R: Cronbach's Coefficient Alpha

CronbachAlpha {DescTools} | R Documentation

## Cronbach's Coefficient Alpha

### Description

Cronbach's alpha is a measure of internal consistency and often used for validating psychometric tests. It determines the internal consistency or average correlation of items in a survey instrument to gauge its reliability. This reduces to Kuder-Richardson formula 20 (KR-20) when the columns of the data matrix are dichotomous.

### Usage

    CronbachAlpha(x, conf.level = NA, cond = FALSE, na.rm = FALSE)

### Arguments

`x` | k x m matrix or dataframe with item responses, k subjects (in rows) m items (in columns).
`conf.level` | confidence level of the interval. If set to `NA` (which is the default) no confidence interval will be calculated.
`cond` | logical. If set to `TRUE`, alpha is additionally calculated for the dataset with each item left out.
`na.rm` | logical, indicating whether `NA` values should be stripped before the computation proceeds. If set to `TRUE` only the complete cases of the ratings will be used. Defaults to `FALSE`.

### Value

Either a numeric value or
a named vector of 3 columns if confidence levels are required (estimate, lower and upper ci) or

a list containing the following components, if the argument `cond` is set to `TRUE`:

`unconditional` | Cronbach's Alpha, either the single value only or with confidence intervals
`condCronbachAlpha` | The alpha that would be realized if the item were excluded

### Author(s)

Andri Signorell <andri@signorell.net>, based on code of Harold C. Doran

### References

Cohen, J. (1960), A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37-46.

### See Also

`CohenKappa`, `KappaM`

### Examples

    set.seed(1234)
    tmp <- data.frame(
      item1 = sample(c(0,1), 20, replace=TRUE),
      item2 = sample(c(0,1), 20, replace=TRUE),
      item3 = sample(c(0,1), 20, replace=TRUE),
      item4 = sample(c(0,1), 20, replace=TRUE),
      item5 = sample(c(0,1), 20, replace=TRUE)
      )

    CronbachAlpha(tmp[,1:4], cond=FALSE, conf.level=0.95)
    CronbachAlpha(tmp[,1:4], cond=TRUE, conf.level=0.95)

    CronbachAlpha(tmp[,1:4], cond=FALSE)
    CronbachAlpha(tmp[,1:2], cond=TRUE, conf.level=0.95)

    ## Not run:
    # Calculate bootstrap confidence intervals for CronbachAlpha
    library(boot)
    cronbach.boot <- function(data,x) {CronbachAlpha(data[x,])[[3]]}
    res <- boot(datafile, cronbach.boot, 1000)
    quantile(res$t, c(0.025,0.975))   # two-sided bootstrapped confidence interval of Cronbach's alpha
    boot.ci(res, type="bca")          # adjusted bootstrap percentile (BCa) confidence interval (better)

    ## End(Not run)

[Package DescTools version 0.99.28 Index]