The New York Times' Michael Shear passed along the Obama administration's unsubstantiated claim that 40% of gun purchases take place without a background check, in Wednesday's "Background Checks Are Still Stumbling Block in Gun Law Overhaul ."
Since the existing background-check system began, in 1994, officials have screened more than 108 million people before they could buy a gun, according to the Bureau of Justice Statistics; the federal government has blocked 1.9 million attempted purchases because of felony convictions or other problems with the would-be buyers’ background.
But no background check is required for about 40 percent of gun purchases, including those made online or at gun shows, federal officials estimate. Requiring checks for those purchases would be the single most effective way to keep guns out of the hands of dangerous people, advocates say.
Obama indeed said in a White House speech last week, “Why wouldn’t we want to close the loophole that allows as many as 40 percent of all gun purchases to take place without a background check?”
But the Washington Post's "Fact Checker" Glenn Kessler again refuted Obama's claim  on Tuesday.
There are two key problems with the president’s use of this statistic: The numbers are about two decades old, yet he acts as if they are fresh, and he refers to “purchases” or “sales” when in fact the original report concerned “gun acquisitions” and “transactions.” Those are much broader categories of data.
As we noted before, the White House said the figure comes from a 1997 Institute of Justice report, written by Philip Cook of Duke University and Jens Ludwig of the University of Chicago.
This study was based on data collected from a survey in 1994, the same year that the Brady Act requirements for background checks came into effect. In fact, the questions concerned purchases in 1993 and 1994, and the Brady Act went into effect in early 1994 — meaning that some, if not many, of the guns were bought in a pre-Brady environment.
Digging deeper, we found that the survey sample was just 251 people. (The survey was done by telephone, using a random-digit-dial method, with a response rate of 50 percent.) With this sample size, the 95 percent confidence interval will be plus or minus six percentage points.
Moreover, when asked whether the respondent bought from a licensed firearms dealer, the possible answers included “probably was/think so” and “probably not,” leaving open the possibility the purchaser was mistaken. (The “probably not” answers were counted as “no.”)
When all of the “yes” and “probably was” answers were added together, that left 35.7 percent of respondents indicating they did not receive the gun from a licensed firearms dealer. Rounding up gets you to 40 percent, although as we noted before, the survey sample is so small it could also be rounded down to 30 percent.