cronbach.alpha.CI {cocron} R Documentation

## Confidence interval for Cronbach's Alpha

### Description

Calculates a confidence interval for Cronbach's alpha (Cronbach, 1951).

### Usage

cronbach.alpha.CI(alpha, n, items, conf.level = 0.95)


### Arguments

 alpha A numeric specifying the alpha coefficient. n A numeric defining the number of individuals who provided the data for the test for which the alpha coefficient was determined. items A numeric specifying the number of items the alpha coefficient is based on. conf.level A number defining the level of confidence for the confidence interval (default is .95).

### Details

The lower bound of a confidence interval for an \alpha that is based on the data of n individuals who responded to k items is defined as

L = 1 - \left((1 - \alpha) F(1 - c/2)\right)

where c is the level of confidence and F(1 - c/2) the 100(1 - c/2) percentile of the F-distribution with df_1 = n - 1 and df_2 = (n - 1)(k - 1) (Feldt, Woodruff, & Salih, 1987, p. 95, formula 6). The upper bound of the confidence interval is computed as

U = 1 - \left((1 - \alpha) F(c/2)\right)

(Feldt et al., 1987, p. 95, formula 7).

### Value

Returns a confidence interval for Cronbach's alpha as a numeric vector.

### References

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.

Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11, 93-103.