Statistical Analysis

Z-scores

• A z-score = how many standard deviations a score is from the mean (-/+)

• Z-scores thus allow us to transform the mean to 0 and the standard deviation to 1. How might this be helpful? Well, it is one of the ways raw scores can be translated into Standard score. Or the first step in obtaining percentiles and T-scores. (IQ testing X=100 SD=15, SATs X=500 SD=100)

Z-scores

Z = xi – X

SD

Z scores can be transferred into T scores to reduce decimals and negative number. You arbitrarily set a mean and a SD and use the following formula

T = (SD) z + X so if you set the mean at 50 and SD at 10

T= 10z + 50

Chi-Square

• Answers whether membership in one category effects membership in another.

• No relationship=categories are independent of each other

• Relationship=categories contingent upon each other

• Relationship does not infer causation

• What type of scale is categorical?

Chi-Square

Males FemalesWhite 2 10 Tr1=12

Hispanic 2 3 Tr2=5 Tc1=4 Tc2=13 TN=17 Fe for cell A= (Tr1) (Tc1) = 12 x 4 = 2.08 TN 17

Chi Square

• Compare your expected frequencies FE to you observed frequencies FO

X²= Σ (FO – FE)² = (2- 2.08)² = (.08)² = .0064 =

FE 2.08 2.08 2.08

Add all four X² together

Compare with the critical values table. With p < .05, X² needs to be to be significant

T-Tests

• T-tests are used to test the difference between two groups when:

IV is nominal with two levels

DV is ratio or interval

Analysis of Variance

• Used to compare several groups on a particular measure

IV are nominal

DV are interval or ratio

Correlation

• Used to study relationships (without causation) between two variables

• Magnitude and direction• r = -1 to 1 with -1 and 1 equaling a perfect

correlation and 0 equaling no correlation• Pearson r is used when interval or ratio data is

available and is the most commonly used correlation test.

I

Regression

• To understand how one variable might predict another variable.

For this formula the IV = X and the DV = Y

Power