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Chapter 5

Ch. 5 - z-Scores.docx

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York University
PSYC 2530
Anne Russon

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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