5. Standardized distributions
You are doing research with people who are homeless. You want to be able to identify those who are depressed so that you can refer them to treatment. You consider two depression-screening tools. One is a very quick nine-item measure crafted by the psychiatrist working at a local free clinic. The other is the Beck Depression Inventory (BDI), created by Dr. Aaron T. Beck, which is a widely used 21-question multiple-choice self-report inventory. You would prefer to use the quick measure, but you want to make sure it is as effective as the BDI. You decide to use both on a sample of your population to make sure that the quick measure is identifying depression in the same people as the BDI.
After testing 50 people, you find that the average score on the BDI is 14 with a standard deviation of 2. The average score on the quick measure is 5 with a standard deviation of 2. Below are five pairs of scores. Use the dropdown menus to complete the table.
Participant
BDI Score
BDI z-score
Quick Measure Score
Quick Measure z-score
1
15.5
+0.75
6.5
+0.75
2
13
-0.50
4
-0.50
3
12
-1.00
3
-1.00
4
15
+0.50
6
+0.50
5
18
+2.00
9
+2.00
Use the table above to think about whether the quick measure is similar to the BDI. Do the participants receive similar scores on the quick measure and the BDI?
You are finding the negative values and decimals of z-scores difficult to explain to your staff, so you decide to convert the scores to T-scores. T-scores are standardized scores in which a score of 50 represents the mean and 10 indicates one standard deviation. Thus, a score of 60 is one standard deviation above the mean, while a score of 30 is two standard deviations below the mean. Use the dropdown menus to complete the table.