Think back to your first few weeks of Bachelor’s in Psychology. You had just been told that you will have to go through one year of statistical courses and the only thing that was hardest about stats was the formula for standard deviation.
Good times were they not?
That was until the second semester arrived. It brought along with it the demon of hypothesis testing and a smaller, actually cuter monster called the normal probability curve.
When I first read about the curve, I liked it a lot. It is such a simple representation of what universal probability and randomness tend towards. Take a look at this demo, a huge number of balls dropped over a Galton board.
The idea was that organized chaos can be simplified using the Gaussian curve as most of the agents of chaos (in this case, the tiny balls) tended towards the center. This idea had its roots in algebra and probability but soon it was taken used by psychologists as well.
Quetelet, the father of Quantitative Social Science believed that the concept of the normal curve didn’t just apply to probability but could be used for social phenomena as well. He called this The Theory of the Average Man (Quetelet, 1969)
Take the example of intelligence. Modern IQ measures assume that there is such a thing as the ‘normal human intelligence’ of IQ 100. 68% of the human population has an IQ between 85-115. These are normal people. They make up the center peak of the curve. The extremes on either side make up the extremes of intelligence spectrum.
What gets hidden in the fine print quite often is…this is an ASSUMPTION. This is not an empirical claim. This is an assumption that is used since it makes it easier and more convenient to assess intelligence in large populations.
Much of quantitative psychology is founded on the very assumption that psychological traits like intelligence, resilience, vocabulary or stress, etc are normally distributed.
Have you ever used a Student’s t-test? One-way ANOVA? Pearson’s correlation? One of the many assumptions that these tests have is that the data is normally distributed in the population. But is it?
We don’t know!
Does that stop us from using these tests because they are easier?
Absolutely not!
Unicorns and Normal Distribution
I borrow the title of my article today from the work of Theodore Micceri, a doctorate student at the University of South Florida who wrote a paper in 1989 with the same name. In his paper, he collected data from large samples across 440 psychological traits and wanted to see if they were really normally distributed or not.
What did he find?
Only 19 of the 440 were normally distributed🤯🤯 and even in those 19, there were lots of contamination. The distribution wasn’t perfectly normal.
It seemed like the idea of a bell curve of human nature was on its death kneel and suddenly, it all just disappeared. Discussions on the validity of the normal curve for psychology went out of vogue. It was as if most of the psychologists collectively decided that the convenience of the curve was more important than its scientific validity.
Ways out of this quagmire were found by statisticians though. They created tests that did not require normal distribution as an assumption but be honest and tell me you know how to perform any of the tests in the right-hand column.
Now What?
Do I mean to tell you that all the tears that rolled down your cheek while trying to understand the paired and unpaired t-test were a waste?
Well, in a manner of speaking, yes, that is exactly what I want to say
BUT
It is not the end of the world. It is more important that we are humble about the faults in our knowledge of human psychology derived from these tests. Science, statistics, data - all of these things are simply tools to reach an approximation of some form of truth about human psychology. Will we ever achieve a perfect form of truth? It is unlikely, but that does not mean we must stop trying.