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

1.
2.
3.
4.
Purpose of Z-scores:
Describe location of raw score
Standardize distributions
Make direct comparisons
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
 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

 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

3.
4.


1.
2.
Properties of Standardized Distributions:
Shape: Same as original distribution
Score position: Same as original distribution
Mean: 0
SD: 1
Figure 5.3, p 145

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
Biology Exam Distribution:
µ = 48

= 4
Z = X µ / 
Z = 60 – 50 / 10
Z = 1.0
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:
 Descriptive
 Parametric

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

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