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New Audit Allegations Show Flawed Statistical Thinking

The Internal Revenue Service is under fire for inappropriately targeting conservative groups that sought tax-exempt status. As I wrote earlier this week, the revelation has the potential to motivate conservative turnout in the 2014 elections, perhaps costing Democrats as they seek to gain seats in the House and retain control of the Senate.

William B. Plowman /NBC Peggy Noonan has offered anecdotal evidence but no proof that the I.R.S. targeted taxpayers for political reasons.

Some conservatives, however, are alleging that there is another component to the scandal. They accuse the I.R.S. of targeting not just conservative groups that sought 501(c)(4) status, but also individual taxpayers who oppose President Obama or have supported conservative causes. “The second part of the scandal is the auditing of political activists who have opposed the administration,” the Wall Street Journal columnist Peggy Noonan wrote on Thursday, describing the I.R.S.’s actions as the “worst Washington scandal since Watergate.”

What evidence does Ms. Noonan present for this second allegation? She reports on four cases of conservatives who she says were targeted for audits, and infers that there were undoubtedly many more:

The Journal’s Kim Strassel reported an Idaho businessman named Frank VanderSloot, who’d donated more than a million dollars to groups supporting Mitt Romney. He found himself last June, for the first time in 30 years, the target of I.R.S. auditors. His wife and his business were also soon audited. Hal Scherz, a Georgia physician, also came to the government’s attention. He told ABC News: “It is odd that nothing changed on my tax return and I was never audited until I publicly criticized Obamacare.” Franklin Graham, son of Billy, told Politico he believes his father was targeted. A conservative Catholic academic who has written for these pages faced questions about her meager freelance writing income. Many of these stories will come out, but not as many as there are.

Ms. Noonan is surely correct that many conservative taxpayers were audited. In fact, based on some simple math that I’ll present in a moment, it’s likely that hundreds of thousands of Mitt Romney voters were selected for an audit in 2012.

However, it’s also likely that hundreds of thousands of Mr. Obama’s supporters were audited. Although the percentage of taxpayers who are audited is relatively low — about 1 percent — the number of taxpayers in the United States is so large that this still yields well more than a million audits every year, across the political spectrum.

The I.R.S. publishes data each year on the number of taxpayers it audits. In 2012, it conducted just shy of 1.5 million audits out of 144 million individual income tax returns.

The probability of being audited is highest for high-income taxpayers — about 12 percent of individuals who made more than $1 million were audited in 2012 — although taxpayers who report little to no income are audited at higher rates than those with average incomes. In fact, about one-third of audits pertained to people who claimed the Earned Income Tax Credit, a benefit for low-income taxpayers.

In the table below, I’ve estimated the number of taxpayers in each income group who were audited in 2012, as derived from statistics in the I.R.S.’s 2012 Data Book. It is also possible to estimate how many Mitt Romney and Barack Obama voters would have been audited last year. The calculation assumes that an individual’s chance of being audited was related to their income, but not to their political views.

I estimate the number of voters in each income bracket from the 2012 Current Population Survey. I then estimate the share of the vote in each income bracket that went to Mr. Romney and Mr. Obama based on last year’s national exit poll. (Note that the income brackets used in the exit poll and the Current Population Survey do not exactly match the income brackets listed in the I.R.S.’s audit data, so I use the closest available approximations.)

This results in an estimate that about 380,000 of Mr. Romney’s voters were audited last year, as were about 480,000 of Mr. Obama’s voters.

To be clear, this calculation assumes that individuals’ risk of being audited is independent of their political views. In fact, there is no way to know exactly how many supporters of each candidate were chosen for an audit — nor could there be, since individual-level voting records and audit records are private.

The point is, however, that even with no political targeting at all, hundreds of thousands of conservative voters would have been chosen for audits in the I.R.S.’s normal course of business. Among these hundreds of thousands of voters, thousands would undoubtedly have gone beyond merely voting to become political activists.

The fact that Ms. Noonan has identified four conservatives from that group of thousands provides no evidence at all toward her hypothesis. Nor would it tell us very much if dozens or even hundreds of conservative activists disclosed that they had been audited. This is exactly what you would expect in a country where there are 1.5 million audits every year.

None of this ought to take away from the major part of the I.R.S. scandal — the targeting of conservative groups that applied for 501(c)(4) status, which the I.R.S. has admitted to and for which the statistical evidence is very clear. And evidence could yet emerge that there was targeting of politically active individual taxpayers.

But the principle is important: a handful of anecdotal data points are not worth very much in a country of more than 300 million people. Ms. Noonan, and many other commentators, made a similar mistake last year in their analysis of the presidential election, when they cited evidence like the number of Mitt Romney yard signs in certain neighborhoods as an indication that he was likely to win, while dismissing polls that collectively surveyed hundreds of thousands of voters in swing states and largely showed Mr. Obama ahead.

A version of this article appears in print on 05/19/2013, on page A19 of the NewYork edition with the headline: Claims on I.R.S. Are Challenged By Probability.

Nate Silver founded and was the editor in chief of FiveThirtyEight.