PsychStats- Chapter 5: z-Scores, Location of Scores, and Standard Distributions

1. Introduction to z-Scores 2. z-Scores and Locations in a Distribution 3. Other Relationships Between z, X, standard deviation and mean 4. Using z-Scores to Standardize a Distribution 5. Computing z-Scores for Samples 6. Looking Ahead to Inferential Statistics

z score (or standard score or standardized value)

aims to identify the exact location of each score in a distribution.

Formula for z-score

(x-mean)/standard deviation

• (+) z-score = above the mean

• (-) z-score = below the mean

Properties of a z-score distribution

shape, mean, standard deviation

Shape

The distribution of z-scores will have exactly the same shape as the original distribution of scores. If the original distribution is negatively skewed, the distribution of z-scores will also be negatively skewed.

The Mean

The z-score distribution will always have a mean of zero.

The Standard Deviation

The z-score distribution will always have a standard deviation of 1. Thus, in the figure below, the standard deviation in a 10-point distance in the X-distribution, is transformed into a 1-point.

Sample Variance Formula

s^2= SS/n-1

Sample Standard Deviation Formula

square root of SS/n-1