Z-Scores
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Transcript of Z-Scores
Z-Scores
Quantitative Methods in HPELS
440:210
Agenda
Introduction Location of a raw score Standardization of distributions Direct comparisons Statistical analysis
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
Introduction
Purpose of Z-scores:1. Describe location of raw score
2. Standardize distributions
3. Make direct comparisons
4. Statistical analysis
Agenda
Introduction Location of a raw score Standardization of distributions Direct comparisons Statistical analysis
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
Z-Scores: Locating Raw Scores Example 5.3, 5.4 p 144
Z-Scores: Locating Raw Scores
Can also determine raw score from a Z-score:
X = µ + Z
Agenda
Introduction Location of a raw score Standardization of distributions Direct comparisons Statistical analysis
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
Z-Scores: Standardizing Distributions
Properties of Standardized Distributions:1. Shape: Same as original distribution2. Score position: Same as original
distribution3. Mean: 04. SD: 1 Figure 5.3, p 145
Z-Scores: Standardizing Distributions
Example 5.5 and Figure 5.5, p 147
µ = 3 = 2
Agenda
Introduction Location of a raw score Standardization of distributions Direct comparisons Statistical analysis
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?
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
Psychology Exam Distribution:
µ = 50
= 10
Z = X - µ /
Z = 60 – 50 / 10
Z = 1.0
Biology Exam Distribution:
µ = 48
= 4
Z = X - µ /
Z = 56 - 48 / 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
Agenda
Introduction Location of a raw score Standardization of distributions Direct comparisons Statistical analysis
Z-Scores: Statistical Analysis
Appropriate usage of the Z-score as a statistic:DescriptiveParametric
Z-Scores: Statistical Analysis Review: Experimental Method Process: Manipulate one variable
(independent) and observe the effect on the other variable (dependent) Independent variable: TreatmentDependent variable: Test or measurement
Z-Scores: Statistical Analysis Figure 5.8, p 153
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
Textbook Problem Assignment
Problems: 1, 2, 9, 17, 23