Mathematics - Statistics

Scales and Norms

Information about test norms allows you to equate scores across different tests of the same construct and lets you compare individuals to each other. Once you have the standard deviation of a score, you can calculate an individuals z-score. Z-scores, also known as standard scores, tell you how many standard deviations away from the mean an individual is. Scores that are two standard deviations away from the mean represent the most extreme 5% of the population and often are considered to be unusual enough to warrant special consideration, such as a clinical diagnosis. For instance, IQ scores that are two standard deviations above the mean (130 or greater) are considered in a gifted range and scores two standard deviations below the mean (70 or lower) are considered intellectually deficient. Scores on measures of depression that are two standard deviations above the mean often are considered to represent clinical depression.

T-scores are another kind of standard score; the MMPI is the best known example of a test that uses T-scores. (Note that T-scores have nothing to do with t-tests.) Z-scores have a mean of 0 and a standard deviation of 1; T-scores have a mean of 50 and a standard deviation of 10. Thus, the average score on a test would be assigned a T-score of 50 and a z-score of zero. A score that was one standard deviation below average would be assigned a T-score of 40 and a z-score of -1.

For this Knowledge Assessment, you consider how raw test scores can be converted into more meaningful standardized scores, allowing you to meaningfully compare tests and to compare individuals.

In the provided dataset, you previously created a Risk-Taking scale by adding items R1 through R6.

Note: Please refer to the following image to complete question #3.

Multiple AttemptsNot allowed. This test can only be taken once.Force CompletionThis test can be saved and resumed later.

Expand Question Completion Status:

QUESTION 1

  1. What are the mean and standard deviation for the Risk-Taking scale (ANALYZE>DESCRIPTIVE STATISTICS>DESCRIPTIVES)?a.17.08, 5.02b.14.23, 6.01c.18.95, 3.76d.16.23, 7.22

2.5 points   

QUESTION 2

  1. George obtained a raw score of 20 on the Risk-Taking scale. What is his z-score?a.-0.23b.0.03c.0.58d.1.63

2.5 points   

QUESTION 3

  1. Given Georges z-score, what is his approximate percentile? Use the chart above to formulate your answer.a.56b.58c.72d.80

2.5 points   

QUESTION 4

  1. T-scores are used on some psychological tests, such as the MMPI. T-scores have a mean of 50 and a standard deviation of 10; therefore, a z-score of -1 (one standard deviation below the mean) would be converted to a T-score of 40. What is Georges T-score on the Risk-Taking scale?a.45b.56c.58d.66