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Chapter 2C Statistical Tools in Evaluation

Chapter 2C Statistical Tools in Evaluation. Standard Scores. Change variables to a constant mean and standard deviation. Different units of measurement are converted to the same unit (standardized) and can then be averaged. Z - score.

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Chapter 2C Statistical Tools in Evaluation

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  1. Chapter 2CStatistical Tools in Evaluation

  2. Standard Scores • Change variables to a constant mean and standard deviation. • Different units of measurement are converted to the same unit (standardized) and can then be averaged.

  3. Z - score • standard score with a mean = 0 and standard deviation = 1. • Z = (X - X) ÷ S

  4. T -score • standard score with a mean = 50 and standard deviation = 10. • T = 10(Z) + 50

  5. Z-scores • Provide descriptions of relative performance on one or more tests.

  6. Example use of Z-scores Student A Subject Raw Score Math 30 English 70 Science 120 On which test did Student A perform best?

  7. Don’t know

  8. Example use of Z-scores Student A Subject Raw Score Mean Math 30 25 English 70 65 Science 120 140 On which test did Student A perform best?

  9. Still Don’t Know

  10. Example use of Z-scores Student A Subject Raw Score Mean SD Math 30 25 5 English 70 65 10 Science 120 140 10 On which test did Student A perform best?

  11. Now we know

  12. Example use of Z-scores Student A Subject Raw Score Mean SD Z-score Math 30 25 5 1.00 English 70 65 10 0.50 Science 120 140 10 -2.00 On which test did Student A perform best? Math The test with the highest standard score.

  13. So we convert raw scores to standardized scores in order to see where students rank. • Rank is defined as where you fall on the normal bell curve. • The normal bell curve is divided into 6 equal parts (standard deviations, SD). • Scores that fall between +1 and -1 SD make up ~68% of all scores. • +2 and -2 SD make up ~95% of all scores. • +3 and -3 SD make up ~99% of all scores.

  14. Normal Bell Curve (parametric) 68% 95% 99%

  15. Standardized Scores • Two types. • Z-scores. • Between +3 & -3 • T-scores. • Between 20 & 80 • Determine standard distance from mean. • Allows comparison between different tests with different units.

  16. Z-Scores • (Raw score - mean)/SD. • Positive and negative numbers. • Use decimal points. • Zero is mean • Pos scores are greater than the mean • Neg scores are less than the mean

  17. T-Scores • (10 x Z-score)+50. • NO decimal places. • Always positive. • 50 is mean. • Scores >50 are better than average.

  18. Why use standard scores? • To combine different units of measurement. • To assign different weights to each score.

  19. Characteristics of Normal Curve • Symmetric • Asymptotic • Unimodal • Area

  20. Normal Curve-Inclusion Criteria 68% 95% 99%

  21. Calculate Inclusion • The range of scores between the mean +1 SD and -1SD = ~68% of all scores. • The range of scores between the mean +2 SD and -2SD = ~95% of all scores. • The range of scores between the mean +3 SD and -3SD = ~99% of all scores.

  22. Inclusion Criteria • Mean + 1SD=68%. • Mean + 2SD=95%. • Mean + 3SD=99%. • Mean = 35.4 • SD = 6.72 • 35.4 - 6.72 = 28.68 • 35.4 + 6.72 = 42.12 • Therefore, ~68% of all scores should fall between 28.68 & 42.12

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