Compute various measures of internal consistencies for tests or item-scales of questionnaires.
Value
A data frame with the item-total correlations (column
Item_Total_Correlation), corrected item-total correlations (item
discrimination, column Discrimination) 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.
Details
This function calculates the item-total correlations, 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. The absolute value of the item discrimination indices should be above
0.2. An index between 0.2 and 0.4 is considered as "fair", while an index
above 0.4 (or below -0.4) is "good". The range of satisfactory values is from
0.4 to 0.7. Items with low discrimination indices are often ambiguously
worded and should be examined. Items with negative indices should be examined
to determine why a negative value was obtained (e.g. reversed answer
categories regarding positive and negative poles).
See check_itemscale() and item_discrimination() for more details on
the interpretation of the results.
Note
Item difficulty should range between 0.2 and 0.8. Ideal value is
p+(1-p)/2(which mostly is between 0.5 and 0.8). Seeitem_difficulty()for details.For item discrimination, also known as corrected item-total correlations, acceptable values are 0.20 or higher; the closer to 1.00 the better. See
item_discrimination()for more details. If an item discrimination is negative, the corresponding item probably need to be reverse-coded (which can be done withdatawizard::reverse()).In case the total Cronbach's alpha value is below the acceptable cut-off of 0.7 (mostly if an index has few items), the mean inter-item-correlation is an alternative measure to indicate acceptability. Satisfactory range lies between 0.2 and 0.4. See also
item_intercor().
References
Briggs SR, Cheek JM (1986) The role of factor analysis in the development and evaluation of personality scales. Journal of Personality, 54(1), 106-148. doi: 10.1111/j.1467-6494.1986.tb00391.x
Examples
data(mtcars)
x <- mtcars[, c("cyl", "gear", "carb", "hp")]
item_reliability(x)
#> Some of the values are negative. Maybe affected items need to be
#> reverse-coded, e.g. using `datawizard::reverse()`.
#> # Item Reliability
#>
#> Item | Alpha if deleted | Total Correlation | Discrimination
#> ------------------------------------------------------------
#> cyl | 0.05 | 0.83 | 0.83
#> gear | 0.11 | -0.12 | -0.13
#> carb | 0.06 | 0.76 | 0.75
#> hp | 0.41 | 1.00 | 0.88
#>
#> Mean inter-item-correlation = 0.294 Cronbach's alpha = 0.095