Exam 1

1. Metainformation

   Tag	Value
   file	Reliability_eur-reliability-214-en_eur-reliability-214-en
   name	eur-reliability-214-en
   section	Reliability/Analysis/Cronbach's alpha
   type	num
   solution	0.38
   tolerance	0
   Type	Calculate
   Program	Calculator
   Language	English
   Level	Statistical Literacy

   Question

   Exams aim at measuring a person’s true score. The accuracy of this measurement of the true score will likely be lower if the reliability of the test is too low. One way to theoretically compensate for this lower accuracy is by calculating the adjusted true score: $X_{est} = x̄ + R_{xx}(X_o-x̄)$

   Suppose that the average score of a psychometric exam is 5.8. The reliability of this test is .31 (Cronbach’s alpha); A grade of at least 5.5 is needed to pass the exam. A student who had a 5.0 complains to the examination board that he doesn’t want to do the retake because his true score is in fact 5.5. Calculate which reliability of the exam will give this student a right to complain.

   Round to two decimals.

   
   

   Solution

   We can calculate the observed score which is accompanied with an adjusted true score 5.5. $5.5 = 5.8 + R_{XX}(5.0 - 5.8)$ $-.3 = R_{XX} \times -.8$ $R_{XX} = .375 = .38$

   A reliability of .38 (or lower) would give the student a right to complain