Mistake, transgression. OK, not that use of the word! For MH/therapy change measurement this is about how the word is used in psychometrics.

#### Details #

There are various schools of psychometrics: of approaches using maths and statistics to help us measure psychological phenomena and experiences but the first and still very dominant one is CTT: Classical Test Theory. In CTT any score on a measure (questionnaire or rating) is seen as composed of an unknowable “true score” and “error”. That’s utterly logical and linked with the fundamental idea about reliability: that a reliable set of measurements has a high ratio true score variance to observed score variance: that the numbers we have are a pretty good reflection of this set of true scores that we’d really love to have but which are unknowable but only approached by our unreliable measures.

So error is all about unreliability. To make things amenable to more thinking and then to maths and statistics, the fundamental idea in CTT about error is that it is uncorrelated with true scores. That’s logical: if it were correlated to some extent with true score variance then to some extent it would no longer be error but partly an indicator of the true scores. In CTT a number of other assumptions turn this simple and entirely logical model into something that really can be turned into a set of equations and used to give us tools to explore data from our measures and get some reflections on our measures, including the key one of how much it appears that the variance in our data looks to be reliable or unreliable: largely free of error versus largely (or entirely) error.

The added assumptions are generally the usual parametric statistical ones:

* that the observations in the dataset are independent of one another (can be relaxed but only by invoking much more complex maths and new assumptions that take us to multilevel models)

* that they come by random sampling from infinitely large populations (lots of issues here for typical MH/therapy data but that’s another story)

* that both true score and error variance in the population are Gaussian

From there statisticians and psychometricians in the CTT tradition get to things like factor analysis, Cronbach’s alpha and McDonald’s omega.

Psyhometricians belonging to the often warring tradition of IRT (Item Response Theory) use a different set of assumptions in which the idea of error is a little less in the foreground but just as vital but that’s for another glossary item.

#### Try also #

Classical Test Theory (CTT)

Correlation

Cronbach’s coefficient alpha\

Factor analysis

Gaussian (“Normal”) distribution

Item Response Theory (IRT)

McDonald’s omega

Orthogonal

Psychometrics

Reliability

Validity

#### Chapters #

Chapter 3.

#### Online resources #

None yet.

#### Dates #

First created 9.xii.23.