The field of Psychometrics is defined in The Encyclopedia Britannica as follows: "PSYCHOMETRICS, systematic use of tests to quantify psychophysical behaviour, abilities, and problems and to make predictions about psychological performance."

Now, I am not a psychogist, and bypass this aspect of psychometrics. But the above definition uses the terms "quantify" and "predictions". I am a mathematician and former math prof, so have expert opinion on "quantifying". I am also a statistician and former teacher of this subject, so have expert opinion on the statisics used in prediction.

To put my complaint UP FRONT, any student of mine who committed the junk passed on by psychomericians would receive an "F"!

I'll explain by a simple example in everyday language.

You may say, "He is going to the store." Read that as "He presently exists in the process of going to the store." The verbal "is" graammatically appears as an "auxiliary verb". The term "going" is a gerund -- a verbal noun -- effectively used for processes. But suppose you say the alternative, "He goes to the store." Here we have a simple active verb: "goes".

You will agree, I hope, that the two statement are SEMANTICALLY EQUIVALENT -- "say the same thing". What happened to the auxiliary verbal form in the second version? It isn't needed. A mathematician would say, "It is transformed away."

For those who have survived a course in analytic geometry (a.k.a. coordinate gometry), I'll give another example. The following is a second degree algebraic equation: 2x² + 3y² - 8x + 6y = 7. It can be shown that this is EQUIVALENT to 2u² + 3v² = 18 -- easily recognizable as an ELLIPSE -- by the transforming equations: u = x - 2, v = y + 1. But what happened to the linear terms of the first equation, namely, - 8x + 6y? As with the auxiliary verb and gerand in the previous paragraph, linear ters were transformed away by a translation of coordinates to the point (2, -1) in the old coordinate system. That means that the LINEAR TERMS DO NOT EXIST IN THE GEOMETRY, BUT IN THE LANGUAGE USED ABOUT THE GEOMETRY -- just as "is going" EXISTS ONLY IN THE LANGUAGE, NOT IN THE REAL EVENT.

My POINT: PSYCHOMETRICS IS PSYCHO OVER EXISTENTS IN THE MATHEMATICAL LANGUAGE WHICH GET TRANSFORMED AWAY, SHOWING THEY ARE NOT IN THE REAL PERFORMANCE!

I would give an "F" to any student in Analytic Geometry who failed to arrive at the above conclusion. So it's only fair to give "F" to a psychometrician for a similar boo-boo!