1. Quantitative Methods in HPELS HPELS 6210
Z-Scores
Quantitative Methods in HPELS
HPELS 6210

2. Agenda Introduction Location of a raw score
Standardization of distributions
Direct comparisons
Statistical analysis

3. Introduction
Z-scores use the mean and SD to transform raw scores  standard scores
What is a Z-score?
A signed value (+/- X)
Sign: Denotes if score is greater (+) or less (-) than the mean
Value (X): Denotes the relative distance between the raw score and the mean
Figure 5.2, p 141

5. Introduction Purpose of Z-scores: Describe location of raw score
Standardize distributions
Make direct comparisons
Statistical analysis

6. Agenda Introduction Location of a raw score
Standardization of distributions
Direct comparisons
Statistical analysis

7. Z-Scores: Locating Raw Scores
Useful for comparing a raw score to entire distribution
Calculation of the Z-score:
Z = X - µ /  where
X = raw score
µ = population mean
 = population standard deviation

8. Z-Scores: Locating Raw Scores
Can also determine raw score from a Z-score:
X = µ + Z

9. Agenda Introduction Location of a raw score
Standardization of distributions
Direct comparisons
Statistical analysis

10. Z-Scores: Standardizing Distributions
Useful for comparing dissimilar distributions
Standardized distribution: A distribution comprised of standard scores such that the mean and SD are predetermined values
Z-Scores:
Mean = 0
SD = 1
Process:
Calculate Z-scores from each raw score

11. Z-Scores: Standardizing Distributions
Properties of Standardized Distributions:
Shape: Same as original distribution
Score position: Same as original distribution
Mean: 0
SD: 1
Figure 5.3, p 145

13. Agenda Introduction Location of a raw score
Standardization of distributions
Direct comparisons
Statistical analysis

14. Z-Scores: Making Comparisons
Useful when comparing raw scores from two different distributions
Example (p 148):
Suppose Bob scored X=60 on a psychology exam and X=56 on a biology test. Which one should get the higher grade?

15. Z-Score: Making Comparisons
Required information:
µ of each distribution of raw scores
 of each distribution of raw scores
Calculate Z-scores from each raw score

16. Psychology Exam Distribution:
µ = 50
 = 10
Biology Exam Distribution:
µ = 48
 = 4
Z = X - µ / 
Z = 60 – 50 / 10
Z = 1.0
Z = X - µ / 
Z = / 4
Z = 2.0
Based on the relative position (Z-score) of each raw score, it appears that the Biology score deserves the higher grade

17. Agenda Introduction Location of a raw score
Standardization of distributions
Direct comparisons
Statistical analysis

18. Z-Scores: Statistical Analysis
Appropriate usage of the Z-score as a statistic:
Descriptive
Parametric

19. Z-Scores: Statistical Analysis
Review: Experimental Method
Process: Manipulate one variable (independent) and observe the effect on the other variable (dependent)
Independent variable: Treatment
Dependent variable: Test or measurement

20. Z-Scores: Statistical Analysis
Figure 5.8, p 153

21. Z-Score: Statistical Analysis
Value = 0  No treatment effect
Value > or < 0  Potential treatment effect
As value becomes increasingly greater or smaller than zero, the PROBABILITY of a treatment effect increases