# Classical Test Theory

**In psychology, tests are either psychological or psycho-technical, and are designed to study or evaluate a function. **Thus, psychological tests are tools that assess or measure the **psychological characteristics of a subject**. Read on to find out more about classical test theory (CTT).

## Test theory

The tests are sophisticated measuring instruments. **In many cases, they are incredibly helpful in the context of a psychological evaluation. **However, a test must at least meet **a psychometric number scale** to be useful. In addition, the specialist who uses it must know the protocol to administer it and respect it.

On the other hand, test theory tells us how we can evaluate the quality of a test, and in many cases how we can reduce errors to a minimum. **In this way, perhaps the two most important concepts in classical test theory are reliability and validity.**

Reliability is the consistency or stability of data when the measurement process is repeated. This is basically a utopia because in practice it is impossible to recreate the same conditions in two different measurements. It is relatively easy to trade on external variables, for example to ensure that the temperature or noise level is exactly the same. However, it is much more difficult to control the internal variables of the person taking the test.

**Validity refers to the extent to which empirical evidence and theory support the interpretation of test results** (2). Otherwise, we can say that validity is the ability of a measuring instrument to quantify what was created to measure.

There are two good theories when it comes to construction and analysis of tests: **classical test theory (CTT) and item response theory (element- response theory , IRT)**. Below we explain the most important aspects of CTT.

## Classical Test Theory (CTT)

**This approach tends to be the most widely used in the analysis and creation of tests. **The answers that a person gives in a test are compared through statistical or qualitative methods to the answers of other people who took the same test. This allows comparisons to be made.

But classification is not that simple. The psychologist, like all other professionals, must ensure that the instrument they use is accurately calibrated and error-free (1).

When a psychologist uses a test on one or more people, it is thus the empirical results of these people. However, this does not say much about the degree of accuracy of these results. For example, the person may have received a low score because they were not feeling well that day, or because the physical conditions of the place where they took the test were not optimal.

## Classical linear regression model

Spearman proposed classical test theory in the early 20th century. The researcher then proposed a very simple model for the test results: **Classical linear regression model.**

This model consists of assuming that a particular test score or “empirical score” (X) has two variables. The first variable is the true score (V) and the second is the error (s). The latter may be caused by things beyond our control. Therefore, CTT is responsible for determining the measurement error.

The formula is: X = V + e

After this, Spearman added three prerequisites to the model:

## The three assumptions about the classical linear regression model

- The true score (V) is the mathematical expectation of the empirical score: V = E (X).
- Thus, a person’s true test result is the average score of the same test if someone were to take it infinitely.

- There is no correlation between the number of true points and the errors that affect these results: r (v, e) = 0
- The true score is independent of the measurement error.

- The measurement errors in a particular test are not related to the measurement errors in another test: r (ex, ek) = 0
- Mistakes on one occasion
**will not covariate with those made on another test**.

- Mistakes on one occasion

Classical test theory is simple. It can be used for any context and be put to use without the need for particularly **advanced mathematical skills**. The problem, however, is that the results it gives will always be related to the population where the test was validated. In addition, the tests require a minimum of acceptable points.