The Denominator Law

Education policy debates should have a law.  No one should be allowed to highlight numerators without also presenting denominators.  That is, it is often misleading to describe a big number without putting that number in perspective.  In almost every education policy issue we see debates distorted by large numbers (the numerators) without the benefit of perspective that comes from also mentioning the denominator.

For example, the placement of disabled students in private schools is a regular sore spot for school districts and the topic of numerous alarming articles in the media.  New York City complained as part of its lawsuit in the Tom F. case that private placements initiated by parent request were costing NYC schools $49.3 million in a single school year.

Wow, that sounds like a huge burden — it’s millions of dollars!  But that is just the numerator.  If we add the denominator to the discussion, private placements no longer seem like a large financial burden.  NYC has a total annual budget of about $17 billion.  Once we add the denominator we see that private placement consists of about .3% of the NYC budget.  And if we consider that disabled students would have to be educated in the public schools if they were not placed in private schools, the additional cost of private placement is less than .1% of the total NYC budget.  See what a difference a denominator can make?

Articles in the New York Times, Time Magazine, the San Francisco Chronicle, Boston Globe, etc… lament the crushing burden of private placements.  One would think from all of these articles that private placements happen all of the time.  In fact, there are 57,708 disabled students using public funds to be educated in private schools at parental request.

Wow, that’s tens of thousands of students.  But wait.  There are more than 6 million disabled students and almost 49 million total students in K-12 education.  So privately placed students represent less than 1% of all disabled students and about one-tenth of one percent of all students.  Enforcing the denominator law would have a huge effect on news coverage of this issue.

The presentation of numerators without denominators also distorts the “boy crisis” debate.  In a recent report issued by the American Association of University Women, they argue that boys are doing fine since the number of men graduating college has increased over time: “More men are earning college degrees today in the United States than at any time in history. During the past 35 years, the college educated population has greatly expanded: The number of bachelor’s degrees awarded annually rose 82 percent, from 792,316 in 1969–70 to 1,439,264 in 2004–05.” It’s true that the number of women enrolled in college has increased even faster, they claim, but as long as college enrollment is rising for both men and women, there is no cause for alarm.

But there are also more people in the United States over time.  How do things look when we add a denominator to the discussion?  In 2006 25.3% of men between the ages of 25 and 29 had a BA or higher.  If we look at the cohort of men three decades earlier (ages 55-59) 34.7% have a BA or higher.  Educational attainment is declining for men once we add the denominator.  The same comparisons for women show an increase from 27.4% holding a BA or higher among those ages 55-59, rising to 31.6% among women ages 25-29.

The Denominator Law is important because the number of people and dollars involved in education is so huge that everything seems big without the benefit of the perspective that denominators bring.

2 Responses to The Denominator Law

  1. Sam Lubell says:

    But at a time when the average college student takes more than four years to graduate, many men will get diplomas later than age 25 or 26. Instead of comparing men ages 25-29 to men 55-59, wouldn’t a better comparison be to men ages 25-29 thirty years ago?

    Also, there seems to be something unusual about the 55-59 age group as both the next younger (50 to 54) and older (60 to 64) age group were 3.5 percentage points lower.

    For that matter, with the exception of the two age groups you picked, all others (under age 65) are no more than 1.5 points in either direction from 30, suggesting a rather high level of continuity, not a decline.

    So the difference between age 30-34 and 50-54 is just 2.2 percentage points.
    The difference between ages 30-34 and 60-64 is 2.3 percentage points.

  2. If students start college at 18 and don’t get a BA by 25, they’d be taking more than 7 years to finish what is normally a 4 year degree. If male students are increasingly unable to finish a 4 year degree in as many as 7 years, then that would be a sign of a growing “boy crisis.”

    Yes, it would be better to have data for 25-29 year olds from three decades ago, but I’m just illustrating a point. I suspect if you dig those data up you will find exactly what I have presented here.

    And the pattern shows a decline for males no matter which age groups you use for the start and end point. Now we are only talking about how big the decline is. Meanwhile the rate for females is increasing and has reached a much higher level than for males. If there were no problems with the education of boys, shouldn’t the two rates be roughly the same?

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