What this calculator does
Scale Reliability is the first half of Module 13 of Analysis Studio, Scale Reliability and Factor Analysis. Load a dataset with three or more items scored in the same direction, mark any items that need reverse coding, and the module reports:
- Cronbach alpha, with a Feldt confidence interval
- Standardized alpha, built from the average inter-item correlation
- McDonald omega total from a one-factor model
- Corrected item-total correlations for every item
- Alpha if item deleted for every item, so a weak item shows its cost directly
- Item means and standard deviations
The second half of the module continues into exploratory factor analysis on the same items: principal axis factoring by default, factor retention by parallel analysis, oblimin rotation by default, with KMO and Bartlett tests reported. Reliability and dimensionality belong in the same conversation, and the module keeps them there.
Promotion, stated with its date: through March 31, 2027, this module runs free on screen, like every module. Downloads and Copy Results stay with the subscription throughout. After the promotion, the module returns to the subscription set at $299 per year.
The method, in plain terms
Alpha compares the variance of the total score with the sum of the item variances:
alpha = (k ÷ (k − 1)) × (1 − (sum of item variances ÷ variance of the total score)),
where k is the number of items. When the items move together, the total variance is much larger than the sum of the parts, and alpha approaches one. When the items are unrelated, the total variance equals the sum of the parts, and alpha approaches zero.
Two cautions travel with the number wherever it appears. Alpha rises with the number of items even when the average correlation between items stays fixed, so a long scale earns a high alpha more cheaply than a short one. And alpha is not evidence that a scale measures one thing: a scale with two unrelated clusters of items can post a strong alpha. The factor analysis half of the module exists for the dimensionality question.
Worked example
Four items, each scored from one to five, answered by six respondents:
- Respondent one: 4, 4, 5, 4
- Respondent two: 5, 5, 4, 5
- Respondent three: 2, 3, 2, 3
- Respondent four: 3, 2, 3, 2
- Respondent five: 5, 4, 5, 5
- Respondent six: 1, 2, 1, 2
The module reports:
- Cronbach alpha: 0.955
- Standardized alpha: 0.961, from an average inter-item correlation of 0.859
- Item means: 3.33, 3.33, 3.33, and 3.50, with a mean total score of 13.5
- Alpha if item deleted: 0.926 without item one, 0.951 without item two, 0.954 without item three, and 0.933 without item four
- Corrected item-total correlations: 0.946, 0.879, 0.863, and 0.923
Read as a scale builder reads it: every item pulls in the same direction, deleting any item lowers alpha, and the third item is the weakest of a strong set. Six respondents is a teaching example, not a sample size to publish on, and the interval around alpha at that n would be wide. The module prints the interval so the width is visible rather than implied.
When the calculator fits, and when it does not
It fits when:
- The scale has three or more items intended to measure one construct, scored on the same metric, with reverse-worded items recoded before the run.
- The report needs the full item picture, not a single coefficient: item-total correlations and alpha if deleted are where scale repair actually happens.
- A factor analysis should follow, to test whether one construct is a fair description of the items.
It does not fit when:
- The scale has two items. Report their correlation instead; alpha on two items adds nothing.
- The items are formative, meaning the items cause the score rather than reflect it, as in an index of life events. Internal consistency is the wrong standard for formative measures.
- The sample is tiny. Alpha from a handful of respondents is unstable, and no calculator fixes that.
Run it
Module 13: Scale Reliability and Factor AnalysisOpen in Analysis Studio →Load your item data, set the reverse-coding map if any items are worded in the opposite direction, and run the reliability report first.
Questions
What is a good Cronbach alpha? The conventional bands: 0.70 and above is acceptable for research use, 0.80 and above is good, and 0.90 and above is excellent, with a caution that values past roughly 0.95 often mean redundant items asking the same question twice. The bands are conventions, not laws, and the right standard depends on the decisions the score feeds.
Why is my alpha negative? Almost always because one or more items run in the opposite direction and were not reverse coded. The total score then cancels itself out. Check the corrected item-total correlations: the reversed item shows a negative value and names itself.
What is the difference between alpha and standardized alpha? Alpha works from the item variances as scored. Standardized alpha works from the correlations, which puts every item on the same footing first. When items share a metric and similar variances, the two sit close together, as in the worked example: 0.955 and 0.961. When they diverge, the items have uneven variances and the gap is worth a look.
Should I delete the item with the lowest item-total correlation? Not on that number alone. Read alpha if item deleted next to it: if deleting the item raises alpha materially, the item is a repair candidate. If alpha barely moves, the item may still earn its place on content grounds. The module reports both figures so the judgment has its evidence in view.
Does a high alpha prove my scale is unidimensional? No. Alpha measures internal consistency, and a scale built from two correlated clusters can be consistently multidimensional. The factor analysis in the same module answers the dimensionality question.