Statistics and research
Cronbach’s alpha calculator
Internal-consistency reliability of a scale: Cronbach’s α with Feldt’s confidence interval, standardized α and α-if-item-deleted for each item.
Runs in your browser. What you enter stays on this page and is not uploaded.
Paste the item columns from a spreadsheet. Every line needs the same number of scores.
Results
Cronbach’s α0.955695% CI0.889 to 0.987Items5Respondents10
- Cronbach’s α
- 0.95560213
- Standardized α (from correlations)
- 0.95611822
- Mean inter-item correlation
- 0.813353
- 95% interval (Feldt)
- 0.88935 to 0.987401
- Sum of item variances
- 6.8666667
- Variance of total scores
- 29.155556
| Item | Mean | SD | Corrected item–total r | α if item deleted |
|---|---|---|---|---|
| Item 1 | 3.4 | 1.26491 | 0.9488 | 0.9323 |
| Item 2 | 3.6 | 1.07497 | 0.8321 | 0.9526 |
| Item 3 | 3.5 | 1.08012 | 0.8422 | 0.951 |
| Item 4 | 3.4 | 1.26491 | 0.8694 | 0.947 |
| Item 5 | 3.7 | 1.1595 | 0.9003 | 0.941 |
α = k/(k − 1) · (1 − Σ item variances / total variance). Reverse-score negatively worded items before pasting.
Method and limits
How to use it
Paste the item scores with one respondent per line and one column per item, straight from a spreadsheet. Reverse-score negatively worded items first, and remove respondents with missing answers.
Formulas
- α = k/(k − 1) × (1 − Σsi² / sT²), with k items, item variances si² and the variance of the total score sT². It equals Hoyt’s ANOVA reliability 1 − MSresidual/MSpersons.
- Standardized α = k r̄ / (1 + (k − 1) r̄), from the mean inter-item correlation r̄.
- Feldt’s interval: (1 − α)/(1 − α̂) follows F(n − 1, (n − 1)(k − 1)), giving 1 − (1 − α̂)F1−γ/2 to 1 − (1 − α̂)Fγ/2.
- Corrected item–total correlation: each item against the sum of the other items; α if item deleted recomputes α without it.
Assumptions and limits
- α measures internal consistency, not that the scale measures one thing; a long scale can have a high α with several dimensions.
- It assumes items measure the same trait on the same scale (tau-equivalence); otherwise it underestimates reliability (consider McDonald’s ω).
- Rules of thumb (0.7 acceptable, 0.8 good, 0.9 excellent) depend on the use; above 0.95 may signal redundant items.
Worked example
The example has 10 respondents and 5 items. The item variances sum to 6.867 and the total-score variance is 29.156, so α = 5/4 × (1 − 6.867/29.156) = 0.956, with a 95% Feldt interval of 0.889 to 0.987.
References
- Cronbach (1951), Coefficient alpha and the internal structure of tests, Psychometrika 16
- Feldt (1965), The approximate sampling distribution of Kuder–Richardson reliability coefficient twenty, Psychometrika 30
- Sijtsma (2009), On the use, the misuse, and the very limited usefulness of Cronbach’s alpha, Psychometrika 74
Related tools
- Correlation coefficient calculatorPearson’s r and Spearman’s rank correlation ρ for paired data, with p-values, r² and a confidence interval for r.
- Linear regression calculatorLeast-squares line with standard errors, t-tests, R², ANOVA table, residuals and leverage, plus confidence and prediction intervals at any x.
- Cohen’s kappa calculatorAgreement between two raters beyond chance: Cohen’s κ, linear or quadratic weighted κ, standard error, confidence interval and z-test.
- Standard deviation calculatorPaste data to get the standard deviation (sample and population), variance, mean, median, mode, quartiles with the method stated, IQR, outliers, skewness and kurtosis.
- T-test calculatorOne-sample, independent two-sample (Welch and pooled) and paired t-tests from raw data or summary statistics, with confidence intervals and Cohen’s d.
- P-value calculatorFind the p-value and critical values for a z, t, chi-square or F test statistic, one- or two-tailed, accurate far into the tails.