If the true score variance is equal to 10 and error variance is equal to 2, what is our estimate of reliability? [Hint: Think about the conclusions that we draw from the assumptions of classical test theory]
To estimate reliability in classical test theory, we can use the formula:
Reliability = True Score Variance / (True Score Variance + Error Variance)
Given that the true score variance is equal to 10 and the error variance is equal to 2, we can substitute these values into the formula:
Reliability = 10 / (10 + 2)
Simplifying the expression:
Reliability = 10 / 12
Dividing numerator and denominator:
Reliability ≈ 0.833
Therefore, our estimate of reliability is approximately 0.833.
To estimate reliability in classical test theory, we typically use the formula for the reliability coefficient, also known as the internal consistency coefficient or Cronbach's alpha.
The formula for the reliability coefficient is:
Reliability = (True Score Variance) / (True Score Variance + Error Variance)
In this case, you mentioned that the true score variance is equal to 10 and the error variance is equal to 2. Plugging these values into the formula, we get:
Reliability = 10 / (10 + 2) = 10 / 12 = 0.833
So, our estimate of reliability is 0.833 (or approximately 0.83).
It is important to note that this estimate assumes that the test is measuring a single construct, and that the errors in the measurements are random and not related to the construct being measured. Classical test theory makes several other assumptions as well, such as the assumption that the true score and error are uncorrelated and that there are no systematic biases in the test administration or scoring.