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Chapter 5

# Ch. 5 - z-Scores.docx

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York University

Psychology

PSYC 2530

Anne Russon

Fall

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Ch. 5 - z-Scores
Sunday, November 11, 2012
5:52 PM
PSYC 2530 Introductory Statistics
Chapter 5: z-Scores: Location of Scores and Standardized Distributions
Z-scores have two purposes:
o 1) Each z-score tells the exact location of the original X value within the
distribution
o
2) The z-scores form a standardized distribution that can be directly compared
to other distributions that also have been transformed into z-scores
Z-scores have two components:
o 1) The sign: tells whether the score is located above (+) or below (-) the mean
o 2) The number: tells the distance between the score and the mean in terms of
the number of standard deviations
o
Z is the deviation of X
A z-score establishes a relationship between the score, the mean, and the standard
deviation
If every X value is transformed into a z-score, then the distribution of z-scores will
have the following properties:
o Same shape as the original distribution
o μ (or M) = 0
o σ (or s) = 1

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