Check internal consistency of a test or questionnaire

Description

These function compute various measures of internal consistencies for tests or item-scales of questionnaires.

Usage

reliab_test(x, scale.items = FALSE, digits = 3, out = c("txt", "viewer",
  "browser"))

split_half(x, digits = 3)

cronb(x)

mic(x, cor.method = c("pearson", "spearman", "kendall"))

Arguments

Details

reliab_test()

This function calculates the item discriminations (corrected item-total correlations for each item of x with the remaining items) and the Cronbach's alpha for each item, if it was deleted from the scale.

split_half()

This function calculates the split-half reliability for items in the data frame x, including the Spearman-Brown adjustment. Splitting is done by selecting odd versus even columns in x.

cronb()

The Cronbach's Alpha value for x.

mic()

This function calculates a mean inter-item-correlation, i.e. a correlation matrix of x will be computed (unless x is already a matrix as returned by the cor-function) and the mean of the sum of all item's correlation values is returned. Requires either a data frame or a computed cor-object.

Value

reliab_test()

A data frame with the corrected item-total correlations (item discrimination, column item.discr) and Cronbach's alpha (if item deleted, column alpha.if.deleted) for each item of the scale, or NULL if data frame had too less columns.

split_half()

A list with two values: the split-half reliability splithalf and the Spearman-Brown corrected split-half reliability spearmanbrown.

cronb()

The Cronbach's Alpha value for x.

mic()

The mean inter-item-correlation value for x.

Note

reliab_test() is similar to a basic reliability test in SPSS. The correlations in the Item-Total-Statistic are a computed correlation of each item against the sum of the remaining items (which are thus treated as one item).

For split_half() and cronb(), a value closer to 1 indicates greater internal consistency.

For the mean inter-item-correlation: “Ideally, the average inter-item correlation for a set of items should be between .20 and .40, suggesting that while the items are reasonably homogenous, they do contain sufficiently unique variance so as to not be isomorphic with each other. When values are lower than .20, then the items may not be representative of the same content domain. If values are higher than .40, the items may be only capturing a small bandwidth of the construct.” (Piedmont 2014)

References

Spearman C. 1910. Correlation calculated from faulty data. British Journal of Psychology (3): 271–295. doi: 10.1111/j.2044-8295.1910.tb00206.x

Brown W. 1910. Some experimental results in the correlation of mental abilities. British Journal of Psychology (3): 296–322. doi: 10.1111/j.2044-8295.1910.tb00207.x

Piedmont RL. 2014. Inter-item Correlations. In: Michalos AC (eds) Encyclopedia of Quality of Life and Well-Being Research. Dordrecht: Springer, 3303-3304. doi: 10.1007/978-94-007-0753-5_1493

Examples

library(sjlabelled)
# Data from the EUROFAMCARE sample dataset
data(efc)

# retrieve variable and value labels
varlabs <- get_label(efc)

# recveive first item of COPE-index scale
start <- which(colnames(efc) == "c82cop1")
# recveive last item of COPE-index scale
end <- which(colnames(efc) == "c90cop9")

# create data frame with COPE-index scale
x <- efc[, c(start:end)]
colnames(x) <- varlabs[c(start:end)]

# reliability tests
reliab_test(x)

# split-half-reliability
split_half(x)

# cronbach's alpha
cronb(x)

# mean inter-item-correlation
mic(x)

## Not run: 
library(sjPlot)
sjt.df(reliab_test(x), describe = FALSE, show.cmmn.row = TRUE,
       string.cmmn = sprintf("Cronbach's &alpha;=%.2f", cronb(x)))

# Compute PCA on Cope-Index, and perform a
# reliability check on each extracted factor.
factors <- sjt.pca(x)$factor.index
findex <- sort(unique(factors))
library(sjPlot)
for (i in seq_len(length(findex))) {
 rel.df <- subset(x, select = which(factors == findex[i]))
 if (ncol(rel.df) >= 3) {
   sjt.df(reliab_test(rel.df), describe = FALSE, show.cmmn.row = TRUE,
          use.viewer = FALSE, title = "Item-Total-Statistic",
          string.cmmn = sprintf("Scale's overall Cronbach's &alpha;=%.2f",
                                cronb(rel.df)))
   }
 }
## End(Not run)