Statistics: Not just for sports fans!
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Four out of five dentists recommend Super Paste toothpaste. Americans carry an average of $3,600 in credit card debt. The population of bobcats is directly correlated to the population of snowshoe hares in a given location. All of these are examples of statistics. But what do we mean when we say that “statistics” show something?
Well, in the “real world” we use the word “statistics” to refer mostly to the number of people or things doing something, like the dentists recommending toothpaste. But in the world of math, statistics has a more important function, one that seeks to probe the relationship between two variables to see whether their relationship is due purely to chance or to other factors. For example, in our example about bobcats and snowshoe hares, we would collect a large about of population data about both species year after year and look for variations in population size. Only then can we apply the tools of statistics to determine how likely it is that there is a real relationship between the two variables and not just an imaginary one due to random chance.
One example of this is used often in statistics classes. It often looks something like this:
There are two hospitals: in the first one, 120 babies are born every day, in the other, only 12. On average, the ratio of baby boys to baby girls born every day in each hospital is 50/50. However, one day, in one of those hospitals twice as many baby girls were born as baby boys. In which hospital was it more likely to happen? The answer is obvious for a statistician, but as research shows, not so obvious for a lay person: It is much more likely to happen in the small hospital. The reason for this is that technically speaking, the probability of a random deviation of a particular size (from the population mean) decreases with the increase in the sample size. [1]
This is an important concept in statistics: Sample size matters. The fewer data points you have, the more likely that random chance will move you away from the average that you would see in the population as a whole. Or, to put it in a blunter way, let’s look again at our four out of five dentists.
Let’s say we had one hundred dentists and eighty of them hate the Super Paste toothpaste, but twenty like it. If you select dentists at random for a sample of just five, every now and then you’re going to get four out of five liking the paste, which is the exact opposite of the “full” population of dentists! That’s why the study of statistics is crucial for helping us understand our world.
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[1] “Elementary Concepts in Statistics,” The Statistics Homepage, 2003, StatSoft, <http://www.statsoft.com/textbook/stathome.html> (25 September 2006).
