Psychometric tests are a standard and scientific method used to measure individuals' mental capabilities and behavioural styles. Psychometric tests are designed to measure candidates' suitability for a role based on the required personality characteristics and aptitude (or cognitive abilities).
Could you elaborate further (in plain words) for my student? How will psychometric tests be used to test hypothesis in regression equations?
http://www.jstor.org/stable/pdf/1175619.pdf?seq=1#page_scan_tab_contents
When both, the predictor/s* and the response variable**, are on a continuous interval scale.
The regression equation describes the assumed functional relationship for the expected value for the response depending on the value/s of the predictor/s. Observed data is used to find suitable values for the coefficients*** in the equation. "Suitable" means that these values are chosen so that the likelihood of the observed data is maximal.
Often, psychomertic response variables are not on a continuous interval scale but rather on a discrete ordinal scale (e.g. a Likert scale). One could represent the categorial values as numbers, and often the ranks are used for that purpose. The scale of the average ranks of multiple items may be taken as a (quasi-) continuous interval scale, and this is often understood to be sufficint to perform a regression analysis (or t-tests, ANOVAs, ANCOVA, ...). BUT: this is NOT anymore an analysis about the expected values or the response. It is now about the expexted ranks, what is quite a different thing. The conclusions of a rank-analysis can be drastically different to conclusions that would have been made on the analysis of quantitative values. I am therefore sceptical about using such procedures (regression, t-tests, ...) based on the ranks when the response is ordinal.
If there is a way to assign substantial values (not ranks) to the categories, a regression analysis can be sensible. Otherwise there is simply no point in doing a regression analysis at all, because the information required is not available (doing as if the ranks were this information very likely is self-deception****).
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* =independent variable/s = the factor/s that is/are experimentally controlled/varied
** =dependent variable = what is measured and believed to depend on the values of the independent variable/s
*** these coefficients are usually denoted by the greek letter beta (beta1, beta2,...) and are sometimes called "beta weights". Their values can indicate the "effect size" of the corresponding predictor. They can also relate to a products of predictors, what is called an "interaction".
**** I am not denying that it could make sense in some cases to actually use ranks, but usually authors that do use ranks do not provide any argument why this would make sense in their case, and often it is quite obvious from the kind of reaponse they are analysing that there wouldn't be any good agrument!
When both, the predictor/s* and the response variable**, are on a continuous interval scale.
The regression equation describes the assumed functional relationship for the expected value for the response depending on the value/s of the predictor/s. Observed data is used to find suitable values for the coefficients*** in the equation. "Suitable" means that these values are chosen so that the likelihood of the observed data is maximal.
Often, psychomertic response variables are not on a continuous interval scale but rather on a discrete ordinal scale (e.g. a Likert scale). One could represent the categorial values as numbers, and often the ranks are used for that purpose. The scale of the average ranks of multiple items may be taken as a (quasi-) continuous interval scale, and this is often understood to be sufficint to perform a regression analysis (or t-tests, ANOVAs, ANCOVA, ...). BUT: this is NOT anymore an analysis about the expected values or the response. It is now about the expexted ranks, what is quite a different thing. The conclusions of a rank-analysis can be drastically different to conclusions that would have been made on the analysis of quantitative values. I am therefore sceptical about using such procedures (regression, t-tests, ...) based on the ranks when the response is ordinal.
If there is a way to assign substantial values (not ranks) to the categories, a regression analysis can be sensible. Otherwise there is simply no point in doing a regression analysis at all, because the information required is not available (doing as if the ranks were this information very likely is self-deception****).
---
* =independent variable/s = the factor/s that is/are experimentally controlled/varied
** =dependent variable = what is measured and believed to depend on the values of the independent variable/s
*** these coefficients are usually denoted by the greek letter beta (beta1, beta2,...) and are sometimes called "beta weights". Their values can indicate the "effect size" of the corresponding predictor. They can also relate to a products of predictors, what is called an "interaction".
**** I am not denying that it could make sense in some cases to actually use ranks, but usually authors that do use ranks do not provide any argument why this would make sense in their case, and often it is quite obvious from the kind of reaponse they are analysing that there wouldn't be any good agrument!
I assume the tests you refer to provide some kind of categorical responses (e.g., levels of agreement to a statement). If so, you might consider a member of the Rasch family of models. They, in short, allow for deriving a measurement on a latent scale. There are extensions allowing for latent regression (e.g. using ConQuest, as of Version 3 - see the "structural" command). Alternatively, Structural Equation Models might also be of interest for your research question.
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