Quick Review

Central tendency: Mean, Median, Mode

Shape: Normal, Skewed, Modality

Variability: Standard Deviation, Variance

SAMPLE POPULATION

XX 2 2X XS X XS

X

X n 2

2 ( )

1X

X XS

n

2( )

1X

X XS

n

XN

22 ( )XX

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2( )XX

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N

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)

The standard normal curve - Bell shaped, symmetrical, unimodal, asymptotic - Mean, Median and mode all equal - Mean = 0, σ2 = 1, σ = 1

A THEORETICAL PROBABILITY DISTRIBUTION

The standard normal curve: - Bell-Shaped, symmetrical, asymptotic - Mean, Median and Mode all equal - Mean = 0; SD (δ) = 1; Variance (δ2) = 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 -1.96 1% + and – 2.58

THE NORMAL CURVEONE-TAILED CRITICAL VALUES

5% + OR - 1.645 1% + OR – 2.33