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2 useful purposes of z-scores
1. each z-score tells the exact location of the original X value within the distribution
2. z-score form a standardized distribution that can be directly compared to other distributions that also have been transformed into z-scores
z-score
specifies the precise location of each x value withing a distribution. Always includes a + or - sign
z-scores to standardize a distribution: shape
z-score shape will be the same as the original distribution of raw scores
z-scores to standardize a distribution: The mean
z-score distribution will always have a mean of 0
z-scores to standardize a distribution: standard deviation
distribution of z-scores will always have a standard deviation of 1
standard deviation
is composed of scores that have been transformed to create predetermined values for u and o. standardized distributions are used to make dissimilar distributions comparable
procedure for standardizing a distribution to create new values for u and o (2 steps)
1. the original raw scores are transformed into z-scores
2. the z-scores are then transformed into new X values so that the specific u and o are attained
standardizing a sample distribution
1. the sample of z-scores will have the same shape as the original sample of scores
2. the sample of z-scores will have a mean of 0
3. the sample of z-scores will have a standard deviation of 1.