Classical test theory (TCT)

The tclassical theory of testing (TCT) appears for the first time in the 20th century from Spearman’s work. It can, in some way, be considered the beginning of psychometrics. The word test It is an English word accepted by the Royal Spanish Academy (RAE) and refers to tests designed to evaluate knowledge, skills or functions.

In psychology, tests are psychological or psychotechnical tests to study or evaluate a function. So, Psychological tests are tools designed to evaluate or measure the psychological characteristics of a subject.

Why are test theories needed?

Tests are sophisticated measurement instruments that, In many cases, they constitute an invaluable aid in the context of a psychological evaluation. For this to be the case, the test must meet psychometric minimums and the specialist who passes it must know the administration protocol and respect it.

On the other hand, test theories tell us about how we can evaluate the quality of a test and also, in many cases, about how can we debug the instrument to reduce the error to a minimum. In this sense, perhaps the two most important concepts within classical test theory are reliability and validity.

Reliability is understood as the consistency or stability of the measurements when the measurement process is repeated.. Basically we are talking about a utopia because in practice it is impossible to replicate the same conditions in two different measurements. It will be relatively easy to act on external variables, such as controlling that there is a similar temperature or a similar noise level; However, controlling the internal variables of the person taking the test will be more complicated. Let’s think about the state of mind, for example.

Validity refers to the degree to which empirical evidence and theory support the interpretation of test scores. (2) In another way, we could say that validity is the ability of a measuring instrument to significantly and adequately quantify the trait for which it has been designed to be measured.

Thus, there are two main theories when it comes to constructing and analyzing tests. The first one we talked about is the classical test theory (TCT). The second is item response theory (IRT). Below we present the key aspects of TCT.

The classical theory of testing

This approach tends to be the most used in the analysis and construction of tests. The answers given by a person in a test are compared through statistical or qualitative methods. with the responses of other individuals who completed the same test. This allows for a classification.

However, making this classification is not so simple. The psychologist, like any other professional, has to ensure that the instrument he uses measures accurately, with little error. (1)

Thus, when a psychologist applies a test to one or several people, what he or she obtains are the empirical scores that that person or people obtain in the test. However, it does not inform us about the degree of precision of those scores: We do not know whether or not these empirical scores correspond to the scores that truly correspond to that person on the test.

For example, it could happen that the scores were lowered because the person being tested was not feeling well that day. Or even because the physical conditions in which the test was administered were not the best.

The classical linear model

It is at the beginning of the 20th century, as we have mentioned, when Spearman proposed this classic theory of testing. The researcher proposes a very simple model for people’s test scores: The classic linear model.

This model consists of assume that the score that a person obtains on a test, which we call his or her empirical score, and which is usually designated with the letter X, is made up of two components. The first is the true score (V) and the second is the error (e). The latter can be due to many causes that we cannot control. That is why TCT is responsible for precisely determining the measurement error.

This could be expressed as follows: X = V + e

Thus, after this, Spearman adds three assumptions to the model.

The three assumptions of the classical model

The true score (V) is the mathematical expectation of the empirical score. It would be written like this: V = E(X)Thus, a person’s true score on a test is defined as the score they would obtain on average if they were given the same test infinitely many times.There is no relationship between the number of true scores and the size of the errors that affect these scores.. It can be expressed: r(v, e) = 0The true score value is independent of measurement error.Measurement errors in a specific test are not related to measurement errors in another different test. This is expressed: r(eg, ek)=0 Errors made on one occasion do not covary with those made on another occasion.

Classical test theory is simple, advanced mathematical knowledge is not needed to put it into practice and it can be applied in any context. The problem is that the results it gives us will always be linked to the population in which the test has been validated. Besides, In many cases, the minimum requirements required for tests to be considered acceptable are actually not sufficient..

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