Saturday, September 29, 2012
Defining Standard Scores
In norm-referenced measurements, standard scores show the relative position of a score compared to other scores, whereas a raw score provides little to no information about the test takers results, such as how the raw score compares to the average of all scores (Little, n.d.; Whiston, 2009). Standard scores explain raw scores in terms of the distance they fall from the mean (Little, n.d.). The measurement used for this distance is a standard deviation (SD). Standard scores provide a visual example on a normal distribution, for example, exactly where the score falls on the normal curve. When scores are standardized, they are translated to a common language, so to speak. After being standardized, the scores show the results in comparison to other test takers. They also make it easier to compare the results of more than one test. For example, if the test taker scored 8 on one test and 32 on another, if both tests scores are standardized, it is easier to see where each test falls on the normal distribution, or how they compare with other test takers. Standard scores determine how a score relates to the test-taking population as well as the variability of all the scores (Little, n.d.; Whiston, 2009).
If I were to measure the intelligence of an individual, I would want to determine how the raw score compares to the average scores and where on the range of scores his or her score lies. Using the handy 68-95-99.7 rule (Little, n.d.), which states that on the normal distribution, approximately 98% of scores fall within ±3 SD of the mean; 95% fall between ±2 SD of the mean; and 68% fall between ±1 SD of the mean, I can easily determine the test taker's level of intelligence. (For a nice visual of this rule, please see Figure 2.5 on page 37 in Whiston (2009)).
Two Standard Deviations Above and Below the Mean
So, a score of 2 SD below the mean would tell me that the scores were in the bottom 2.5% (or so) of all the scores (2nd-3rd percentile). As long as the intelligence test was fair and ethical for the individual test taker, I would assume the individual scored quite low in intelligence. This may prompt me to check for cognitive deficiencies, mental retardation, or other issues that will be beneficial for creating an overall case conceptualization for this particular client. On the other hand, if the scores were 2 standard deviations above the mean, I would know the individual's score is in the top 2.5% of all scores (98th percentile). I can assume, if the test is reliable and valid, this individual is highly intelligent and I would tailor an intervention accordingly. Any intelligence test used on a client should be carefully reviewed to make sure the norming group is an appropriate comparison for the client. The ultimate responsibility for utilizing appropriate assessments lies with the counselor (Laureate Education, Inc., n.d.) .
One Standard Deviation Above and Below the Mean
As Whiston (2009) explained, when a standard score is used, counselors understand the relative position of how the test taker scored compared to other test takers without having to consider other statistical data. If the test taker's score was 1 SD below the mean, I would know that the individual's score fell within the bottom 16% of all test takers (16th percentile). If the score was 1 SD above the mean, the test taker has scored in the top 16% of test takers, or in the 84th percentile. If the individual's score was between -1 and +1 SD, it would be within the 16th and 84th percentile.
Examples Utilizing Intelligence Tests
For example, if I utilize an intelligence test and my client has a raw score of 95, and the test has a mean of 80 and a SD of 15, the client's score is 1 SD above the mean, and in the 84th percentile. If the raw score is 65, it is 1SD below the mean, and in the 16th percentile. If the score was between ± 1 SD, the score was between 65 and 95, or between the 16th and 84th percentile. Two SD above the mean was a raw score of 110, and the score was right around the 97th percentile; the raw score for 2 SD below the mean was 50, and in the 2.5th percentile.
Laureate Education, Inc. (Executive Producer). (n.d.). Introduction to Assessment. Baltimore, MD: Executive Producer.
Little, S. G. (n.d.). Standard Scores [PowerPoint slides]. Retrieved from http://mym.cdn.laureate-media.com/2dett4d/Walden/COUN/6360/04/mm/standard_scores/index.html
Whiston, S. C. (2009). Principles and applications of assessment in counseling (3rd ed.). Belmont, CA: Brooks/Cole, Cengage Learning