Psychometry It can be defined as: “Methodological discipline, within the area of Psychology, whose fundamental task is the measurement or quantification of psychological variables with all the implications that this entails, both theoretical and practical.” The origin of Psychometrics can be placed towards the middle of the 19th century and, from that moment on, it will be developed, fundamentally through these two ways: Psychophysics studies: gave rise to the development of models that allowed values to be assigned. numerical to the stimuli and, therefore, that allowed the scaling of stimuli.
Introduction
Thus, psychometrics must first deal with the justification and legitimation of psychological measurement, for which it must:
- Develop formal models that allow representing the phenomena that you want to study and enable the transformation of facts into data.
- Validate the models developed to determine to what extent they represent the reality they intend and establish the conditions that allow the measurement process to be carried out.
Psychological measurement
According to Coombs, Dwes and Tversky (1981), it is considered that the fundamental roles assigned to Science are the description, explanation and prediction of observable phenomena through a few general laws that express the relationships between the properties of the objects investigated. . Psychology as a science will have its scientific basis in measurement, which will allow it to empirically contrast the proposed hypotheses. According to Nunnally (1970), measurement is reduced to something very simple, it consists of a set of rules for assigning numbers to objects in such a way that these numbers represent quantities of attributes, with attributes being understood as the characteristics of the objects and not the objects themselves.
However, the difficulty involved in measuring psychological characteristics is recognized given their uniqueness and, therefore, the difficulties that had to be overcome until the need and possibility of measuring this type of variables was accepted. . The differences with physical attributes when measuring this type of (psychological) variables, a new conception of measurement was proposed (Zeller and Carmines 1980) they considered that it is a process through which unobservable abstract concepts (constructs) are linked directly, with indicators. directly observable empirical data (behaviors). This type of measurement is often called measurement by indicatorsgiven that psychological variables cannot be measured directly, it is necessary to select a series of indicators that can be measured directly.
Historical tour of psychometrics
The studies on individual differences that gave rise to the development of tests and the different theories of tests made it possible to assign numerical values to subjects and therefore, the scaling of subjects. Three decisive factors can be considered in the development of the tests:
- The opening of Galton’s anthropometric laboratory in London
- The development of Pearson correlation
- Spearman’s interpretation of it, considering that the correlation between two variables indicates that both have a common factor. Tests as instruments have anticipated their theoretical foundation.
The closest origins are located in those first sensorimotor tests used by Galton (1822-1911) in his anthropometric laboratory in Kensington. Galton also has the honor of being the first to apply statistical technology to analyze the data from his tests. work that will continue with Pearson.
James McKeen Cattell (1860-1944) will be the first to use the term “mental test”, but his tests, like Dalton’s, were of a sensory nature and the analysis of the data made clear the null correlation between this type of tests and the intellectual level of the subjects. It will be Binet who gives a radical turn in the philosophy of tests, by introducing into his scale tasks of a more cognitive nature aimed at evaluating aspects such as judgment, etc. In the revision of the scale carried out by Terman at Stanford University, known as the Stanford-Binet revision, intelligence quotient (IQ) was used for the first time to express subjects’ scores. The idea was originally from Stern, who in 1911 proposed dividing the mental age (ME) by the chronological age (CE), multiplying by one hundred to avoid decimals: IQ= (ME/CE)x100.
The next step in the historical development of the tests will be marked by the appearance of collective intelligence testsprompted by the need of the North American Army in 1917 to select and classify the soldiers who were going to take part in the First World War, a committee led by Yerkes designed from the diverse material already existing, especially from Otis’s unpublished tests, the now famous Alpha and Beta test, the first for the general population and the second for use with illiterate people or prisoners without a command of English, these tests are still in use today. For the appearance of today’s classic test batteries we have to wait until the 30s and 40s, whose most genuine product will be the Primary Mental Aptitudes of Thurstone.
The different models will give rise to numerous test batteries (PMA, DAT, GATB, TEA, etc.) commonly used today. For his part, the Swiss psychiatrist Roschach proposed in 1921 his famous projective inkblot test, which will be followed by other projective tests with very different types of stimuli and tasks, including the TAT, CAT, Rosenzweig Frustration Test, etc. However, the projective technique that can be considered pioneering is the Word Association or Free Association Test, described by Galton.
Origins and development of classical test theory (tct)
As a consequence of the boom achieved by the tests, the need arises to develop a theoretical framework that serves as a basis for the scores obtained by the subjects when they are applied, enables the validation of the interpretations and inferences made from it, and allows the estimation of the measurement errors inherent to any measurement process through the development of a series of models.
Thus, a general theoretical framework was developed, the Theory of Tests, which will allow establishing a functional relationship between the observable variables based on the empirical scores obtained by the subjects in the tests or in the items that compose them and the variables. unobservable. TCT was developed, fundamentally, from the contributions of Galton, Pearson and Spearman, which revolve around three basic concepts: empirical or observed scores (X), true scores (V) and scores due to error (e). The central objective was to find a statistical model that adequately bases the test scores and allows the estimation of measurement errors associated with the entire measurement process.
Spearman’s linear model is an additive model in which the observed score (dependent variable) of a subject in a test (X) is the result of the sum of two components: their true score (independent variable) in the test ( V) and the error (e) X = V + e Based on this model and some minimal assumptions, TCT will develop a whole set of deductions aimed at estimating the amount of error that affects test scores.
Assumptions:
- The score (V) is the mathematical expectation of the empirical score (X): V=E(X)
- The correlation between the true scores of “n” subjects in a test and the measurement errors is equal to zero. rve=0
- The correlation between the measurement errors (re1e2) that affect the subjects’ scores in two different tests is equal to zero. re1e2=0.
Starting from these three assumptions of the model, the following deductions are established:
- The measurement error (e) is the difference between the empirical score (X) and the true score (V). e=XV
- The mathematical expectation of measurement errors is zero, therefore they are unbiased errors E(e)=0
- The mean of the empirical scores is equal to the mean of the true scores.
- True scores do not covary with errors. Cov(V,e)=0
- The covariance between the empirical and true scores is equal to the variance of the true scores: cov(X,V)=S2 (V)
- The covariance between the empirical scores of two tests is equal to the covariance between the true ones: cov(Xj,Xk)=cov(Vj,Vk) g) The variance of the empirical scores is equal to the variance of the true scores plus the errors: S2(X) = S2(V) + S2 (e)
- The correlation between the empirical scores and the errors is equal to the ratio between the standard deviation of the errors and that of the empirical ones. rxe=Se/S
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