Exam 1

1. Metainformation

   Tag	Value
   file	Reliability_eur-reliability-211-en_eur-reliability-211-en
   name	eur-reliability-211-en
   section	Reliability/Analysis/Cronbach's alpha
   type	num
   solution	5.31
   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 .81 (Cronbach’s alpha); A grade of at least 5.5 is needed to pass the exam.

   Calculate the adjusted true score for a student who has grade 5.2. Round to two decimals

   
   

   Solution

   For a student who has a 5.2 the adjusted true score becomes: $X_{est} =5.8 + .81(5.2 - 5.8) = 5.8 - .486 = 5.314 = 5.31$