Guttman's Lambda-6 Calculator

Guttman's Lambda-6 Formula

Guttman's Lambda-6 is a reliability coefficient used to assess the internal consistency of a psychometric scale. It provides an estimate of the scale's reliability, similar to Cronbach's Alpha, but is considered a more precise measure in certain contexts (Guttman, 1954). Lambda-6 is especially useful for scales with a small number of items, offering a more accurate reliability estimate compared to other coefficients.

The formula for Guttman's Lambda-6 is expressed as follows:

\[ \lambda_6 = 1 - \frac{\sum_{i=1}^{k} \sigma^2_{Y_i}}{\sigma^2_X} \]

Where:

• \( k \) represents the number of items on the scale.
• \( \sigma^2_{Y_i} \) is the variance of the scores for each individual item \( i \).
• \( \sigma^2_X \) refers to the variance of the total test scores across all items.

Guttman's Lambda-6 provides a reliable measure of internal consistency, indicating how well the items in a scale measure the same underlying construct. A higher Lambda-6 value suggests greater reliability, meaning the items are more consistently measuring the intended trait.

One of the strengths of Lambda-6 is its applicability to scales with fewer items, where other reliability coefficients like Cronbach's Alpha might be less accurate. However, like all reliability measures, Lambda-6 should be interpreted within the context of the specific research and the nature of the scale being assessed.

References

Guttman, L. (1954). Coefficient Lambda-6: Reliability Measurement. Psychometrika, 19, 371-375. https://doi.org/10.1007/BF02289563

Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). McGraw-Hill. https://doi.org/10.1177/014662169501900308

Nunnally, J. C. (1978). Psychometric theory (2nd ed.). McGraw‐Hill.