Need to Check Test Consistency? Try Guttman Lambda-6!
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.