Numbers Don't Lie!

​You have heard it many times before, “Numbers don’t lie, people do.” The other day while I was enjoying my brother’s hot tub he said, “If I told you that one product had a rating in the seventies and another had a rating in the sixties, wouldn’t you get the impression that one had a higher rating than the other?” “Well sure”, I said. He responded, “Well, the ratings were actually, 70.1 and 69.9.” He got me! It took me back many years to a time when a colleague asserted that his favorite method of data conversion was superior because it yielded a correlation of .71 when predicted scores were compared to actual scores, versus an alternate method which yielded a correlation of .70. He knew better than to make that assertion and I took him to task for it.  The point is that these kinds of situations abound. Small differences may or may not be real. Remember the margin of error.  And remember to look at the details.
Our discussion moved on to talking about misleading with averages. If you averaged the temperatures of his swimming pool and his hot tub the average would give you a very comfortable 81 degrees. But the pool was 60 degrees and the hot tub was a near scalding 102 degrees. The weighted average might have been more accurate and oh, by the way what about using the centigrade scale which starts at absolute zero (not necessary in this case, work it out).  What about average height of the family? Does that tell you anything meaningful? Probably not. You may want the range or even the height of individual family members.
One of the most well known deceptions with numbers is when a salesperson tells you, “It costs only …”. What they are telling you may be the price of item or service but it is most certainly not the cost to you. There’s sales tax, dealers fee, transportation fee, license fee and many other well known price add-ons. And of course, let’s not forget training costs, insurance costs, and all the other big ticket costs that come with some products. Oh, you actually want to use that telescope? Well, you need software. What’s that you have a Mac, well the software will run only on a PC. And on and on it goes. No one really lied to you but none the less you were certainly deceived.
It can be much more subtle than that. In science accuracy is everything. While to those of us mortals who only deal with simple measurements the recent change in the length of the official foot doesn’t mean a whole lot. But if you are a surveyor or a maker of maps the change can be profound. The length of a foot, strangely enough, is defined in terms of meters. The standard American survey foot up until recently was 0.304800609601 m. But now they have gone to the international standard foot which is 0.3048 m. By looping off those extra digits they have made a bit shorter and the width of the USA is a whopping 30 miles, or so, wider! Okay, so when we measure the kids’ height it doesn’t make a difference so who cares? But, if your sending a missile from say North Korea to the US it could make a big difference. Maybe that’s why the changed it, to confuse the North Koreans.
 
Knowing what a number means and knowing how to obtain the correct number is what statistics is really all about. One of these days we may talk about the simple yet fundamental concept of measurement theory T + e = X. True value plus error equals measured value. Until then think about it.