Statistics Basics: What Does “4 out of 5 Dentists” Really Mean
People like to throw around statistics because they sound good and can help you “make your case” in an argument, “over 60% of all people polled are voting for Snoopy.” The problem is that many statistical quotes are fake and even the real statistical data are rarely understood by most people.
A common commercial for years stated, “4 out of 5 dentists recommend ________ Toothpaste” (fill in the blank with your favorite brand name). What does this really mean? In the world of statistics data is collected so, in this case they would probably have asked a group of dentists which toothpaste they would recommend and so out of 1000 dentists surveyed 800, or 799, dentists recommended Toothfairy toothpaste (not a real brand). They reduce the fraction to lowest terms and get 4 out of 5. The math is fine but here is the problem, I have a whole lot of questions about how they got their data and how they represented it.
Questions I have about this statistical statement:
- How many dentists did you actually survey? Was it just 5, 50, 100, 1000, 5000?
- What question did you ask on the survey? How you ask a question is very important because it can influence the answer you get. Examples:
- Would you recommend Toothfairy toothpaste to your patients?
- What toothpaste do you recommend most often to your patients?
- Given the following list of toothpastes (not included here) which would you recommend to your patients?
- Please list the top three toothpastes you would recommend to patients?
- If these 4 out of 5 dentists recommend Toothfairy toothpaste would they recommend any other toothpastes as well?
The original claim “4 out of 5 dentists recommend Toothfairy toothpaste” may be a perfectly correct statement but it doesn’t give you all the information about how they got their data. Data and statistics can be a powerful tool but it is frequently a misused tool that is made to prove what the writer or presenter wants without regard to the truth.
The point here is that someone is trying to sell their product or idea and using data and statistics to get people to literally buy in to their pitch. The more you know about how statistics work will help you be a more informed consumer and protect you against the unscrupulous.