Example for Measurement Scales

Assume there were a "true" measurement scale for job satisfaction and that it maps onto a 7-point rating scale as follows:

"True scale" 7-point scale
   1-5               1
  6-40               2
 41-42               3
 43-75               4
 76-90               5
 91-94               6
95-100               7

Thus if someone's "true" job satisfaction were 55 he or she would have a rated score of 4. Now consider the following two sets of job satisfaction scores:

	Group A		Group B
	True Scale	Rating	True Scale	Rating
	6 6 43 91 95	2 2 4 6 7	5 40 74 90 100	1 2 4 5 7
Mean	48.2	4.2	61.8	3.8

On the "true" scale the mean for Group B is 61.8 which is much higher than the mean for Group A which is 48.2. However on the 7-point rating scale, the mean for B is only 3.8 which is lower than the mean for A of 4.2.