Exam 1

1. Metainformation

   Tag	Value
   file	Reliability_vufsw-cronbach's_alpha-1170-en_vufsw-cronbach's_alpha-1170-en
   name	vufsw-cronbach's alpha-1170-en
   section	reliability/analysis/cronbach's alpha
   type	schoice
   solution	FALSE, FALSE, TRUE, FALSE, FALSE
   Type	performing analysis
   Program	calculator
   Language	English
   Level	statistical thinking

   Question

   We investigate survey data of a sample of 239 respondents. Given is the following correlation matrix (Pearson correlation coefficient) of three questions of a scale.

   	Item1	Item2	Item3
   Item1	1
   Item2	.312	1
   Item3	.357	.451	1

   The data furthermore shows that the average correlation between the three items is 0.373. Assume that the variances of the three items are the same. How high is Cronbach’s alpha?

   
   
   1. FALSE: 0.877
   2. FALSE: 0.728
   3. TRUE: 0.641
   4. FALSE: 0.942
   5. FALSE: 0.801
   
   

   Solution

   You can calculate it with: (3*0,373)/(1+(2*0,373))=0,641
   Cronbach’s alpha can be written as a function of the number of test items and the average inter-correlation among the items. Below, we show the formula for the standardized Cronbach’s alpha:

   

   Here k is equal to the number of items, r-bar is the average inter-item correlation among the items.
   One can see from this formula that if you increase the number of items, you increase Cronbach’s alpha.  Additionally, if the average inter-item correlation is low, alpha will be low.  As the average inter-item correlation increases, Cronbach’s alpha increases as well (holding the number of items constant).

   
   
   1. False
   2. False
   3. True
   4. False
   5. False