Uji Reliabilitas Kuder Richardson KR20 KR21

Introduction

This tutorial provides a step-by-step guide on calculating the Kuder-Richardson reliability coefficients KR-20 and KR-21. These coefficients are used to assess the reliability of tests with binary outcomes (correct/incorrect). Understanding these methods is crucial for educators and researchers who want to ensure the consistency and accuracy of their assessments.

Step 1: Understand Kuder-Richardson Coefficients

• Definition: Kuder-Richardson coefficients (KR-20 and KR-21) are statistical methods used to measure the reliability of assessments with dichotomous items.
• Usage: These coefficients are particularly useful for tests that score answers as either correct (1) or incorrect (0).
• Importance: A higher KR value indicates greater reliability, meaning the test scores are consistent across different administrations.

Step 2: Gather Your Data

• Collect Test Scores: Gather the scores from your test, ensuring each item is scored as 0 or 1.
• Sample Size: Ensure you have a sufficient number of responses to get a reliable estimate (ideally, at least 30 participants).

Step 3: Calculate the Mean and Variance

• Calculate Mean: Use the formula to find the mean of the test scores.

  [ \text{Mean} = \frac{\sum X}{N} ]

• Calculate Total Variance: Determine the variance for the total scores using:

  [ \text{Variance} = \frac{\sum (X - \text{Mean})^2}{N - 1} ]

Step 4: Calculate Item Variance

• Calculate Item Variance: For each item, calculate the variance using the same variance formula.

  [ \text{Variance}_{item} = \frac{\sum (X - \text{Mean})^2}{N - 1} ]

• Sum of Item Variances: Add the variances of all items together.

Step 5: Use the KR-20 and KR-21 Formulas

• KR-20 Formula:

  [ KR-20 = \frac{k}{k - 1} \left( 1 - \frac{\sum \text{Variance}_{item}}{\text{Total Variance}} \right) ]

• KR-21 Formula:

  [ KR-21 = \frac{k}{k - 1} \left( 1 - \frac{\text{Variance}_{item}}{\text{Total Variance}} \right) ]

Where k is the number of items in the test.

Step 6: Interpret the Results

• Interpreting KR Values:

  • KR values range from 0 to 1.
  • A value closer to 1 indicates high reliability, while values below 0.7 suggest the need for test revision.

• Practical Implications: Use these reliability measures to determine if modifications are necessary for your assessment.

Conclusion

Calculating the Kuder-Richardson coefficients KR-20 and KR-21 is vital for evaluating the reliability of tests with binary responses. By following this step-by-step guide, you can effectively analyze your assessment tools and ensure their reliability. For next steps, consider applying these calculations to various tests or exploring additional statistical methods for reliability assessment.