Well, my little one, if you insist. Just one more bedtime story.
A long, long time ago, a bunch of people who really loved weather and biology and space and other areas of natural science noticed a lot of patterns on earth and in space. They created neato datasets about the weather, about the rising and setting of the sun, and about how long people lived. They added new points to their datasets everyday because the planets always revolved and the cells always went in the petri dish and the clouds could always be observed. All this happened even when the scientists were tired or hungry or angry. The planets moved and the cells divided and the clouds rained because they didn’t care that they were being watched or measured. And, the rulers and scales worked the same whether they were made of wood or plastic or titanium.
Over time, the scientists came up with really neat equations to figure out things like how often certain natural and biological events happened and how often their predictions based on those data were right and wrong. They predicted when the sun would rise depending on the time of year, when the cells would divide depending on the moisture and oxygen, and when the clouds would rain depending on where the lakes and mountains were. This, my little curious one, is where p-values and probability sampling and t-tests and type 1 errors came from.
The scientists realized that using these statistical equations allowed them to gather small datasets and generalize their learnings to much larger datasets. They learned how small a sample could be or how large a sample had to be in order to feel more confident that the universe wasn’t just playing tricks on them. Scientists grew to love those equations and the equations became second nature to them.
It was an age of joy and excitement and perfect scientific test-control conditions. The natural sciences provided the perfect laboratory for the field of statistics. Scientists could replicate any test, any number of times, and adjust or observe any variable in any manner they wished. You see, cells from an animal or plant on one side of the country looked pretty much like cells from the the same animal or plant on the other side of the county. It was an age of probability sampling from perfectly controlled, baseline, factory bottled water.
In fact, statistics became so well loved and popular that scientists in all sorts of fields tried using them. Psychologists and sociologists and anthropologists and market researchers started using statistics to evaluate the thoughts and feelings of biological creatures, mostly human beings. Of course, thoughts and feelings don’t naturally lend themselves to being expressed as precise numbers and measurements. And, thoughts and feelings that are often not understood and are often misunderstood by the holder. And, thoughts and feelings aren’t biologically determined, reliable units. And worst of all, the measurements changed depending on whether the rulers and scales were made of English or Spanish, paper or metal, or human or computer.
Sadly, these new users of statistics grew to love the statistical equations so much that they decided to ignore that the statistics were developed using bottled water. They applied statistics that had been developed using reliable natural occurrences to unreliable intangible occurrences. But they didn’t change any of the basic statistical assumptions. They didn’t redo all the fundamental research to incorporate the unknown, vastly greater degree of random and non-randomness that came with measuring unstable, influenceable creatures. They applied their beloved statistics to pond water, lake water, and ocean water. But treated the results as though it came from bottled water.
So you see, my dear, we all know where statistics in the biological sciences come from. The origin of probability sampling and p-values and margins of error is a wonderful story that biologists and chemists and surgeons can tell their little children.
One day, too, perhaps psychologists and market researchers will have a similar story about the origin of psychological statistics methods to tell their little ones.