Measures of Relative Position

Topics Covered in this Session

Measures of Relative Position

Definition – are conversions of values, usually standardized test scores, to show where a given value stands in relation to other values of the same grouping. The most common example in education is the conversion of scores on standardized tests to show where a given student stands in relation to other students of the same age, grade level, etc. Converted scores are based on the standard deviation or distance of a raw score from the mean for a normal curve or distribution. In a normal distribution, the distance from one S.D. above the mean to one S.D. below the mean includes approximately 68 percent of all the scores. Plus two to minus two S.D. includes approximately 95 percent of all scores and plus three to minus three S.D. includes over 99 percent of all scores.

Standard Deviation, Sigma (z) Score, T Score, College Board Score

Converted scores, also referred to as standard scores are based on the standard deviation or distance of a raw score from the mean for a normal curve or distribution. Examples of standard scores used in educational research are: Sigma (z) scores, T scores, College Board scores, percentiles, and stanines.
Remember z scores can have negative as well as positive values. If your answers are +1.50, +2.00 and -2.00, they are correct.
T score = 50 + 10 x Sigma (z) score
For example, a z score of -2.00 would have a T score = 50 + 10 x -2.00 or 50 + (-20) or 30.
College Board score = 500 + 100 x Sigma (z) score
For example, a z score of -2.00 would have a College Board score = 500 + 100 x -2.00 or 500 + (-200) or 300

Percentile and Stanines

Percentiles and stanines help give comparative meanings to raw scores.

FOR MORE INFORMATION ON THE TOPICS COVERED IN THIS SESSION, PLEASE REFER TO THE APPENDIX IN A.G. PICCIANO "EDUCATIONAL RESEARCH PRIMER" AS WELL AS THE MANUALS AND DOCUMENTATION PROVIDED BY SPSS, INC.