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Reliability Coefficient E6213B

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Reliability Coefficient E6213B


1. The problem is to compute the reliability coefficient for a data table with 15 participants and 25 statements, where each cell contains a numeric value from 2 to 5. 2. The reliability coefficient often refers to Cronbach's alpha, which measures internal consistency of a test or questionnaire. 3. The formula for Cronbach's alpha is: $$\alpha = \frac{N}{N-1} \left(1 - \frac{\sum_{i=1}^N \sigma_i^2}{\sigma_T^2} \right)$$ where: - $N$ is the number of items (statements), here $N=25$, - $\sigma_i^2$ is the variance of item $i$ across participants, - $\sigma_T^2$ is the variance of the total scores (sum across items) for each participant. 4. Steps to compute: 1. Calculate the variance $\sigma_i^2$ for each of the 25 items across the 15 participants. 2. Sum all item variances: $\sum_{i=1}^{25} \sigma_i^2$. 3. For each participant, sum their scores across all 25 items to get total scores. 4. Calculate the variance $\sigma_T^2$ of these total scores across the 15 participants. 5. Substitute values into the formula to find $\alpha$. 5. Interpretation: - $\alpha$ ranges from 0 to 1. - Values closer to 1 indicate higher internal consistency (reliability). - Common thresholds: $\alpha \geq 0.7$ acceptable, $\alpha \geq 0.8$ good, $\alpha \geq 0.9$ excellent. 6. Without the actual data values, the exact numeric value cannot be computed here, but this is the method to follow. 7. Once computed, interpret the value according to the thresholds above to assess the reliability of the questionnaire or test.