Interpreting statistics: Misleading presentation of data

​ ​Have you seen the video on how statistical data can be presented in misleading ways? Here are a few other ways, where statistics don't tell the whole truth, but the errors were made when the information was collected. Here's a news headline: "75% of all women have cats. No men have cats." Can this really be true? Look under the headline.

There's the data on which the headline claim is based. Someone chose 17 people, and asked them if they had cats, but only five people answered - four women and one man. 12 people didn't answer at all, so we don't know how many of them have cats. If only one more person had answered, the results would have been completely different. With so many non-respondents, you can't make the conclusion presented in the headline.

Another thing to consider is who were these 17 respondents and how were they chosen? If you pose this question to 17 people in a store selling cat food, then it's likely that more of them own a cat, than if you ask 17 people in a hardware store, so the method of selection matters. If the selection is not representative of the group that you want to make conclusions about, the results are biased, even if all calculations and diagrams are completely error-free. ​ ​Here is a commercial: "9 out of 10 people prefer Steve's toothpaste." 9 out of 10, this is 90% or almost everyone, so it has to be good toothpaste, right? Look below the ad. There you can find what questions were asked to get this result.

What do you think about Steve's toothpaste? Very good, it's okay, or the worst I've ever tasted. The last choice is put down in a way that makes it unlikely that anybody would pick it. And the conclusion that 90% like the toothpaste is only true if you combine those people who chose the first and second alternatives. Is the claim in the headline false, or is it simply misleading?

Bad statistical results can be caused by negligence, but they can also be intentional and the purpose can be to push you toward a certain conclusion. When interpreting statistical data, it's useful to consider who is behind the study and what interest they they might have in influencing you. Is it a company wishing to sell something, or a political party that wants you to vote for them? Think about how they selected the respondents and what kind of questions they asked. How did they put the questions, and whom did they ask?