How Much Do You Weigh?
An Example of Great Reliability
Here's another possible outcome regarding the reliability of your 5 bathroom scales. When you weigh yourself, your 5 scales give different weights. Scale #3 says you weigh only 103 pounds. Scale #4 says you weigh 135 pounds. Which do you believe?
The best answer is to take the average of all five scales. That average is an index that one could test for reliability. That is, one could compute Cronbach's alpha for the 'bathroom scale index.' Suppose Scale #1 gives the same weight as the (reliable) scale at your doctor's office. While the different scales give different weights, the average (your index score) is only a pound less than what you actually weigh.
Again, your friends Jill, Bob, Ellen, and Mike drop by. They try your 5 scales. Each scale provides different weights for everyone. But the average (the Index column) is within a few pounds of their actual weight (as shown on Scale #1). The Cronbach's alpha reliability coefficient for these five scales is .92. That indicates that—although the 5 scales give different weights—the average of all five scales gives a generally reliable estimate of each person's true weight.