Classical test theory (CTT) has been the foundation for measurement theory for over 80 years. The conceptual foundations, assumptions, and extensions of the basic premises of CTT have allowed for the development of some excellent psychometrically sound scales.

Classical test theory (CTT) is based on the assumption that the raw score (X) obtained by any one individual is made up of a true component (T) and a random error (E) component:

The true score of a person can be found by taking the mean score that the person would get on the same test if they had an infinite number of testing sessions. Because it is not possible to obtain an infinite number of test scores, T is a hypothetical, yet central, aspect of CTT.

There are several types of CTTs. The foundation for them all rests on aspects of a total test score made up of multiple items. Domain sampling is the most common CTT used for practical purposes. Domain sampling theory assumes that the items that have been selected for any one test are just a sample of items from an infinite domain of potential items. The parallel test theory assumes that two or more tests with different domains sampled (i.e., each is made up of different but parallel items) will give similar true scores but have different error scores.

For example if one was to administer the Analytical ability test to a candidate every day for two years. Sometimes his score would be higher and sometimes lower. The average of his raw scores (X), however would be the best estimate of his true score (T). It is also expected that the random errors around his true score would be normally distributed. That is, sometimes when he took the test his scores would be higher and sometimes when he took the test his scores would be lower (maybe he was tired, distracted). Because the random errors are normally distributed, the expected value of the error (i.e., the mean of the distribution of errors over an infinite number of trials) is 0. In addition, those random errors are uncorrelated with each other; that is, there is no systematic pattern to why his scores would fluctuate from time to time. Finally, those random errors are also uncorrelated to the true score, T, in that is there is no systematic relationship between a true score (T) and whether or not that person will have positive or negative errors. All of these assumptions about the random errors form the foundations of CTT. An important point to remember is that the theory of true and error scores developed over multiple samplings of the same person (i.e., the candidate taking the test himself 1,000 times) can be extended to a single administration of an instrument over multiple persons (i.e., administering the test to a group of 1,000 different people once). Thus it is possible to collect data once (single administration) on a sample of individuals (multiple persons).

Based on the assumption of the 'True score' and the 'Error score', the index of the usefulness of ISAI test is assessed though the following:

• In the validation of the 16PF, this test was compared to a test called the Neo Personality Inventory, Revised (NEO PI-R). The NEO PI-R is designed to measure 5 major dimensions of the Five Factor Model (which is the basis of developing the GPQ) that measures factors such as Neuroticism, Extraversion, Openness, Conscientiousness, and Agreeableness.

• Predictably, the 16PF Extraversion correlated strongly with the NEO Extraversion facets (r = 0.43)
• Anxiety Global Factor correlated with the Neuroticism domain. (r = 0.61)
• The Tough mindedness Global Factor correlated negatively with Openness facets.
• The Independence Global Factor correlated with the Neo Extraversion facets especially with
• Assertiveness (r = 0.60).
• The Anxiety factor also correlates negatively with the NEO facet of Trust, suggesting that high anxiety is associated with skepticism and distrust (r = -0.44).

• Verbal Reasoning - is appropriate for measuring general cognitive ability and for placing employees in professional, managerial, and other positions of responsibility requiring higher order thinking skills.
• Numerical Ability - test the understanding of numerical relationships and facility in handling numerical concepts. Good prediction of success of applicants in such fields as mathematics, physics, chemistry, engineering, and in occupations such as laboratory assistant, bookkeeper, statistician, shipping clerk, carpenter, tool-making, and other professions related to the physical sciences.
• Abstract Reasoning - is a nonverbal measure of the ability to perceive relationships in abstract figure patterns. Useful in selection when the job requires perception of relationships among things rather than among words or numbers, such as mathematics, computer programming, drafting, and automobile repair.
• Clerical Speed and Accuracy Paper Administration Only- measures the speed of response in a simple perceptual task. This is important for jobs such as filing and coding, and for jobs involving technical and scientific data.
• Mechanical Reasoning - closely parallels the Bennett Mechanical Comprehension Test and measures the ability to understand basic mechanical principles of machinery, tools, and motion. It is useful in selection decisions about applicants for jobs such as carpenter, mechanic, maintenance worker, and assembler.
• Space Relations - measures the ability to visualize a three dimensional object from a two dimensional pattern, and how this object would look if rotated in space. This ability is important in fields such as drafting, clothing design, architecture, art, die making, decorating, carpentry, and dentistry
• Spelling Paper Administration Only - measures an applicant's ability to spell common English words, a basic skill necessary for success in a wide range of jobs including business, journalism, proofreading, advertising, or any occupation involving written language.
• Language Usage - measures the ability to detect errors in grammar, punctuation, and capitalization. When Language Usage and Spelling are both administered, they provide a good estimate of the ability to distinguish correct from incorrect English usage, which is important in business communication.