Continuing on in my How To Lie With Statistics series, let’s talk about “Much Ado About Practically Nothing.”

For the sake of simplicity and consistency we have many standards in this world that involve thresholds. An abortion can only happen prior to the 20th week of gestation, a person is of normal intelligence if his or her IQ is above 100, and a warrant expires after 30 days. We follow these rules as if the cut off period were determined by some all knowing entity and set in stone.

In fact, we’re missing something. That something is the standard error (or standard deviation…I won’t get into the difference right now…but there’s a big one). When we report a threshold, what we’re really reporting is the average time at which something should occur. In the case of abortions, one is termed as “late-term” if 20 weeks have passed. But the reality is that some fetuses mature faster than others and some mature slower than others. So really, we should talk about 20 weeks + or – some number of weeks. We should provide a range of possibilities based on the standard error associated with the underlying data.

Similarly, we can look at the warranty example. Firms know full well how long a product should last and often determine the length of a warranty to be somewhere in that range. What they are ostensibly saying is that their product will last approximately the length of the warranty. But what happens when your laptop break after 1 year and 2 days (assuming a 1 year warranty)? According to the firm, you’re out of luck. But really, the expectation of a 1 year life time is just an average and needs an associated standard error. The life span is really 1 year, plus or minus some number of days/weeks. Firms take advantage of this fact and customers suffer.

The point is that whenever you see an average, make sure to find out the standard error as well. This is done very frequently in political polls when you see that X is beating Y by 3% but the error on the result is also 3%. This suggests that it is very possible that the margin that X is beating Y by doesn’t actually exist in the population. Be aware of this and know you’ll be much better off when reading (and creating) statistics!

Part 1 - The Sample with the Built-in Bias
Part 2- The Well-Chosen Averge
Part 3 - The Little Figures That Are Not There

This entry was posted on Wednesday, April 16th, 2008 at 10:25 am and is filed under Science. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.