Discrimination and Item-Total Correlation of Questionnaire Items

Compute various measures of internal consistencies for tests or item-scales of questionnaires. item_discrimination() calculates the corrected item-total correlations for each item of x with the remaining items. item_totalcor() by default calculates the item-total correlations (without correction).

Usage

item_discrimination(x, standardize = FALSE, corrected = TRUE, verbose = TRUE)

item_totalcor(x, standardize = FALSE, corrected = FALSE, verbose = TRUE)

Arguments

x: A matrix or a data frame.
standardize: Logical, if TRUE, the data frame's vectors will be standardized. Recommended when the variables have different measures / scales.
corrected: Logical, if TRUE, the item-total correlations are corrected for the item itself (default). If FALSE, the item-total correlations are calculated without correction.
verbose: Toggle warnings and messages.

Value

A data frame with the item discrimination (corrected item-total correlations) for each item of the scale.

Details

item_totalcor() calculates the item-total correlations (without correction). A positive item-total correlation indicates that an item successfully aligns with the overall test, with higher values signifying a better fit. Conversely, a value near zero suggests the item is not measuring the intended construct, while a negative correlation is a major red flag that the item is flawed, miskeyed, or measures the opposite of what is intended. This means a positive correlation is desired, a zero correlation is problematic, and a negative correlation requires immediate attention.

The standard item-total correlation has an inherent flaw: the score of the item being analyzed is included in the total score. This inclusion can artificially inflate the correlation coefficient, as an item will always correlate with itself. The corrected item-total correlation, or item discrimination, addresses this issue by calculating the correlation between the score on a single item and the sum of the scores of all other items on the scale. This is done with item_discrimination(). 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 a satisfactory index ranges 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 - in such cases, use datawizard::reverse() to reverse-code items in advance).

Interpretation of the Corrected Item-Total Correlation Values:

Corrected Item-Total Correlation Value	Interpretation	Action
Above 0.40	The item has a very good discrimination and is strongly related to the underlying construct.	Retain the item.
0.30 to 0.39	The item has good discrimination and contributes positively to the scale's internal consistency.	Retain the item.
0.20 to 0.29	The item has marginal discrimination. While not ideal, it may still be acceptable, especially in shorter scales or when measuring a very broad construct.	Consider revising the item for clarity or content. If other items have stronger correlations, this one might be a candidate for removal if the scale needs to be shortened.
Below 0.20	The item has poor discrimination. It does not correlate well with the rest of the scale and may be measuring something else. Its inclusion is likely to decrease the overall reliability (e.g., Cronbach's Alpha) of the scale.	Revise the item substantially or, more likely, remove it from the scale.
Negative Value	The item is negatively related to the rest of the scale. This is a serious issue.	The item must be revised or removed. Check for scoring errors (e.g., a reverse-keyed item that wasn't properly recoded).

item_discrimination() and item_totalcor() only differ in the default value of the corrected argument. The former calculates the corrected item-total correlations, while the latter calculates the item-total correlations.

References

Kelava A, Moosbrugger H (2020). Deskriptivstatistische Itemanalyse und Testwertbestimmung. In: Moosbrugger H, Kelava A, editors. Testtheorie und Fragebogenkonstruktion. Berlin, Heidelberg: Springer, 143–158

Examples

data(mtcars)
x <- mtcars[, c("cyl", "gear", "carb", "hp")]
item_discrimination(x)
#> Some of the values are negative. Maybe affected items need to be
#>   reverse-coded, e.g. using `datawizard::reverse()`.
#> Item Discrimination
#> 
#> Item | Discrimination
#> ---------------------
#> cyl  |           0.83
#> gear |          -0.13
#> carb |           0.75
#> hp   |           0.88
item_totalcor(x)
#> Some of the values are negative. Maybe affected items need to be
#>   reverse-coded, e.g. using `datawizard::reverse()`.
#> Item-Total Correlation
#> 
#> Item | Total Correlation
#> ------------------------
#> cyl  |              0.83
#> gear |             -0.12
#> carb |              0.76
#> hp   |              1.00