How reliably does my scale measure? (Cronbach's alpha, McDonald's omega)

In brief

At least two questions are to be combined into a scale, and the aim is to check whether they are answered consistently (internal consistency). The questions must be numbers with the same direction; reverse-worded questions are reverse-coded (Statable points out negative item-total correlations and creates the new column). Rule of thumb: at least 5 people per question, ideally 10.

Reading alpha

Cronbach's α usually lies between 0 and 1; from .70 it counts as acceptable, from .80 as good, with a 95% interval. "Alpha if item deleted" shows whether a single question worsens the scale; the item-total correlation should be positive and preferably above .30. Alpha measures internal consistency. It does not show whether the questions measure one common trait (unidimensionality) - a factor analysis tests that - nor whether the scale measures what is meant (validity).

McDonald's omega

Next to alpha there is a line "McDonald's omega" (from three questions). Omega uses the estimated strength with which each question contributes to the scale; alpha assumes equal contributions. The same rules of thumb apply. If omega is clearly above alpha, the questions contribute unequally. For this, Statable loads R once the first time (about 30 MB), afterwards it takes about a second and happens by itself. Omega assumes a single common construct; if the questions measure several, a factor analysis helps.

Cronbach's α = .82, 95% CI [.76, .87] (4 items, n = 118); McDonald's ω = .84, 95% CI [.79, .88]

For specialists

ω total from a one-factor model (lavaan, ML): ω = (Σλ)² / ((Σλ)² + Σθ), as in JASP. jamovi uses psych::omega with one factor and shows no interval. The interval is the delta method by default; optionally a percentile bootstrap (1000 draws, fixed seed, as in JASP), which takes much longer in the browser. Missing values: people left out, or FIML. ωh (hierarchical) comes from psych::omega with 2 to 4 group factors and is available from six questions. A negative residual variance or loading above 1 (Heywood case) is reported. Checked against R: HolzingerSwineford1939 and psych::bfi.

More cards below the result

• Rasch model (right/wrong tasks): difficulty of each task, fit (infit and outfit between 0.7 and 1.3), Wright map.
• 2PL model: additionally a discrimination for each task and the characteristic curves; sensible from about 500 people.
• Graded response model (answers 1 to 5): discrimination and thresholds per question, answer curves.
• Fair tasks (DIF): do groups of equal ability have different chances on a task? Conspicuous tasks are only a reason to look at the content.
• Map of the questions: questions with a strong relation lie close together; shows groups of questions even before a factor analysis.

Typical examples

• Eight questions on test anxiety, one worded in reverse ("I go into exams confidently"): reverse first, then Cronbach alpha.
• A questionnaire with 20 questions on motivation: alpha for each subscale.