Cronbach's alpha

Cronbach's (alpha ) is a named after Lee Cronbach measure of the internal consistency of a scale and refers to the extent to which the tasks or issues of scale related to each other ( interrelatedness ). However, it is not a measure of homogeneity or unidimensionality of a scale. Cronbach's alpha is used primarily in the social sciences or in psychology - particularly in test construction and evaluation. It is used to estimate the internal consistency of a psychometric instrument.

History

The first designation as alpha happened in 1951 by Cronbach, although the Kuder - Richardsonsche formula represents an older version for dichotomous items and Guttman had already developed in 1945 the same measure under the name lambda -3.

Definition

Assuming that a sample with respect to a group was examined by k items, then Cronbach is defined as the average correlation between these items, adjusted upwards by k by the Spearman - Brown formula. Cronbach's alpha therefore is also referred to as a measure of the internal consistency of a scale. Cronbach is related to the result of analysis of variance of the item data in terms of the variance between the subjects and the variance between the items. The higher the proportional variance between subjects, the higher Cronbach.

Interpretation

Can take values ​​between minus infinity and 1 ( although only positive values ​​make sense to interpret ). As a general rule, any psychometric instrument should be used only when a value of 0.65 or more is achieved. For smaller values ​​can be checked by means of a factor analysis, whether the items are distributed to several factors.

The problem with this requirement, however, is that the reliability of an instrument very easily to the detriment of the bandwidth can be achieved. This problem is also referred to as bandwidth Fidelitätsdilemma. The wider and more general measures an instrument, the more opportunities are generally predict too broad and distant criteria. On the other hand, suffers from the width of the reliability. A solution to this problem is usually only the extension of the test.

Cronbach's alpha is often mistakenly interpreted as evidence for a one-dimensional scale. A scale can be multidimensional and yet a high internal consistency, so therefore have a high Cronbach's alpha. Here is an example of a scale can be argued that the mixed presents, so is two-dimensional, for example, depression and anxiety, and yet has a high consistency.

Cronbach should be used when the items measure substantially different areas within a single construct. Conversely, can be artificially inflated by the items of the construct are formulated so that they differ only superficially.

Formula

The formula for calculating a standardized Cronbach's is:

Where N is the number of components ( or items subscales ) and the average correlation between the items. Alternatively, Cronbach's results from

With,

Where the number of components (items or subscales ) and corresponds corresponds to the variance of the observed total test scores and the variance in component ( item, subscale ). For Likert scales usually applies.

Example

In the General Social Survey 1993 asked with by different genres with the response categories (1 = Mag genre, 2 = Draws, 3 = Mag music direction is not ). Now, if a scale Mag music formed as the sum of the individual scales for each genre, we obtain

And

Or ( with SPSS).

In this case, the new scale is usually not considered to be reliable ( reliable); is there. The reason is that the correlation matrix least two subscales shows: Classical / Opera, Jazz / Blues / R & B ie when using Cronbach you should be sure that the items really only one scale form (check with the factor analysis ).

Calculation of Cronbach's with common statistical software

For the free statistical software R, there are several packages that contain functions for the calculation of Cronbach, eg multilevel :: Cronbach, psy :: Cronbach, psych :: alpha and psychometric :: alpha.

In the command line SAS proc corr data = variable1 variable2 ... variable alpha plots is, .

In SPSS, choose " Analyze " then " scaling ", then " reliability analysis " and selects the desired variables. For this then Cronbach's alpha is calculated. The command syntax for program version 17.0 is RELIABILITY VARIABLE = [ VARIABLES] / MODEL = ALPHA ..

With the program package Stata to Cronbach's alpha can with the statement varlist [ if] [in] [, options] compute. The Item Test and Item - rest correlations are specified item by selecting the option. With the option generate ( newvar ) the determined scale is stored as a variable. If the items of the scale are previously standardized ( to the mean 0 and variance 1), so the std option is in addition to add.