What is Cronbach's alpha?

Also called Coefficient alpha, Internal consistency

Cronbach's alpha is an index of internal consistency: how far the items in a scale behave as though they measure one thing. It runs from 0 to about 1 and rises with both the average correlation between items and the sheer number of items, which is why a high alpha on its own proves very little.

How to read a reported alpha

The conventional rules of thumb — 0.70 acceptable, 0.80 good, 0.90 excellent — are widely quoted and were never intended as thresholds. What matters is the decision the score supports: an alpha that is comfortable for a research scale is not comfortable for a scale used to reject an individual candidate.

Alpha above roughly 0.95 is usually a warning rather than a triumph. It generally means items are near-duplicates of each other, so the scale is long, narrow and redundant, and it measures a smaller slice of the construct than its name suggests.

Alpha is the wrong input for a question about two scores

Alpha is not only a number to compare instruments by; it is an input. Both of the calculations a reliability coefficient actually feeds — the Spearman–Brown formula for how much longer a test must be, and the standard error of the difference for whether two scores differ — take a reliability figure and return a decision. Which figure you put in is not a detail, and alpha is frequently the wrong one.

The clearest statement of this comes from clinical psychology, where the same arithmetic has been in routine use since 1991 and has been argued about ever since. Blampied's 2022 open-access review records the position: Jacobson and Truax, who introduced the difference-score test to practice, "recommended that rxx should be used" — test–retest reliability — and "McAleavey (2021) has argued that only test–retest reliability estimated over short inter-test intervals should be used, because it is the measure of reliability matching the pre–post repeated measures aspect of the data being analysed, and coefficient α should not be used."

The reasoning is about matching the coefficient to the question. Alpha describes agreement between items inside one sitting. A question about whether a person's score has changed, or whether two people's scores differ, is a question about stability across sittings, which is what test–retest reliability measures and what alpha does not. Substituting one for the other is not conservative in a useful direction: the standard error of measurement is the scale's standard deviation times the square root of one minus the reliability, so the higher coefficient produces the narrower error band — and where alpha is the higher of a vendor's two figures, using it makes the instrument look more decisive than it is.

The practical ask is one line long. When a vendor quotes an alpha, ask for the test–retest figure and the interval over which it was measured, and run any difference arithmetic on whichever of the two is lower.

Why the length effect matters commercially

Because alpha rises with item count, a vendor can raise it simply by adding paraphrases of existing questions. This makes alpha the easiest reliability figure to inflate and the least informative to compare across instruments of different lengths.

The more defensible modern practice is to report McDonald's omega alongside or instead of alpha, because omega does not assume every item contributes equally to the underlying factor — an assumption that is almost never true of real questionnaires.

What the item count does on its own

Average inter-item correlation 0.30, 5 items → alpha ≈ (5 × 0.30) ÷ (1 + 4 × 0.30) = 0.68
Same 0.30 correlation, 10 items → alpha ≈ (10 × 0.30) ÷ (1 + 9 × 0.30) = 0.81
Same 0.30 correlation, 20 items → alpha ≈ 0.90

Nothing about the quality of the items changed between those three lines. Ask for the item count whenever an alpha is quoted, and be sceptical of a high figure on a long scale.

Not the same as test–retest reliability

Alpha describes agreement between items within a single sitting. Test–retest describes agreement between two sittings by the same people. A scale can be internally consistent and still give a different answer next month.

Test–retest reliability

Sources

More terms beginning with C

Construct validity Criterion validity Cut score

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Last reviewed 2026-09-25