Lecture Outline 14 (Independent Samples t-Test)
PSYC 210 (Burnham)
1. Bivariate Relationships
a. Limits of z-Test and one sample t-Test?
b. Univariate
c. Bivariate relationships
d. Parametric statistics
e. Non-parametric statistics
f.
Experimental Designs
i.
Between-subjects design (Independent groups/samples design)
ii.
Within-subjects design (Correlated Samples Design, Repeated Measures Design)
2. Independent Groups t-Test
a. Assumptions
b. Hypotheses
i.
Null
ii.
Alternate
c. Sampling distribution of the difference between independent means
i.
Mean is equal to μ1 - μ2
ii.
Standard deviation is the standard error of the difference between independent sample means
Lecture Outline 14 (Independent Samples t-Test)
PSYC 210 (Burnham)
d. Standard error of the difference between independent sample means (estimated, of course!)
i.
This assumes unequal variances:
̂
̂
̂ = +
e. Homogeneity of variance assumption
f.
Estimated pooled variance:
̂
=
̂
− 1 + ̂ 2 − 1
+ − 2
g. Standard error of the difference between independent sample means (estimated, of course!)
i.
This assumes equal variances:
̂
̂
̂ = +
h. The t-Test:
=
− − − − =
̂ ̂ 3. Example 1: We develop an antianxiety drug and want to know whether anxiety is affected by taking the drug vs.
taking a placebo.
a. Sample information
b. Hypotheses
c. α = .05
d. Estimated pooled variance:
e. Estimated standard error of the difference between independent means:
f.
Test statistic:
g. p-value:
h. Decisions?
i.
Strength of relationship (effect size)
i.
Eta-squared (η2)
ii.
Cohen’s d
iii.
Estimated pooled standard deviation
Lecture Outline 14 (Independent Samples t-Test)
4. Example 2: Does drinking coffee lead to better quiz scores compared to drinking Red Bull?
a. Sample information
b. Hypotheses
c. α = .01
d. Estimated pooled variance:
e. Estimated standard error of the difference between independent means:
f.
Test statistic:
g. p-value:
h. Decisions?
i.
Strength of relationship (effect size)
i.
Eta-squared (η2)
ii.
Cohen’s d
iii.
Estimated pooled standard deviation
PSYC 210 (Burnham)