andrew_gelman_stats andrew_gelman_stats-2011 andrew_gelman_stats-2011-549 knowledge-graph by maker-knowledge-mining
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Introduction: Matthew Yglesias links approvingly to the following statement by Michael Mandel: Homeland Security accounts for roughly 90% of the increase in federal regulatory employment over the past ten years. Roughly 90%, huh? That sounds pretty impressive. But wait a minute . . . what if total federal regulatory employment had increased a bit less. Then Homeland Security could’ve accounted for 105% of the increase, or 500% of the increase, or whatever. The point is the change in total employment is the sum of a bunch of pluses and minuses. It happens that, if you don’t count Homeland Security, the total hasn’t changed much–I’m assuming Mandel’s numbers are correct here–and that could be interesting. The “roughly 90%” figure is misleading because, when written as a percent of the total increase, it’s natural to quickly envision it as a percentage that is bounded by 100%. There is a total increase in regulatory employment that the individual agencies sum to, but some margins are p
sentIndex sentText sentNum sentScore
1 Matthew Yglesias links approvingly to the following statement by Michael Mandel: Homeland Security accounts for roughly 90% of the increase in federal regulatory employment over the past ten years. [sent-1, score-1.187]
2 what if total federal regulatory employment had increased a bit less. [sent-7, score-0.995]
3 Then Homeland Security could’ve accounted for 105% of the increase, or 500% of the increase, or whatever. [sent-8, score-0.069]
4 The point is the change in total employment is the sum of a bunch of pluses and minuses. [sent-9, score-0.903]
5 It happens that, if you don’t count Homeland Security, the total hasn’t changed much–I’m assuming Mandel’s numbers are correct here–and that could be interesting. [sent-10, score-0.429]
6 The “roughly 90%” figure is misleading because, when written as a percent of the total increase, it’s natural to quickly envision it as a percentage that is bounded by 100%. [sent-11, score-0.442]
7 There is a total increase in regulatory employment that the individual agencies sum to, but some margins are positive and some are negative. [sent-12, score-1.767]
8 If the total happens to be near zero, then the individual pieces can appear to be large fractions of the total, even possibly over 100%. [sent-13, score-0.637]
9 I’m not saying that Mandel made any mistakes, just that, in general, ratios can be tricky when the denominator is the sum of positive and negative parts. [sent-14, score-0.909]
10 In this particular case, the margins were large but not quite over 100%, which somehow gives the comparison more punch than it deserves, I think. [sent-15, score-0.281]
11 We discussed a mathematically identical case a few years ago involving the 2008 Democratic primary election campaign. [sent-16, score-0.174]
12 The funny thing is that the denominator has to be small (so that the numerator seems like a lot, “90%” or whatever) but not too small (because if the ratio is over 100%, the jig is up). [sent-20, score-0.498]
13 Mandel replies that, yes, he agrees with me in general about the problems of ratios where the denominator is a sum of positive and negative components, but that in this particular case, “all the major components of regulatory employment change are either positive or a very tiny negative. [sent-23, score-1.952]
14 ” So it sounds like I was choosing a bad example to make my point! [sent-24, score-0.138]
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