cocron (version 1.0-1)

cronbach.alpha.CI: 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 $.95$).

Value

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

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).

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.

See Also

cronbach.alpha

Examples

cronbach.alpha.CI(alpha=.83, n=100, items=20, conf.level=.95)