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Cronbach's Alpha Calculator

Measure of internal consistency reliability.

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Cronbach's α

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Overview

Cronbach's Alpha is a fundamental coefficient used to estimate the internal consistency reliability of a psychometric test or survey. It quantifies the degree to which all items in a test measure the same latent construct by comparing the variance of individual items to the variance of the total score.

Symbols

Variables

\alpha = Cronbach's α, k = Num Items, \Sigma \sigma_i^2 = Sum Item Var, \sigma_t^2 = Total Variance

Cronbach's α
Num Items
Sum Item Var
Total Variance

Apply it well

When To Use

When to use: Apply this coefficient when assessing the reliability of Likert-type scales or any multi-item instrument designed to measure a single trait. It assumes that items are essentially tau-equivalent, meaning they all reflect the same underlying factor with potentially different error variances.

Why it matters: High alpha values ensure that the measurement tool is stable and that the observed scores are not merely the result of random measurement error. This is vital in clinical settings where test results might determine a diagnosis or the effectiveness of a treatment intervention.

Avoid these traps

Common Mistakes

  • Using it on scales that measure multiple distinct concepts.

One free problem

Practice Problem

A psychometrician is validating a 5-item personality scale. The sum of the individual item variances is 4.0, and the total variance of the composite scores is 10.0. Calculate Cronbach's Alpha for this scale.

Num Items5
Sum Item Var4
Total Variance10

Solve for:

Hint: First calculate the variance ratio (sumV / totV), subtract it from 1, and then multiply by the correction factor k / (k-1).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Psychometric Theory by Jum C. Nunnally and Ira H. Bernstein
  2. Psychometrics: An Introduction by R. Michael Furr and Verne R. Bacharach
  3. Wikipedia: Cronbach's alpha
  4. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334.
  5. Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage Publications.
  6. Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric Theory (3rd ed.). McGraw-Hill.
  7. Kline, P. (2013). An Introduction to Psychometric Theory (2nd ed.). Routledge.
  8. Cohen, R. J., & Swerdlik, M. E. (2018). Psychological Testing and Assessment: An Introduction to Tests and Measurement (9th ed.).