# Chapter5 - Chapter 5 z-scores z-Scores and Location By itself a raw score or X value provides very little information about how that particular

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Chapter 5: z-scores

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z-Scores and Location By itself, a raw score or X value provides very little information about how that particular score compares with other values in the distribution. A score of X = 53, for example, may be a relatively low score, or an average score, or an extremely high score depending on the mean and standard deviation for the distribution from which the score was obtained. If the raw score is transformed into a z-score, however, the value of the z-score tells exactly where the score is located relative to all the other scores in the distribution.
Purposes of Transforming X values into Z-scores Each z-score tells the exact location of the original X value within the distribution The z-scores form a standardized distribution that can be directly compared to other distributions that also have been transformed into z-scores.

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z-Scores and Location (cont.) The process of changing an X value into a z- score involves creating a signed number, called a z-score , such that a. The sign of the z-score (+ or –) identifies whether the X value is located above the mean (positive) or below the mean (negative). b. The numerical value of the z-score corresponds to the number of standard deviations between X and the mean of the distribution.
z-Scores and Location (cont.) A score that is located one standard deviation above the mean will have a z- score of +1.00. A z-score of +1.00 always indicates a location above the mean by one standard deviation. A score that is located two standard deviations above the mean will have a z- score of +2.00.

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Transforming back and forth between X and z The basic z-score definition is usually sufficient to complete most z-score

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## This note was uploaded on 09/21/2009 for the course PSY 360 taught by Professor Tamrabeckman during the Spring '09 term at University Of Southern Mississippi .

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Chapter5 - Chapter 5 z-scores z-Scores and Location By itself a raw score or X value provides very little information about how that particular

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