Standard Scores

A presentation I made for our subject, Assessment and Evaluation of Learning. Topic: Standard Scores

1. STANDARD SCORES Mirasol S. Madrid III-9 BS Psychology

2. STANDARD SCORES Also called as z scores Measures the difference between the raw score and the mean of the distribution using standard deviation of the distribution as a unit of measurement

3. STANDARD SCORES Reflects how many standard deviations above or below the mean a raw score is

4. STANDARD SCORES By itself, a raw score or X value provides very little information about how that particular score compares with other values in the distribution.

5. STANDARD SCORES A score of X = 53, for example, may be a relatively low score, or an average score, or an extremely high score depending on the mean and standard deviation for the distribution from which the score was obtained.

6. 50 60 70 80 40 30 20 1 2 3 -1 -2 -3 x z NORMAL DISTRIBUTION

7. STANDARD SCORES If the raw score is transformed into a z-score, however, the value of the z-score tells exactly where the score is located relative to all the other scores in the distribution.

8. FORMULA Where: Z = standard score/z-score X = Raw Score = Mean S = Standard Deviation  

9. FORMULA Where: Z = standard score/z-score X = Raw Score = Mean = (sigma) Standard Deviation  

10. STANDARD SCORES Z-scores can be positive (above the mean), negative (below the mean), or zero (equal to the mean)

11. EXAMPLE #1

12. EXAMPLE #1 In a distribution of statistic test score, having the mean of 75 and a standard deviation of 10, find the z score, scoring 85

13. EXAMPLE #1 X = 85 = 75 S = 10  

14. EXAMPLE #1 1. Step 1 2. Step 2 z = 1  

15. INTERPRETATION A score of 85 is one (1) standard deviation above the mean

16. EXAMPLE #2

17. EXAMPLE #2 Find the Z score of 60 having a mean of 75 and a standard deviation of 10

18. EXAMPLE #2 X = 60 = 75 S = 10  

19. EXAMPLE #2 1. Step 1 2. Step 2 z= -2  

20. INTERPRETATION A score of 60 is two (2) standard deviation below the mean

21. EXAMPLE #3

22. EXAMPLE #2 X = 100 = 100 S = 10  

23. EXAMPLE #2 1. Step 1 2. Step 2 z=  

24. INTERPRETATION A score of 100 is falls on the given mean.

25. MORE EXAMPLES

26. MORE EXAMPLES X = 58, µ = 50, σ = 10 X = 74, µ = 65, σ = 6 X = 47, µ = 50, σ = 5 X = 87, µ = 100, σ = 8 X = 22, µ = 15, σ = 5

27. ANSWERS z = +.8 z = +1.5 z = -.6 z = -1.625 z = +1.4