# Internal Consistency Reliability

Certain quantities of interest in medicine, psychology, etc., can not be measured explicitly. Accordingly, the assessment is approached by asking a series of questions and combining the answers into a single numerical value, or by a scale such as pass/fail, yes/no, or other dichotomous items.

To form a scale in this manner requires internal consistency, i.e., the items should all measure the same construct. Aabel provides the following methods for internal consistency reliability estimates:

### Cronbach's Alpha

 For estimating the α coefficient, two or more items are required (k >= 2), and scores from each item should be stored in a separate data column. The left-hand side image below shows part of a data set from a questionnaire with k = 10 items and n = 24. The right-hand side image shows the Cronbach's α, estimated for the full data set.

The value of coefficient a will be between 0 and 1 with the following implications:

• When the items are perfectly correlated, the α = 1; when none is related to another, the &alpha = 0.
• The more consistent within-subject responses are, and the greater the variability between subjects in the sample, the higher Cronbach's α will be.
• The accepted α cut-off for a set of items to be considered a scale varies depending on the application of the method and the nature of questionnaire.

### Kuder-Richardson's ρ Formula 20 and Formula 21

This is a procedure that was initially devised for estimating reliability of a test items. Today, it is used as a coefficient of reliability for scales with dichotomous items (e.g., yes/no, pass/fail, correct/incorrect, etc. There are two slightly different versions of Kuder-Richardson's rho:

• Kuder-Richardson Formula 20 (K-R 20)
• Kuder-Richardson Formula 21 (K-R 21)

Data Requirements

• Kuder-Richardson's ρ is used with dichotomous variables (see the top image below). Each column represents one of the items on the test; each row represents scores taken from a given subject
• Two or more items are required (k >= 2), and scores from each item should be stored in a separate data column.
• If the variables that represent the scores are not already in a binary form, Aabel uses the rules used for treating numeric and textual as binary (the rules are described in the user guide).
• The top image below shows part of a data set from a test with k = 12 items and n = 10. The bottom image below displays the output table providing the ρ (K-R 20) and ρ (K-R 21), estimated for the full data set.

A high reliability coefficient can only indicate that all items on the test are variations of the same skill or knowledge base. If the reliability coefficient is low, it may suggest the items on the test measures diverse knowledge or skills.