6. 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 use a depression-screening tool called the Beck Depression Inventory (BDI), created by Dr. Aaron T. Beck. It is a widely used 21- item multiple-choice self-report inventory. Higher scores indicate higher levels of depression. Because being homeless is stressful, you decide to use z-scores so that you can identify those people who are at least one standard deviation more depressed than the typical person who is homeless. Based on the testing of 50 people, the average score on the BDI in your sample is 15 with a standard deviation of 2. The table that follows consists of the scores of five people that you tested who sleep in the same alcove at a shelter. Use the dropdown menus to complete the third column of the table by selecting the z-score relative to your sample that corresponds to the participants' BDI score. Participant BDI Original Score BDI z-score Location BDI T-score Standardized Score 1 17 2 19 3 5 17.5 16.5 +1.00 +1.25 +0.75 60 70 55 You are finding that the negative values and decimals of z-scores are 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 fourth column in the table. (Hint: You can always draw a normal curve to help you visualize this transformation.)

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