Cronbach’s alpha calculator: reliability with the item analysis SPSS prints

Lee Cronbach published the coefficient in 1951 as a general form of the Kuder–Richardson formula 20. It compares the variance of each item with the variance of the total score: if the items move together, the total varies much more than the items do on their own, and alpha approaches 1.

Raw alpha is what SPSS prints as Cronbach’s Alpha and R’s psych::alpha as raw_alpha; standardised alpha is SPSS’s Cronbach’s Alpha Based on Standardized Items. The two differ when items have very different variances. The interval is Feldt’s (1987), which assumes the items are measured on comparable scales and is the one most reliability software reports.

A worked example

Four respondents answer three items: (1, 2, 2), (2, 3, 3), (3, 3, 4), (4, 5, 4). The item variances are 1.667, 1.583 and 0.917, summing to 4.167. The totals are 5, 8, 10 and 13, with variance 11.333. So α = 3 / 2 × (1 − 4.167 / 11.333) = 1.5 × 0.632 = 0.949. Paste those rows into the calculator and it shows the same number — and an interval from 0.66 to 1.00, which is what four respondents buy you.

There is no law, only conventions, and they are older and looser than the precision with which they are quoted. The bands most theses and papers cite come from George and Mallery’s SPSS textbook:

The 0.70 threshold everybody uses traces back to Nunnally’s Psychometric Theory (1978), which asked for 0.70 in early-stage research and 0.80 for basic research, and 0.90 or more where individual decisions are made from the score. Three things the bands do not tell you:

• Higher is not always better. Above about 0.95 the items are probably near-duplicates: the scale is longer than it needs to be, or measures a narrow slice of the construct.
• Alpha grows with the number of items. Twenty mediocre items can reach 0.90; three good ones may sit at 0.70. Compare the mean inter-item correlation (0.15–0.50 is the usual range for a coherent scale) when scales differ in length.
• Alpha is a property of this sample, not of the questionnaire. A published scale that reached 0.85 elsewhere can fall to 0.65 in a group with less spread in the trait. Report your own alpha, with its interval.

The total alpha says whether the scale holds together; the item table says which item does not. For each item the page shows two numbers:

• Corrected item-total correlation — the item against the sum of the other items. Values above 0.3 are usually taken as a sign the item belongs; near zero it measures something else; negative almost always means the item is worded in reverse and has not been reverse-scored.
• Alpha if item deleted — what alpha would be for the remaining items. If it is clearly higher than the current alpha, the item is pulling the scale down.

In the example data, Q4 is a negatively worded item. Without reverse scoring, alpha is 0.57 and Q4’s item-total correlation is negative; reversing it lifts alpha to 0.85. Q6 then stands out with an item-total correlation of 0.09: deleting it would raise alpha to 0.90. Whether to delete it is a question about wording and content, not arithmetic — an item that covers a real part of the construct can be worth keeping at a small cost in alpha, and dropping items until alpha peaks capitalises on chance in this one sample.

• It is not proof of one dimension. A questionnaire with two correlated factors can still have a high alpha. To claim a scale is unidimensional, run a factor analysis; alpha assumes it, it does not test it.
• It assumes every item counts equally. Alpha is a lower bound on reliability when items load unequally on the construct. McDonald’s omega, from a one-factor model, is the alternative modern methodologists prefer; with roughly equal loadings the two agree closely.
• It is not validity. A perfectly consistent scale can consistently measure the wrong thing.
• Skipped answers change the sample. Leaving out incomplete rows (listwise, as here and in SPSS by default) is honest but can bias alpha if the people who skip are different. Report how many rows were left out.
• Ordinal answers with few points lower Pearson-based alpha a little; ordinal alpha from polychoric correlations is the fix for 3–4 point scales.

Product teams write their own questionnaires all the time — an onboarding satisfaction survey, a “how confident do you feel” block after a tutorial, a five-item trust scale for a fintech app. Before averaging those items into one number for a dashboard, alpha is the check that the average means something.

• Standard instruments come with their scoring. The System Usability Scale has alternating item wording and its own grade curve; the UEQ calculator reports alpha per scale with the UEQ team’s cleaning rules. Use this page for scales you built yourself or adapted.
• Pilot before the launch survey. Thirty respondents are enough to find a reverse-worded item nobody reversed or an item people read differently. Two hundred respondents later is too late.
• Check the size of the sample you will need. The survey sample size calculator tells you how many responses a given margin of error takes.

1. Cronbach L. J. “Coefficient alpha and the internal structure of tests.” Psychometrika 16(3), 1951, 297–334.
2. Feldt L. S., Woodruff D. J., Salih F. A. “Statistical inference for coefficient alpha.” Applied Psychological Measurement 11(1), 1987, 93–103 — the confidence interval used here.
3. Nunnally J. C. Psychometric Theory, 2nd ed. New York: McGraw-Hill, 1978 — the 0.70 / 0.80 / 0.90 recommendations.
4. George D., Mallery P. SPSS for Windows Step by Step: A Simple Guide and Reference, 4th ed. Boston: Allyn & Bacon, 2003 — the excellent-to-unacceptable bands.
5. Streiner D. L. “Starting at the beginning: an introduction to coefficient alpha and internal consistency.” Journal of Personality Assessment 80(1), 2003, 99–103 — on alphas above 0.90 and redundancy.
6. Tavakol M., Dennick R. “Making sense of Cronbach’s alpha.” International Journal of Medical Education 2, 2011, 53–55.
7. McNeish D. “Thanks coefficient alpha, we’ll take it from here.” Psychological Methods 23(3), 2018, 412–433 — alpha’s assumptions and omega.