statistics vs. Statistics

This is one I thought I would do earlier in the posts. I don’t even remember where I first heard someone distinguish between statistics with a lower-case ‘s’ and Statistics with an upper case ‘S’. I apologize if I should be giving credit to someone. I have been using the distinction in conversations, presentations, and teaching for about 10 years. It hasn’t lost its relevance. In my experiences, the distinction is lost on most students, most researchers I have worked with, and even a lot of people with degrees in Statistics. And I think the distinction does matter — not only for the discipline of Statistics, but also for scientists and the public.

Lower-case ‘s’ statistics are simply the numbers we calculate from data, such as an average, a sample median, a minimum, a maximum, etc. All that is needed for little ‘s’ statistics are some numbers and a calculator. Anyone with basic math knowledge can calculate them and report them. Classic example are summaries of census data and sports data. statistics provide an easy way to summarize a lot of numerical data into a single number. My daughter came home from school last week saying they have designated a statistician for their gym class — the person who records and summarizes basic data on 6th grade ultimate frisbee competitions. I tried to embrace and appreciate the acknowledgment and inclusion of the word “statistician” into education of our children, but if I’m really honest, I find it demeaning to my education, my expertise, and potentially harmful to science because it is setting wrong stereotypes and expectations as their first introduction. Maybe what they are describing is a little ‘s’ statistician, but that just gets to be too complicated. They are describing a technician whose job is data entry and data summarizing. They are not describing a scientist. (Another blog post is coming titled An -ologist, not an -ician)

Upper-case ‘S’ Statistics, while it did evolve from the foundation of calculating lower-case ‘s’ statistics, is the scientific field devoted to the study of the whole process of statistical inference. What I mean by statistical inference and even the process of statistical inference will come in more detail later. The point here is that it is not simply the process of calculating little ‘s’ statistics.

In practice, the words are used interchangeably — in ways that are confusing and indistinguishable. It is truly unfortunate that the discipline of Statistics shares a name with little ‘s’ statistics. I used to believe it was really just unfortunate for the Statisticians who struggle to educate people about what they actually do, but I now believe it is unfortunate for science in general. The reasons we struggle to raise awareness about what things are included in our discipline and expertise are related to mis-understandings and mis-uses of statistical methods in practice — like treating statistical inferences as if they are reports of statistics from censuses.

As you will probably hear me say many times in this blog — you can discount it as semantics (as many people have and continue to do), but I do not believe it is just semantics. There are consequences to our use of words.