A recent PolitiFact review of a statement by Sen. Elizabeth Warren, D-Mass., suggests that a statement can be factually inaccurate yet “mostly true.”

In a Jan. 7 speech, Sen. Warren said: “The average family not in the top 10 percent makes less money today than they were making a generation ago.”

This flies in the face of virtually all research on the topic, which, as I told PolitiFact, shows “solid, though not fantastic, income growth for most of the income distribution.”

For a PolitiFact examination of the assertion, the senator’s staff provided reporter Lauren Carroll data from the World Top Incomes Database (WTID). But the information in that database is based on tax units, not families. Families often include more than one tax unit, and tax units cover many single individuals who are not part of any family per standard definitions.

Since the number of tax units increased at almost twice the rate of U.S. population growth since 1979, income is automatically getting split into more pieces, shrinking the average without a fall in any individual’s income. The data exclude health insurance, which is a growing part of compensation. Likewise, they do not distinguish between someone who loses her job and someone who retires comfortably. In short, the information from the World Top Incomes Database is tilted toward low-balling income growth.

For a variety of reasons, most economists do not use the World Top Incomes Database when considering the entire income distribution. For example, the data show no income growth for the bottom 90 percent since 1966. The World Top Incomes Database implicitly acknowledges that it has little accuracy outside the top 10 percent: Only two of the 144 summary variables on its website relate to the bottom 90 percent. Median income, which would be the most sought-after statistic from an accurate income distribution, is not available.

Ms. Carroll’s piece concluded: “According to one measurement, the bottom 90 percent of American earners had a lower income in 2012 than they had 30 years ago.” But none of her sources mentioned “earners.” Earners are not tax units; tax units are not families; and families are not households.

The piece also failed to note that Sen. Warren smuggled the statistic out of context: The senator implied that she was speaking about the past income growth of families currently in the bottom 90 percent of income. But the data she used actually compare two different groups of tax units, not the same families measured over time.

There is no data source that shows falling family incomes since 1980. The balance of related evidence shows that Sen. Warren started with an unreliable statistic, inaccurately re-labeled it, and then misleadingly applied it.

Originally appeared in the Wall Street Journal.