Rounding is not an accounting error

One of the integrity checks on SEC data is simple: earnings per share times the number of shares should equal net income. The first version allowed a 2% gap. By that test, 26.6% of filings failed, which would be alarming if it were true.

Most of those failures weren't errors. Earnings per share is reported to the cent. For a company earning two cents a share, a true value of 2.4 cents is reported as 0.02, and multiplying back gives a figure 17% below net income. Nothing is wrong except the rounding.

The check now allows the larger of 2% and half a cent per share. That changes the result:

• 3,897 of the 18,222 checks pass only because of the rounding allowance;
• the failure rate drops from 26.6% to 5.2%.

The 952 failures that remain are more interesting. Their median gap is about 100% of net income, far too large for arithmetic slips. That pattern looks like a units mismatch, such as share counts reported in thousands. It's the next thing to trace.

The general lesson: a tolerance has to match the precision the data was reported at. Otherwise you're measuring the reporting format, not the accounting.