Why Cronbach's Alpha Is Not Enough

And what should be used instead

"Cronbach's alpha was .83, indicating good internal consistency."

This sentence still appears widely in articles, reports, and theses. It has become the standard way to report the internal consistency of a measurement instrument.

However, being standard does not mean being unproblematic. Cronbach's alpha is based on assumptions that rarely hold in practical measurement. For this reason, alpha should be interpreted with caution.

What alpha assumes

Cronbach's alpha assumes tau-equivalence. This means that all items in the instrument measure the same latent construct with equal strength.

In practice, this assumption rarely holds. In a typical instrument, some items capture central aspects of the phenomenon while others describe it more indirectly or narrowly. Item discrimination varies, and their contribution to the total measure is not uniform.

When tau-equivalence does not hold, alpha no longer accurately represents reliability. In such cases, it typically underestimates true reliability. In some situations, alpha may also yield a seemingly good value for an instrument that does not actually measure a unified construct.

McDonald's omega and the factor-based approach

McDonald's omega (ω) is explicitly based on a factor model. Rather than assuming all items function identically, omega accounts for each item's factor loading when estimating reliability.

ω = (Σλᵢ)² / [(Σλᵢ)² + Σ(1 − λᵢ²)]

This approach better reflects how psychological and social measures actually function. Omega provides a more reliable overall picture, particularly when items differ in discrimination or relevance.

Psychometric research has recommended omega over Cronbach's alpha for some time. Nevertheless, alpha has remained common in practical reporting, partly due to habit and ease of use.

Likert scales and ordinal data

Likert scale data is ordinal in nature. Although response options are often presented numerically, the distances between them cannot be assumed to be equal.

Traditional Cronbach's alpha treats data as continuous and relies on Pearson correlations. This often leads to underestimation of relationships between variables.

Polychoric correlations offer a more appropriate solution for ordinal data. They are based on the assumption of a continuous latent variable that manifests as observed categories. This aligns with the theoretical foundation of psychometrics.

IRT and instrument performance across levels

Classical test theory provides an average estimate of instrument reliability.

Item Response Theory approaches, such as the Graded Response Model (GRM), offer a more precise view of where along the latent distribution the instrument performs well and where it performs poorly.

GRM produces for each item:

• Discrimination: how sensitively the item differentiates between respondents

• Threshold parameters: the transition points between response options

This information allows identification of items that do not add value to the instrument, as well as situations where the instrument only functions within a limited range.

Method selection in practice

evaluoi.ai selects analysis methods based on the data and measurement context:

Situation	Method
Small sample sizes	Split-half with Spearman-Brown correction
Adequate sample sizes	McDonald's omega
Ordinal data	Ordinal omega with polychoric correlations
Larger samples	IRT (Graded Response Model)

The system also produces item-level diagnostics, including item-total correlations, alpha-if-deleted analyses, factor loadings, and item information curves.

Analyses are produced automatically but remain transparently available for expert-level review.

Reporting for different audiences

The same analysis can be reported at different levels:

1. Basic level provides a concise summary of instrument performance.

2. Advanced level includes key statistics such as reliability estimates and confidence intervals.

3. Expert level presents all methods used, assumptions, limitations, and references to the literature.

Why this matters

Reliability directly affects the interpretation of measurement results. Incorrectly estimated reliability leads to incorrect confidence intervals, which in turn distort the assessment of change and decision-making.

In such cases, measurement does not support understanding but may unintentionally mislead.

Conclusion

Cronbach's alpha is not inherently a flawed method. However, it is limited and often poorly suited to contemporary measurement practice.

Psychometrics has advanced significantly over recent decades. Measurement practices should reflect this development.

evaluoi.ai utilises methods aligned with current recommendations, including McDonald's omega, polychoric correlations, and IRT models, with the aim of producing more reliable and interpretatively robust information to support decision-making.

Book a demo or watch the intro video: evaluoi.ai

References

McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum.

Revelle, W., & Zinbarg, R. E. (2009). Coefficients alpha, beta, omega, and the glb. Psychometrika, 74(1), 145-154.

Flora, D. B. (2020). Your coefficient alpha is probably wrong, but which coefficient omega is right? Educational and Psychological Measurement, 80(3), 527-546.

Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44(4), 443-460.