Fillable Transformed Scores - Worksheet printable pdf download

TRANSFORMED SCORES - STANDARD SCORES

OBJECTIVE:

To gain greater understanding of standard scores through first hand experience. Like

percentile ranks, standard and standardized scores have universal meaning. One of

the most popular standardized scores is the IQ score. In this section, we focus on other

ways to report test results by using standard and standardized scores.

GENERAL INFORMATION:

The term standard score, when used in the field of psychological testing, generally

refers to a raw score that has been converted from one scale to another scale. The

scale being converted to is typically a scale that is more widely used and easier to

interpret. This second scale has a mean and standard deviation that have been

arbitrarily set.

A z score, for example, is a raw score that has been transformed to a scale with a mean

of 0 and a standard deviation of 1. To illustrate this point, consider Mary, a senior at

Valdosta State University, who has earned a score of 80 on a test of Comparative

Literature, a score of 72 on a test in Microbiology, and a score of 40 on a test in Art

History. With this information, the raw scores alone, what can you say about Mary's

performance on these tests or her standing in the classes? The answer is that you

cannot say very much. Without knowing more information about where these raw

scores place Mary's performance compared to the total distribution of raw scores for

each of these tests or to some known distribution of scores, drawing any meaningful

conclusions regarding her relative performance in each of these areas is impossible.

Suppose that the scores for all three of the tests were approximately normally

distributed and that a) the distribution of the Comparative literature scores had a mean

of 90 and a standard deviation of 10, b) the distribution of Microbiology test scores had

a mean of 60 and a standard deviation of 12, and c) the distribution of the Art History

scores had a mean of 40 and a standard deviation of 15. Now, what statements can be

made regarding Mary's relative performance on each of these three tests?

Mary did best on the Microbiology test; her raw score of 72 falls at a point one standard

deviation above the mean. Mary's next best score was on the Art History test; her raw

score of 40 falls exactly at the mean of the distribution of scores. And finally there is

Mary's performance on the Comparative Literature test; her raw score of 80 falls at a

point one standard deviation below the mean. Converting Mary's raw scores to a scale

that has a mean of 0 and a standard deviation of 1 - that is converting Mary's raw

scores to z scores - we can say that Mary achieved a z score of +1 on the Microbiology

test, a z score of 0 on the Art History test, and a z score of -1 on the Comparative

Literature test.

Transformed Scores - Worksheet