Calculate a reliability coefficient (Cronbach’s alpha) from item count, item variances and total variance, or from the average inter-item correlation.

Use the same respondents, scoring and variance divisor as the total-score variance.

Target alpha and length planning
Blank skips length planning. Added items are assumed comparable to the existing ones.

Related Calculators

Reliability Coefficient Formula

The following formula is used to calculate the Reliability Coefficient.

RC = (k / (k - 1)) ร— (1 - (ฮฃฯƒยฒ / ฯƒtยฒ))

Variables:

  • RC is the Reliability Coefficient
  • k is the number of items or tests
  • ฮฃฯƒยฒ is the sum of the variances of each item or test
  • ฯƒtยฒ is the total variance of the test scores

For raw Cronbachโ€™s alpha, calculate item variances and the variance of the summed total scores using the same respondents, scoring and variance divisor. Divide the sum of item variances by the total-score variance, subtract that ratio from 1, then multiply by k/(k โˆ’ 1). Standardized alpha instead uses the average Pearson correlation and can differ when item variances differ.

What is a Reliability Coefficient?

This calculator estimates Cronbachโ€™s alpha, a sample internal-consistency coefficient used for scales such as questionnaires and tests. Coherent inputs give alpha no greater than 1, but alpha can be negative when net inter-item covariance is negative. Negative values warrant review of scoring directions and item relationships. Alpha depends on the sample, test length and intended use; it does not by itself establish validity, accuracy or a single underlying dimension. There is no universal acceptable cutoff.

How to Calculate Reliability Coefficient?

The following steps outline how to calculate the Reliability Coefficient.

  1. First, determine the number of items or tests (k).
  2. Next, calculate the sum of the variances of each item or test (ฮฃฯƒยฒ).
  3. Next, determine the total variance of the test scores (ฯƒtยฒ).
  4. Next, use the formula RC = (k / (k - 1)) * (1 - (ฮฃฯƒยฒ / ฯƒtยฒ)).
  5. Finally, calculate the Reliability Coefficient.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Number of items or tests (k) = 5

Sum of the variances of each item or test (ฮฃฯƒยฒ) = 10

Total variance of the test scores (ฯƒtยฒ) = 3. Alpha = (5/4) ร— (1 โˆ’ 10/3) = โˆ’2.916667. This is a negative-alpha example; inspect scoring direction and item relationships rather than treating it as a normal positive reliability estimate.