zcx: Standardized Scale-Center Deviation Scores

In funfield-lab/fancyr: Fancy Statistics for Correlational (r) Analyses

Standardized Scale-Center Deviation Scores

Description

Transforms the scores of interest to a z-score-like metric indicating the number of 'standard scale-center deviations from the scale center'.

This can be understood as a simple alteration of the usual z-score formula, where in every place that the person's mean score is used within an equation, we replace this with the scale-center point instead (e.g., 3 for a 1-5 Likert scale):

zcx = (x-C)/s_C

Where:

s_C = sum(x-C)^2/N

Note that it is proper to divide the equation by N rather than (N-1) because C is not an estimated parameter. So no degrees of freedom are lost.

Usage

zcx(x, center, margin = 1)

Arguments

x	matrix containing set of scores to be transformed
center	center point of the scale
margin	estimate zcx values using sc's calculated from row(=1) or column=2?

Details

Data should be prepared so that all of the person's scores are given in the same row.

* The scale-centered scores do NOT have the usual interpretation of a [regular] z-scores as being translatable to approximate probabilities assuming a normal distribution of responses.

* If the person gives the same score to all items - and if this score is not the scale midpoint) - all zcx values for this person will equal 1.

* If the person answers all items with only two responses that are equally spaced above or below the scale midpoint (for instance, all responses equal 1 & 5 or equal 2 & 4 when the scale midpont is 3, then all scores will equal -1 & 1.

* Note that zcx scores do NOT divide by N_k-1 (where N_k = number of items in profile) because a degree of freedom is not lost to estimate the person's mean response, as done in standard z-scores. Transforms the scores of interest to a z-score like metric indicating the number of 'standard scale-center deviations from the scale center'

* Note that this will tend to make scores more continuous EXCEPT for the scale midpoint, which will be exactly 0 for anyone who provided that value after this transformation.

Value

Standardized scale-centered scores.

funfield-lab/fancyr documentation built on Nov. 21, 2023, 2:42 p.m.