I mention this because it is one of the most common of all conservative ploys. The convenient misuse of one type of statistical comparison to score a point, when, on even the slightest amount of reflection, the method of comparison used is inappropriate to the argument they’re trying to make.

If that’s not clear enough (and it may not be, if there are conservatives reading), I’ll put it more succinctly. I’m sick to death of conservative asshats (intentionally or not) misusing statistics so they can score political points, or make their favored talking point “sound better.” In that spirit, I’m calling them out.

Direct comparisons are applicable only when a given comparison is apples to apples, example:

John makes 100k per year and gave 15k to charity.

Dave makes 100k per year and gave 22k to charity.

Comparing 15k vs. 22k is an apples to apples comparison. Direct comparison works here. Note that you can check yourself. If direct comparison is the right stat to use, you’ll know because direct comparison and proportional comparison will give you the same answer.

Using the above example, we can say that Dave gave more to charity than John, and we can do that by either saying:
Dave gave 22k vs. John’s 15k – thus, Dave gave more.
Dave gave 22% of his income to charity vs. John’s 15%. Thus, Dave gave more.

Because these answers return the same value, we KNOW that we are comparing apples to apples.

Here’s an example where direct comparison doesn’t work:

John makes 50k, and gave 6k to charity.
Dave makes 100k, and gave 7k to charity.

Who gave more?

If you do a direct comparison here, you arrive at the conclusion that Dave gave more, because 7k is larger than 6k. Doing so, however, does not “work” because if you compare proportionality, you get the following values:
For John: 12%
For Dave: 7%

What is this data telling you?

Quite a lot, actually. First, because the values returned (direct vs. comparative) are different, it tells you that what you’re looking at isn’t apples to apples, and thus, it’s telling you that a direct comparison is the wrong statistic to be looking at. Second, it tells you that despite Dave having the larger number nominally, as a proportion of his income (that is to say, as a proportion of those resources available to him), John actually gave a larger percentage to charity than did Dave.

Now, you might (rightly) say that from the vantage point of the recipient of the donations, all that matters is the raw dollars given, in which case, Dave gave more, even if what he gave as a percentage of his income was lower, and you would be correct, but that’s not the reason we’re asking the question. In fact, it doesn’t really make sense (at all) to compare the giving trends of two people from the perspective of the charity they’re giving to. As the argument above states, all the charity cares about is that it’s got money coming in. Who’s giving how much is a (largely) irrelevant statistic to the charity. Dollars are coming in. That’s what they need.

However, the question above is asked not to determine charity funding levels, but to compare two people and their levels of giving, relative to their available resources, and given that, if resources are not equal for the two people in question, then the only measure that makes sense is proportionality.

So why does this matter?

Well, chiefly, it matters because what is true of the people in the above example, is also true of groups of people, and if that’s true, then it’s also true that the same thinking applies whether we’re talking about charitable giving or taxation.

This brings us ’round to where we want to be.

Next time someone tells you that “the rich pay (insert some large number here) in taxes” ask them if they’re looking at raw dollar contributions, or a percentage of total available resources per group (and further, how they are defining said groups).

Those kinds of details are important to know, because they’ll tell you if a) the right statistic is being used, such that the comparison is apples to apples, and b) a good deal about the underlying agenda of the person making the statement.