1. Multivariate Analysis with Parametric Statistics
Review: Central Limit Theorem
what percentage of the time would we make an error in referring to the population?
with one statistic
with two statistics

2. Comparing Two Statistics

3. Alternative (something is going on)
Hypotheses:
Null (nothing is going on)
H0 : x̄1 = x̄2
Alternative (something is going on)
HA : x̄1 ≠ x̄ OR
HA : x̄1 < x̄ OR
HA : x̄1 > x̄2

4. Inference testing = Convoluted Language:
You can “fail to reject the null hypothesis” or
You can “reject the null hypothesis”
margin of error (related to p level)

5. Risks of Inferential Testing
Type 1 Error
the error is in rejecting a true null hypothesis
a false alarm - an alarm without a fire
alpha (p) level of .05 makes it harder to reject null hypothesis
thus harder to make this mistake
Type 2 Error
accepting a false null hypothesis
failing to reject the null hypothesis when the Ha is in fact true
something there – you are missing it
okay to do

6. Confidence intervals My mother understood me: X = 5.54, s = 1.680
My father understood me: X = 5.18, s = 1.916
95% Confidence interval for mother: [5.32, 5.76]
95% Confidence interval for father: [4.91, 5.45]
Overlap means?

7. T-Test, or Student’s T tests the difference of two means
-- one nominal (2-value) variable
-- one interval (or ordinal) variable,
usually the DV
examples: gender and years of education
gender and occupational prestige

8. Formula for t statistic
See Salkind, p. 174

9. Running the t-test Compare means - does it pass the eyeball test?
Construct confidence intervals around the means (optional)
is there overlap in the two in estimation of the true population?
t-test under “compare means,” “independent samples t-test”
two-tailed test is default in SPSS