Telling mean from median and relative from absolute risk is enough to stop many news numbers from fooling you. Worked through with made-up examples.
Every statistic in a news story or an ad is the answer to a question someone asked. So before the number itself, ask what was measured, in whom, and how. The same data can leave very different impressions depending on which measure is chosen, and a number can mislead without being wrong. Every number in this article is a hypothetical example made up to explain the idea, not a real survey result.
The mean is the sum of all values divided by how many there are; the median is the middle value when you line them up in order. When values are evenly spread the two are similar, but a few very large values drag the mean up on their own. As an example, if four employees earn 2,000, 2,200, 2,500 and 2,800 a month and the owner earns 20,000, the mean of the five is 5,900 while the median is 2,500. For data with a long tail on one side, such as income, house prices or wealth, the median is much closer to the typical person.
"This habit raises your risk by 50%" sounds alarming, but you cannot judge it without knowing the original risk. As an example, if a disease went from 2 in 1,000 people to 3 in 1,000, that is a 50% relative increase but an absolute increase of 1 person per 1,000. If the starting risk were large, the same 50% would affect far more people. Whenever you see a relative risk, look for the baseline probability it is measured against. The same applies to claims about drugs or treatments: asking how many people out of how many a halved risk actually represents can change your sense of it dramatically.
This is a common mix-up when comparing two rates. As an example, if a rate goes from 10% to 12%, it rose by 2 percentage points, or by 20% relative to where it started. Both statements are correct, but they leave very different impressions. Changes in numbers already expressed as percentages, such as interest rates, approval ratings or unemployment, are stated precisely in percentage points. When a story mixes the two, check which one it means. In real articles, just keep in mind that the same change can look small or large depending on which wording is used.
A survey result describes the people who took part in the survey. If only visitors to one website were asked, or only people who volunteered to respond, the result may not represent the wider population. With too few respondents, results swing widely by chance. Check whether the survey period, method, sample size and margin of error are reported, and treat a difference inside the margin of error as essentially no difference.
Two numbers rising and falling together does not mean one causes the other. On hot days, for example, ice cream sales and swimming accidents may both go up, but ice cream does not cause accidents; a third factor, the heat, moves both. Cause and effect can also run the other way, or the link can be pure coincidence. Remember that claiming causation requires a study design that controls for other factors.
The same numbers feel different depending on how they are drawn. If the vertical axis does not start at zero, small differences look large, and showing only a convenient slice of time can make a trend appear to reverse. Cumulative charts always climb, which can hide a slowdown in growth. When you see a chart, check the axis starting point, units and time span first, and look at the underlying table if you can.
Being skeptical of statistics does not mean assuming they are all false. It means separating what a number says from what it does not. Make a habit of asking these questions.
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