# Guttman Lambda-6 Calculator

Welcome to the Guttman's Lambda-6 Calculator! Follow the steps below to calculate the Lambda-6 for your data.

**Download the example file:**Click here to download an example file and follow these steps to prepare your data:- Open your original dataset in Excel.
- Ensure that each item/response is in its own column, and each participant's responses are in a separate row.
- Save your file as a CSV (Comma delimited) (*.csv).
- Open the saved CSV file in Notepad to copy the comma-separated values.

**Paste Your Data:**After copying your comma-separated values, paste them into the textarea below.**Generate Table:**Click the "Generate Table" button to view your data in tabular form.**Calculate Lambda-6:**After generating the table, click the "Calculate Lambda-6" button to get the result.

## Guttman's Lambda-6 Formula

Guttman’s Lambda-6 is a reliability coefficient used to assess the internal consistency of tests, particularly those with dichotomous items, such as true/false or yes/no questions. Developed by Louis Guttman in 1945, Lambda-6 is part of the broader family of Guttman’s Lambda coefficients, designed to measure how consistently test items reflect the same underlying construct (Guttman, 1945). Unlike other reliability measures, such as Kuder-Richardson 20 (KR-20), Lambda-6 does not assume that all items have equal variance, which can provide a more accurate assessment of internal consistency in certain test contexts.

Internal consistency refers to the degree to which the items on a test work together to measure a single construct or trait. A higher value for Lambda-6 indicates that the items are well correlated, meaning they consistently measure the same underlying characteristic. This is similar to what KR-20 does, but Lambda-6 is especially valuable when item variances differ significantly, such as when items vary in difficulty or discrimination power.

The formula for Guttman’s Lambda-6 is:

\[ \lambda_6 = \frac{K(K-1)}{\sigma^2_X + (K-1)\bar{P}\bar{Q}} \]Where:

- \( K \) is the number of items in the test.
- \( \bar{P} \) represents the average proportion of participants who answered each item correctly.
- \( \bar{Q} = 1 - \bar{P} \), representing the average proportion of participants who answered each item incorrectly.
- \( \sigma^2_X \) is the variance of the total test scores.

Guttman’s Lambda-6 builds on the idea that internal consistency depends not only on item correlation but also on how much the individual items differ in terms of their variance. KR-20 assumes equal variances across items, which can lead to less precise reliability estimates when item variances vary significantly. In contrast, Lambda-6 adjusts for these differences, potentially yielding more accurate estimates of a test's reliability.

For example, if a test contains both very easy and very difficult items, KR-20 might underestimate or overestimate the reliability depending on how those items affect the overall score variance. Lambda-6, by not assuming uniform item variance, offers a more flexible approach, making it a better choice when dealing with tests where item difficulty or response variability is not uniform.

## References

Guttman, L. (1945). A Basis for Analyzing Test-Retest Reliability. *Psychometrika, 10*(4), 255–282. https://doi.org/10.1007/BF02288892

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