Introduction to Data Science Using R Runestone Version 1

Many of the simplest and most practical methods for summarizing collections of numbers come to us from four guys who were born in the 1800s at the start of the industrial revolution. A considerable amount of the work they did was focused on solving real world problems in manufacturing and agriculture by using data to describe and draw inferences from what they observed.

The end of the 1800s and the early 1900s were a time of astonishing progress in mathematics and science. Given enough time, paper, and pencils, scientists and mathematicians of that age imagined that just about any problem facing humankind including the limitations of people themselves could be measured, broken down, analyzed, and rebuilt to become more efficient. Four Englishmen who epitomized both this scientific progress and these idealistic beliefs were Francis Galton, Karl Pearson, William Sealy Gosset, and Ronald Fisher.

First on the scene was Francis Galton, a half-cousin to the more widely known Charles Darwin, but quite the intellectual force himself. Galton was an English gentleman of independent means who studied Latin, Greek, medicine, and mathematics, and who made a name for himself as an African explorer. He is most widely known as a proponent of "eugenics," and is credited with coining the term. Eugenics is the idea that the human race could be improved through selective breeding. Galton studied heredity in peas, rabbits, and people and concluded that certain people should be paid to get married and have children because their offspring would improve the human race. These ideas were later horribly misused in the 20th century, most notably by the Nazis as a justification for killing people because they belonged to supposedly inferior races. Setting eugenics aside, however, Galton made several notable and valuable contributions to mathematics and statistics, in particular illuminating two basic techniques that are widely used today: correlation and regression.

For all his studying and theorizing, Galton was not an outstanding mathematician, but he had a junior partner, Karl Pearson, who is often credited with founding the field of mathematical statistics.

Pearson refined the math behind correlation and regression and did a lot else besides to contribute to our modern abilities to manage numbers. Like Galton, Pearson was a proponent of eugenics, but he also is credited with inspiring some of Einstein’s thoughts about relativity and was an early advocate of women’s rights.

Next to the statistical party was William Sealy Gosset, a wizard at both math and chemistry. It was probably the latter expertise that led the Guinness Brewery in Dublin Ireland to hire Gosset after college. As a forward looking business, the Guinness brewery was on the lookout for ways of making batches of beer more consistent in quality. Gosset stepped in and developed what we now refer to as small sample statistical techniques, a way of generalizing from the results of a relatively few observations. Of course, brewing a batch of beer is a time consuming and expensive process, so in order to draw conclusions from experimental methods applied to just a few batches, Gosset had to figure out the role of chance in determining how a batch of beer had turned out. Guinness frowned upon academic publications, so Gosset had to publish his results under the modest pseudonym, "Student." If you ever hear someone discussing the "Student’s t-Test," that is where the name came from.

Last but not least among the born-in-the-1800s bunch was Ronald Fisher, another mathematician who also studied the natural sciences, in his case biology and genetics. Unlike Galton, Fisher was not a gentleman of independent means, in fact, during his early married life he and his wife struggled as subsistence farmers. One of Fisher’s professional postings was to an agricultural research farm called Rothhamsted Experimental Station. Here, he had access to data about variations in crop yield that led to his development of an essential statistical technique known as the analysis of variance. Fisher also pioneered the area of experimental design, which includes matters of factors, levels, experimental groups, and control groups that we noted in the previous chapter.

Of course, these four are certainly not the only 19th and 20th century mathematicians to have made substantial contributions to practical statistics, but they are notable with respect to the applications of mathematics and statistics to the other sciences (and "Beer, Farms, and Peas" makes a good chapter title as well).

One of the critical distinctions woven throughout the work of these four is between the "sample" of data that you have available to analyze and the larger "population" of possible cases that may or do exist. When Gosset ran batches of beer at the brewery, he knew that it was impractical to run every possible batch of beer with every possible variation in recipe and preparation. Gosset knew that he had to run a few batches, describe what he had found and then generalize or infer what might happen in future batches. This is a fundamental aspect of working with all types and amounts of data: Whatever data you have, there’s always more out there. There’s data that you might have collected by changing the way things are done or the way things are measured. There’s future data that hasn’t been collected yet and might never be collected. There’s even data that we might have gotten using the exact same strategies we did use, but that would have come out subtly different just due to randomness. Whatever data you have, it is just a snapshot or "sample" of what might be out there. This leads us to the conclusion that we can never, ever 100% trust the data we have. We must always hold back and keep in mind that there is always uncertainty in data. A lot of the power and goodness in statistics comes from the capabilities that people like Fisher developed to help us characterize and quantify that uncertainty and for us to know when to guard against putting too much stock in what a sample of data have to say. So remember that while we can always describe the sample of data we have, the real trick is to infer what the data may mean when generalized to the larger population of data that we don’t have. This is the key distinction between descriptive and inferential statistics.