# cronbach.alpha: Cronbach's alpha In drizopoulos/ltm: Latent Trait Models under IRT

## Description

Computes Cronbach's alpha for a given data-set.

## Usage

 ```1 2``` ```cronbach.alpha(data, standardized = FALSE, CI = FALSE, probs = c(0.025, 0.975), B = 1000, na.rm = FALSE) ```

## Arguments

 `data` a `matrix` or a `data.frame` containing the items as columns. `standardized` logical; if `TRUE` the standardized Cronbach's alpha is computed. `CI` logical; if `TRUE` a Bootstrap confidence interval for Cronbach's alpha is computed. `probs` a numeric vector of length two indicating which quantiles to use for the Bootstrap CI. `B` the number of Bootstrap samples to use. `na.rm` logical; what to do with `NA`'s.

## Details

The Cronbach's alpha computed by `cronbach.alpha()` is defined as follows

alpha = (p / (p - 1)) (1 - (∑_{i=1}^p sigma_{y_i}^2/ sigma_x^2)),

where p is the number of items sigma_x^2 is the variance of the observed total test scores, and sigma_{y_i}^2 is the variance of the ith item.

The standardized Cronbach's alpha computed by `cronbach.alpha()` is defined as follows

alpha_s = (p r) / (1 + (p - 1) r),

where p is the number of items, and r is the average of all (Pearson) correlation coefficients between the items. In this case if `na.rm = TRUE`, then the complete observations (i.e., rows) are used.

The Bootstrap confidence interval is calculated by simply taking `B` samples with replacement from `data`, calculating for each alpha or alpha_s, and computing the quantiles according to `probs`.

## Value

`cronbach.alpha()` returns an object of class `cronbachAlpha` with components

 `alpha` the value of Cronbach's alpha. `n` the number of sample units. `p` the number of items. `standardized` a copy of the `standardized` argument. `name` the name of argument `data`. `ci` the confidence interval for alpha; returned if `CI = TRUE`. `probs` a copy of the `probs` argument; returned if `CI = TRUE`. `B` a copy of the `B` argument; returned if `CI = TRUE`.

## Author(s)

Dimitris Rizopoulos [email protected]

## References

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

## Examples

 ```1 2 3``` ```# Cronbach's alpha for the LSAT data-set # with a Bootstrap 95% CI cronbach.alpha(LSAT, CI = TRUE, B = 500) ```

drizopoulos/ltm documentation built on April 19, 2018, 2:37 a.m.