofollow” target=”_blank” style=”box-sizing: border-box; color: rgb(66, 139, 202); text-decoration: none;”>cafehayek.com for inspiring this post.