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Independent Sample T-test
• Classical design used in psychology/medicine
• N subjects are randomly assigned to two
groups (Control * Treatment).
• After treatment, the individuals are measured
on the dependent variable.
• A test of differences in means between groups
provides evidence for the treatment's effect.
Measures of Variation
• A lot of statistical techniques (using interval
data) use measures of variation in some manner
• What is the difference between a standard
deviation, the standard error of the mean, and
the standard error of the difference between
means? Or How are they related? Look in the
glossary to help you answer these questions?
Using Measures of Variation
• Leaned how to measure variation in data, i.e., variance,
standard deviation (Ch.4)
• Used the normal curve & SD to calculate z-scores and
probabilities (Ch.5)
• Used the normal curve & the z-score & the SE of the
mean to calculate confidence intervals (Ch.6)
• Used the concept of the confidence interval and the
standard error of the differences between means to
calculate the t-test (Ch.7)
• Use the sum of squares Σ(X – Mean)2 [sum of the
squared differences from the mean] in ANOVA
Null Hypothesis
• The two groups come from the same
population or that the two means are equal
• μ 1 = μ2
Levels of Significance
• What does an α = .05 level of significance
mean?
• We decide to reject the null if the
probability is very small (5% or less) that
the sample difference is a product of
sampling error.
• The observed difference is outside the
95% confidence interval of the difference
Choosing a Level of Significance
• Convention
• Minimize type I error – Reject null
hypothesis when the null is true
• Minimize type II error – fail to reject null
when the null is false
• Making alpha smaller reduces the
likelihood of making a type I error
• Making alpha larger reduces the
probability of a type II error
Independent Sample T-test
Formula
t=
X1  X 2
s X1  X 2
 N1s1  N 2 s2
 
 N1  N 2  2
2
s x1  x2
2
 N1  N 2 


 N N 
 1 2 
Assumptions of the t-test
• 1. All observations must be independent of each other (random
sample should do this)
• 2. The dependent variable must be measured on an interval or ratio
scale
• 3. The dependent variable must be normally distributed in the
population (for each group being compared). (NORMALITY
ASSUMPTION) [this usually occurs when N is large and randomly
selected]
• 4. The distribution of the dependent variable for one of the groups
being compared must have the same variance as the distribution
for the other group being compared. (HOMOGENEITY OF
VARIANCE ASSUMPTION)
Don’t worry about these
assumptions to much, but
• Point 1: statistical tools are attempting to
quantify and analyze very complex
social/political phenomenon
• Point 2: For these test to be accurate they relay
on simplifying the world with many assumptions
that might not be true
• Point 3: social science researchers violate
these assumptions quite often, but try to be
honest about it
• Point 4: there are sometimes ways of testing
and adjusting for violations
SPSS & the Independent Sample T-Test
Group Statistics
VAR00001
VAR00002
1.00
2.00
N
10
10
Mean
102.0000
98.0000
Std. Error
Mean
10.03328
9.63789
Std. Deviation
31.72801
30.47768
Independent Samples Test
Levene's Test for
Equality of Variances
F
VAR00001
Equal variances
ass umed
Equal variances
not as sumed
.073
Sig.
.789
t-tes t for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.288
18
.777
4.00000
13.91242 -25.22892
33.22892
.288
17.971
.777
4.00000
13.91242 -25.23230
33.23230