How Correlation Multiple Regression and Factor Analysis Inform on Theory of Psychometric Instrument

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Psychometrics is the study that deals with the technique and theory of psychological measurement. Among the psychological measurements determined are; personal abilities, knowledge, personality traits and attitudes (Rust, 2014, p. 24). The main objective of these measurements is to determine individual differences, to evaluate what differentiates one class of people from another, in a community or a society. Psychometric involves two main tasks; the construction of measurement instrument and the development of theoretical approaches to explain these measurements. To do this, Psychometricians developed various methods for determining and explaining the psychometric measurement: correlation factor analysis and multiple regressionsCITATION Rus14 \p 27 \l 1033 (Rust, 2014, p. 27). This paper discusses how these two approaches explain psychometric measurement.

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Factor analysis

Factor analysis is a statistical technique that is used to determine and identify clusters or group of shared variance among related factors on a test. Factor analysis is carried out to determine the optimal value (Rust, 2014, p. 30). It begins with large amounts of variables then begins reducing the interrelationship existing amongst these variables down to a few groups and clusters known as factors. It finds the maximal relationship or the existing connections from one variable to another as well as the minimal connections among the variables then classifies them accordingly.

For example, several respondents can take a psychology test, and then factor analysis can be done in order to identify the questions the respondents got wrong or right. The classification can also be done based on what number of respondents did best on for instance factual types questions against those who did well on conceptual questions. Ideally, this technique reveals a pattern of relationship (factors) that captures the essence of correlation of data and its classification.

Multiple Regressions

Multiple regressions are statistical techniques used in psychology to predict and determine the relationship between several single independent variables from other dependent variables (Cohen, 2013, p. 102). It allows the researcher to predict the respondent scores based on their scores on several variables. For instance, in order to determine individual job satisfaction variables such as salary, academic qualification, gender, age all contribute to whether individuals enjoy their job or not. Collecting data based on these variables from several respondents would show which variable give accurate prediction of job satisfactionCITATION Coh13 \p 105 \l 1033 (Cohen, 2013, p. 105). The researcher might find that, for instance, the salary is the most accurate predictor of job satisfaction based on the number of respondent identifying with these variables.

According to Cohen (2013), human behaviors are not inherently black and white and as such it would be harder to attain an accurate prediction (Cohen, 2013, p. 106). Therefore, multiple regressions can be used to point out or predict the variable which provides useful estimates of the respondents most likely score on a dependent variable

Relationship between Factor analysis and multiple regressions

Like in factor analysis, the independent variables in multiple regressions are not inherently observable (Cohen, 2013, p. 106). However, while the independent values in multiple regressions are known to determine or predict the dependent variable, in factor analysis these variable are not known and neither can they be used for any predictive purposes.


Cohen, J., Cohen, P., West, S.G. and Aiken, L.S., 2013. Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.

Rust, J., Golombok, S., Kosinski, M. and Stillwell, D., 2014. Modern psychometrics: The science of psychological assessment. Routledge.

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