# Guttman's 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 statistical measure used to assess the internal consistency of assessments with dichotomous choices (Guttman, 1945), similar to Kuder-Richardson-20 (KR-20). However, while KR-20 assumes equal item variance, Lambda-6 does not, potentially providing a more accurate measure of reliability.

Internal consistency refers to the extent to which all the items in a test measure the same construct or trait. A higher internal consistency indicates that the items are well correlated with each other, suggesting that they are all measuring the same underlying characteristic.

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

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

- \( K \) is the number of items
- \( \bar{P} \) is the average proportion of participants that answered items correctly
- \( \bar{Q} = 1 - \bar{P} \) is the average proportion of participants that answered items incorrectly
- \( \sigma^2_X \) is the variance of the total scores

The formula essentially adjusts the KR-20 formula to account for varying item variances, providing potentially more accurate results.

## 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.