Real Examples of Misleading Statistics

Question

I need to give a presentation to a group of students on Tuesday about why one needs to be careful when examining statistics or mathematical results in the media or online.

In his book How Not To Be Wrong, Jordan Ellenberg provides a few examples that I planned on using as case studies to present to the students

1. Wisconsin governor in 2011 claims, since there was a net 18,000 jobs added in 2011 and 9,000 were in Wisconsin, that implies that Wisconsin is doing something right. Failed to mention that net jobs added included states that lost jobs, which reduces the net rate.
2. Mathematicians find proof that the Torah sends messages to the future by looking at sequences of characters that correspond to rabbi names and said rabbi birth/death dates. However, these results only held in the event of very specific names and dates; using any other accepted names or dates for each rabbi resulted in failed tests.

If anyone knew of any other good real world examples of misleading statistics or mathematics. I know of a many examples due to variability in sample size, but the more intricate and (potentially) nefarious, the better.

Thank you!

Answer 1

In 2018 WWF published the Living Planet Report. This report was widely misinterpreted, and many newspapers reported something along the lines of a 60% reduction in wildlife since 1970 without giving a more detailed (or correct) explanation.

WWF ellaborated how their numbers were obtained in a technical supplement to their report. They write:

"Does the trend in the global LPI mean we have lost 60% of all animals? Although the LPI uses time-series of either population size, density, abundance or a proxy of abundance, the overall trend calculated represents an average trend in population change and not an average of total numbers of individual animals or species lost."

They even give an illustrated example, found below, which I have edited slightly to make more compact.

Answer 2

Another example is (bitcoin) by trading volume. Sometimes people will say X (some number) of bitcoins are traded each day, that's the equivalent of Y (number depending on X and the exchange rate) million US dollars!

Sometimes, this is meant to impress, look at how many millions of dollars are traded each day, it must be important.

In reality, even if the figures are correct, it's a baseless number because it doesn't take into account who are parties to the transaction. Even if a lot of money is moved between different accounts, doesn't mean it's actually changing between owners. This is particularly the case with bitcoins because accounts are cheap (only the transaction costs money) so people can easily have large numbers of accounts.

A similar situation would be if you went to the ATM, withdrew 10,000$ and went into the office to deposit it back into your account. Then, to go back to the ATM, etc. etc. until you have withdrawn a 100 times that day. Only to brag to your friends that you are very important because you handled one million dollars that day.