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z-SCORES: LOCATION OR SCORES AND STANDARDIZED DISTRIBUTIONS:
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z-SCORES: LOCATION OR SCORES AND STANDARDIZED DISTRIBUTIONS:
specification of the precise location of each X value within a distribution
z-score transformation
relabeling of X values in a population into precise X-value locations within a distribution
SHAPE: The distribution of z-scores will have exactly the same shape as the original distribution of scores.
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USEFUL PURPOSE #1: each z-score tells the exact location of the original X value within the distribution
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RAW SCORE: original, unchanged datum that is the direct result of measurement
STANDARDIZED SCORE:
result from relabeling data into new table with positive, whole-number predetermined mean and standard deviation
DEVIATION SCORE:
the deviation measures the distance in points between X and μ and the sign of the deviation indicates whether X is located above or below the mean.The deviation score is then divided by s because we want the z-score to measure distance in terms of standard deviation units.
SIGN OF Z-SCORE: The sign of the z-score (+ or −) signifies whether the score is above the mean (positive) or below the mean (negative).
NUMERICAL VALUE:
The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and μ
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MEASUREMENT:
a z-score will tell you if your score is above the mean by a distance equal to two standard deviations, or below the mean by one-half of a standard deviation.
SIGN & NUMERICAL VALUE:
Both parts are necessary to describe completely where a raw score is located within a distribution.
NEGATIVE Z-SCORE: If the z- score is negative, do not forget to include the sign in the formula
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SAMPLE DISTRIBUTION OF Z-SCORES: If all the scores in a sample are transformed into z-scores, the result is a sample distribution of z-scores. .
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SAME PROPERTIES: The transformed distribution of z-scores will have the same properties that exist when a population of X values is transformed into z-scores.
INFERENTIAL STATISTICS: z-scores provide an objective method for determining how well a specific score represents its population
Z-SCORE FORMULA:
the formula produces exactly the same result that is obtained using the z-score definition
VISUAL PRESENTATION: some problerms are easier to understand if they draw a picture showing all the information presented in the problem