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We must take refuge in balanced designs to eradicate as best as we can possible order effects. In addition, we may consider what the time interval should be between the presentation of the first and the second test forms. 4 Reliability estimation with the test–retest method This method for assessing reliability is straightforward enough: present the test at two occasions to the same group of subjects and correlate the outcomes. Assessing reliability with the test–retest method has its problems.
4 Two tests X1 and X2 are congeneric measurement instruments. Their correlations with other variables Y1, Y2, and so on, differ. Is there a pattern to be found in the correlations? 7. a. Compute the observed-score variance, the true-score variance, and the reliability of the difference scores X – Y. b. 18. 6 In a test, several items cover the same subject. Which assumption of classical test theory might be violated? What should we do when we want to estimate reliability with coefficient α? 7 We have three tests X1, X2, and X3 measuring the same construct.
This could easily be remedied by taking all possible splits into two halves. Should we confine ourselves to splits into two halves, however? The answer is no. Several coefficients have been proposed based on a split of a test into more than two parts (see Feldt and Brennan, 1989). We will discuss a method in which all parts or components play the same role. Let test X be composed of k parts Xi. The observed score on the test can be written as X = X1 + X2+⋅⋅⋅+ Xk and the true score as T = T1 + T2+⋅⋅⋅+ Tk The reliability coefficient of the test is k ρXX ′ = σ 2Τ = σ 2X ∑ i σ 2Τ + i k k i 2 X j ≠i ∑∑σ σ Τ iΤ j The covariances between the true scores on the parts in the formula above equal the covariances between the observed scores on the parts.