[PDF] z-SCORES using the unit normal table





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z-SCORES

Frances Chumney, PhD

CONTENT OUTLINE

¾Overview of z-Scores

¾Probability & Normal Distribution

¾Distribution of Sample Means

Z-SCORES 2

OVERVIEW OF Z-SCORES

Z-SCORES 3

OVERVIEW OF z-SCORES

¾Student A earned a score of 76 on an exam

™How many points were possible?

o76 out of 80? Not bad! o76 out of 100? Not so great! ™How does a score of 76 compare to other students? o76 the lowest score in the class? oAnyone earn a score higher than 76?

Z-SCORES 4

OVERVIEW OF z-SCORES

¾z-Score

standardized value that specifies the exact location of an X value within a distribution by describing its distance from the mean in terms of standard deviation units

¾Standard Deviation Unit

™Standardized value

™1 SD unit = value of 1 SD before standardization

Z-SCORES 5

OVERVIEW OF z-SCORES

Z-SCORES 6

SCORE LOCATION

¾z-Scores describe the exact location of a score within a distribution ™Sign: Whether score is above (+) or below (-) the mean ™Number: Distance between score and mean in standard deviation units

¾Example

™z = +1.00

oSign: positive (+) so score is above the mean oNumber: 1.00 SD units from the mean

Z-SCORES 7

SCORE LOCATION

¾Example

™z = - .50

oSign: negative (-) so score is below the mean oNumber: .50 SD units from the mean

Z-SCORES 8

FORMULA: RAW SCORE ĺZ-SCORE

¾Transform raw score (X value) to z-Score

™Numerator = Deviation Score

™Denominator = Standard Deviation

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