Reliability Coefficient Calculator

Formula

To calculate the Reliability Coefficient (RC):

\[ RC = \left( \frac{k}{k - 1} \right) \times \left( 1 - \frac{\Sigma \sigma^2}{\sigma_t^2} \right) \]

Where:

\(RC\) is the reliability coefficient
\(k\) is the number of items or tests
\(\Sigma \sigma^2\) is the sum of the variances of each item or test
\(\sigma_t^2\) is the total variance of the test scores

What is a Reliability Coefficient?

A Reliability Coefficient is a statistical measure that indicates the consistency or stability of a set of measurements or testing scores. It ranges from 0 to 1, where a higher value indicates a more reliable or consistent set of data. This coefficient is often used in psychometrics to evaluate the reliability of psychometric instruments like questionnaires or tests. It helps to determine whether the instrument is measuring the concept consistently and accurately.

Example Calculation 1

Let's assume the following values:

Number of Items or Tests (k) = 10
Sum of the Variances (Σσ²) = 15
Total Variance of Test Scores (σt²) = 20

Using the formula:

\[ RC = \left( \frac{10}{10 - 1} \right) \times \left( 1 - \frac{15}{20} \right) = 0.2778 \]

The Reliability Coefficient is 0.2778.

Example Calculation 2

Let's assume the following values:

Number of Items or Tests (k) = 5
Sum of the Variances (Σσ²) = 8
Total Variance of Test Scores (σt²) = 12

Using the formula:

\[ RC = \left( \frac{5}{5 - 1} \right) \times \left( 1 - \frac{8}{12} \right) = 0.4167 \]

The Reliability Coefficient is 0.4167.