The Evolution of Statistics In Education And Psychology

Psychology and statistics have evolved together. Since the late nineteenth century, statistics has played a pivotal role in the growth and evolution of the science of psychology. Statistics found application in astronomy a full century before psychologists started utilizing statistical methods. In the early days of astronomy, the focus was on the theory of errors as expressed by:

Truth + Error = Observation

The application of statistical methods on astronomical observations began in the late eighteenth century, and the theory of probability found its use starting in the early nineteenth century. Two of the early proponents of this practice were Dr. Carl Friedrich Gauss (1777 – 1855) and Pierre Simon Laplace (1749 - 1827).

When statistical models and methods made their way to Psychology, the models turned out to be inadequate as psychology is fundamentally different from astronomy. The first notable application of probability-based statistical modeling was demonstrated in 1860 in the work of Gustav Fechner as published in Psychophysics (Boring 1961: Stigler I 1986). With the work of Ebbinghaus on memory in 1885, a probability-based approach towards psychology was accepted and established.

One of Gustav Fechner’s experiments was reproduced in December 1883 and January 1884 by Charles S. Peirce while he was on the faculty of John Hopkins. The research (Peirce and Jastrow 1885: Stigler 1978) tabulated the right and wrong cases to the sensation of weights lifted by experimental subjects. The experiment involved two identical boxes, each containing weights. Both boxes contained a weight with the second box contacting an additional smaller weight, making it slightly heavier. The goal of the experiment was to have a subject lift both boxes and identify the heavier box. Right and wrong answers were tabulated. The experiment is repeated with various combinations of weights along with other variables such as time of the day, right hand and left hand, heavy first or light first, and so on.

Peirce’s experiment introduced the idea of a randomized experiment, which was made popular in the mid-nineteenth century by Ronald A. Fisher through his experiments on agriculture. But Peirce’s experiment was equally impactful as he was clear on the method and the goal of the experiment. Through the application of statistical randomization, Peirce created an artificial baseline for the analysis, which was as well-defined as the Platonic constants on Newtonian physics.

Peirce’s work was based on Fechner’s control of the experimental conditions, similar to Muller, Ebbinghaus and Wundt’s works, which formed artificial baselines and a framework that allowed a statistical investigation into psychological matters. This is the point when classical psychology changed forever.

Peirce’s experiment uncovered subjects’ sensitivity to sensations that went below Fechner’s threshold. Even though the sensitivity was marginal, thanks to a well-formed baseline and how the experiment was designed, the sensitivity was definitively observed and recorded. Peirce’s experiment is considered one of the most carefully crafted and laid out psychological experiments that paved the way later for experiments such as Adolphe Quetelet’s distribution of human attributes and anthropomorphic characteristics like stature. This type of application later got popularized as statistical analysis.

However, the application of this idea into other more important areas took more time. Quetelet’s intent to extend the method to quantify moral qualities failed due to a lack of data. But Francis Galton utilized Quetelet’s ideas to apply them on test scores from the Royal Military College at Sandhurst in 1869. Through his study, Galton prepared the framework for the inheritance to evaluate the inheritance of ability, which was measured via examination scores. 

The statistical principles of correlation and regression analysis were direct results of Galton’s work. John Dewey was among the first to accept and appreciate Galton’s work as the modern regression analysis found application into new areas such as educational research. Regression analysis allows a multivariate distribution to define a relationship between its variates via the conditional distributions.

Dewey accepted Galton’s work in his review of Francis Galton’s book Natural Inheritance by proclaiming that statisticians working in varied fields such as finance and other industries should look into Galton’s methods and identify how these methods can be applied to their fields. This review for the American Statistical Association in 1889 established Dewey as one of the earliest critics who understood the efficacy of Galton’s methods.

In 1888, Edgeworth wrote a paper in the Royal Statistical Society journal, providing a tutorial on the application of statistics in analyzing examination and test scores. In this tutorial, Edgeworth discussed the use of normal distribution as a scaling device. Using the scale, certain corrections could be made to the mean based on different examiners. Edgeworth deliberated, in his paper whether analyzing the results on a logarithmic scale would be useful and introduced of variance components to the statistical models in practice. The tutorial also discussed how to estimate the newly introduced variability in the analysis of these scores.

This brief history reveals how the application of statistics began and then blossomed in the field of psychology. As we can understand, the role statistics play in psychology is fundamentally different from that in physics. Numerous educators, researchers, and psychologists provide stellar experimental work to make statistics as useful to psychology as it is to physics.

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