# Reliability and Item Analysis - Notes and Technical Information

## Computations

All Reliability and Item Analysis computations are performed in double precision. The standard formulas from classical testing theory are used to compute Cronbach's Alpha, and for the attenuation correction (see Nunnally, 1970).

Standardized alpha. The standardized Alpha may be interpreted as the reliability that would result if all values for each item were standardized (z transformed) before computing Cronbach's Alpha. The computational formula is:

a = k*ravrg/(1+(k-1)*ravrg)

In this formula, k stands for the number of items in the scale; ravrg stands for the average inter-item correlation.

Guttman split-half reliability. The Guttman split-half coefficient is similar to the Spearman-Brown split-half coefficient, but does not assume equal reliabilities or equal variances of the two halves. It is computed as:

rG = 2*(st2 - st12 - st22)/st2

where

 rG is the Guttman split-half coefficient st2 is the variance of the total scale (both halves) st12 is the variance of the first half st22 is the variance of the second half

## Items With Zero Variances

If an item has zero variance a correlation matrix cannot be computed (a warning will be issued by the program). In that case, either eliminate the item(s) with zero variances, or choose not to compute the correlation matrix. If the latter option is chosen, the item(s) with zero variances will be included in all subsequent computations. Note that if no correlation matrix is requested the following formula is used to compute Cronbach's Alpha:

a = [k/(k-1)]*(1-åsi2/st2)

where

 k is the number of items in the scale åsi2 denotes the sum of item variances st2 is the variance of the scale

If items with zero variances are included, they will not affect the variances but only the factor [k/(k-1)].