We’ve all heard aphorisms about the misuse of statistics. And we’ve all seen those pithy sayings come to life as individuals or groups twist statistics to their advantage. In contrast, one hopes that those in the media would report accurate statistics and would be able to discern accuracy from manipulation.

The basic problem is that any statistic is merely a proxy for the state of the world it attempts to measure. This is a necessary evil. In order to convey information about a sophisticated topic, one must reduce a complex world into some easily digestible form. The same process takes place in a variety of realms — from economic models to scientific experiments. The key in each context is whether what remains after the simplification is still relevant to the more complex reality.

Many statistics are close representations of the state of the world they attempt to measure. Others fall short. For example, the poverty rate is the percentage of people living in households whose income falls below the "poverty line." The poverty line was chosen in the mid-1960s, varies with family size and is annually adjusted for inflation. But what if the poverty line was not chosen well initially? And to revisit a recent debate, what if inflation is consistently exaggerated? These factors could lead the poverty rate to mistate the level of true poverty.

Four other problems arise since the poverty line is a measurement of reported cash income in a given year. First, the Census Bureau can only measure whatever income is reported. Underground economic activity leads to an exaggerated poverty rate. Second, the Census Bureau only measures cash income, omitting any non-cash government benefits (about 75% of redistribution to the poor). Thus, the poverty rate is, to some extent, a measure of dependency rather than low standards of living per se. Third, the poverty rate only deals with income and ignores wealth. As a result, some with low incomes but significant assets, especially the elderly, are measured as poor.

Fourth and most important, the poverty rate is only a snapshot of the economy in a given year. (Ideally, one would have a motion picture — following people for a number of years. Such data exist but are relatively costly to calculate.) As a result, many are measured as "poor" early in their lives — for example, graduate students — who will do well financially later in life. Are the same people poor each year or is there significant movement into and out of poverty? Unfortunately, the poverty rate and income- distribution statistics tell us nothing about the more vital question of income dynamics.

All of this explains some otherwise anomalous statistics. For example, the poorest fifth of all Americans consume almost two times more than their "income" and consume as much as the average family in the early 1970s (adjusted for inflation). And 41% of poor households own their own homes, including 750,000 poor people who own homes worth more than $150,000. The bottom line is that the poverty rate should be taken with a shaker of salt.

Other statistics are inadequate since they compare apples and oranges. Statistics on income differentials between race or gender groups typically fail to hold important variables constant - for example, levels and types of education, age/experience, region, and family structure. In addition, newspapers often report income comparisons between all men and all women — even though the job market preparation and experience of women has changed dramatically over the last 30 years.

Another example is the tired comparison between the average worker’s real wages and average CEO compensation. This one should be obvious — comparing one group’s wages with another group’s compensation. (With a bad year in the stock market, look for statistics manipulators to make this transition by themselves!) In fact, looking at real wages over the last 25 years is itself a dubious exercise since the proportion of compensation devoted to fringe benefits has risen so dramatically. (Higher marginal tax rates have made non-taxed benefits relatively more attractive than taxed wages.)

All in all, statistics have much to offer. The point is not to dismiss the poverty rate, but to be well aware of its inherent flaws and to seek out data on income dynamics. The point is not to downplay the issues of discrimination and worker compensation, but to use honest comparisons. The media have a responsibility to use statistics with discernment and discretion.

D. Eric Schansberg is associate professor of economics at Indiana University (New Albany).

— Rich Noyes