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Guttman Scale (Coefficient of Reproducibility) Calculator

Measures how well a set of items forms a cumulative (Guttman) scale, indicating unidimensionality.

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Coefficient of Reproducibility

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Overview

The Coefficient of Reproducibility (CR) is a key statistic used to evaluate the unidimensionality of a Guttman scale. A Guttman scale is a cumulative scale where agreement with a higher-level item implies agreement with all lower-level items. The CR quantifies the extent to which an individual's responses to a set of items can be reproduced from their total score, indicating how closely the observed data fit the perfect Guttman pattern. A high CR (typically 0.90 or above) suggests that the items form a strong cumulative scale.

Symbols

Variables

= Number of Errors, = Number of Responses, CR = Coefficient of Reproducibility

Number of Errors
Variable
Number of Responses
Variable
CR
Coefficient of Reproducibility
Variable

Apply it well

When To Use

When to use: Apply the Coefficient of Reproducibility when constructing or evaluating a Guttman scale to assess its unidimensionality and cumulative property. It is used to determine if a set of items measures a single underlying construct in a hierarchical manner.

Why it matters: Understanding CR is crucial for developing valid and reliable psychological scales. A high CR ensures that the scale accurately reflects a single, ordered dimension, which is fundamental for meaningful measurement in areas like attitude assessment, developmental stages, or clinical symptom severity.

Avoid these traps

Common Mistakes

  • Incorrectly identifying or counting 'errors' in the Guttman scaling process.
  • Confusing CR with other reliability measures like Cronbach's Alpha, which assess internal consistency differently.
  • Applying Guttman scaling to data that are not inherently cumulative or ordinal.

One free problem

Practice Problem

A researcher constructs a Guttman scale with 5 items administered to 40 participants, resulting in 20 errors. Calculate the Coefficient of Reproducibility (CR).

Number of Errors20
Number of Responses200

Solve for: CR

Hint: Total responses = number of items × number of participants. Then apply CR = 1 - (Errors / Total Responses).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Guttman scale
  2. Psychometric Theory (3rd ed.) by Jum C. Nunnally and Ira H. Bernstein
  3. Psychometric Theory by Jum C. Nunnally and Ira H. Bernstein (3rd ed., 1994)
  4. Guttman, L. (1950). The basis for scalogram analysis. In Stouffer et al., Measurement and Prediction.
  5. Edwards, A. L. (1957). Techniques of Attitude Scale Construction.
  6. Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9(2), 139-150.