Quick Review Central tendency: Mean, Median, Mode Shape: Normal, Skewed, Modality Variability: Standard Deviation, Variance

Quick Review

Evaluating scores Raw score of X: -Measure of absolute standing -Difficult to interpret Z-SCORE - Measure of relative standing

Z-Transformation -Transforming all raw scores in a distribution does not change the shape of a distribution, it does change the mean and the standard deviation

Z Transformation -Z transformation provides a common metric to compare scores on different variables Given X, find Z Given Z, find X

Find Z

Find X

-Used for testing hypothesis -Provide a way of determining probability of an obtained sample result (experimental outcome) -Usually, the probably that experimental result occurred by chance given null distribution -THEORETICAL PROBABILITY DISTRIBUTIONS (Z, F, T)

A THEORETICAL PROBABILITY DISTRIBUTION The standard normal curve: - Bell-Shaped, symmetrical, asymptotic - Mean, Median and Mode all equal - Mean = 0; SD (δ) = 1; Variance (δ 2 ) = 1

THE NORMAL CURVE Area under curve  probability -Z is continuous so one can only compute probability for a range of values

THE (STANDARD) NORMAL CURVE BASIC RULES TO REMEMBER:

THE (STANDARD) NORMAL CURVE BASIC RULES TO REMEMBER: 50% above Z=0, 50% below Z = 0 34% between Z=0 & Z= 1 / between Z=0 & Z = -1 68% between Z = -1 and Z = +1 96% between Z = -2 and Z = +2 99% between Z = -3 and Z = +3

THE (STANDARD) NORMAL CURVE TWO-TAILED CRITICAL VALUES 5% + and % + and – 2.58

THE NORMAL CURVE ONE-TAILED CRITICAL VALUES 5% + OR % + OR – 2.33