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
Comparing Two Statistics
Hypotheses:
 Null (nothing is going on)
H0 : x̄1 = x̄2
 Alternative (something is going on)
HA : x̄1 ≠ x̄2
HA : x̄1 < x̄2
HA : x̄1 > x̄2
OR
OR
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)
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
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?
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
Formula for t statistic
See Salkind, p. 174
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 ttest”
 two-tailed test is default in SPSS