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The T-TEST in
SPSS
- Alternative
models
- Independent
samples
- Paired Samples
(Matched Measures) -- for samples of matched
cases
- Historically, voting
turnout has been lower in southern states than in states
outside the south.
- Did this pattern
continue in the 2000 presidential
election?
- Did the eleven states
in the "old confederacy" reflect a lower rate of
voting than the other states?
- Testing this hypothesis
with the "nustates" data set:
- H1 :
States outside the south had a higher voting turnout
in 2000 than states in the "old south."
- H0 :
States in the old south had a turnout that was
higher or equal to turnout in
non-southern states.
- A test of
H1 is a directional hypothesis, and the
data are in the direction that might disprove
the null hypothesis, H0.
- The T-TEST procedure in
SPSS 10 produces this analysis of the
difference:
t-tests for Independent
Samples
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Group Statistics
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Former confederate state, 1=yes,
0=no
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N
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Mean
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Std. Deviation
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Std. Error Mean
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% turnout in 2000 election
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0
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40
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55.155
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6.977
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1.103
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1
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11
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48.755
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3.289
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0.992
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Mean
Difference = 6.395
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Independent Samples Test
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Levene's Test for Equality of
Variances
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t-test for Equality of
Means
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F
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Sig.
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t
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df
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Sig. (2-tailed)
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Mean Difference
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Std. Error Difference
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95% Confidence Interval of the
Difference
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% turnout in 2000 election
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Lower
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Upper
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Equal variances assumed
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5.647
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0.021
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2.938
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49
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0.005
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6.4
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2.179
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2.022
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10.779
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Equal variances not assumed
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4.315
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35.942
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0
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6.4
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1.483
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3.392
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9.409
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- We see from the
T-Test of voting turnout that the difference is
significant at .01 for a two-tailed test, but what
about a one-tailed test?
- The answer is that
one should halve the 2-tailed probability to
get a one-tailed probability level
- Thus, the difference
in means for the above table is significant at a
smaller level
- A two-tailed test
assumes this model of testing for critical regions
in both tails;
- But a one-tailed
test assumes a model that concentrates the critical
region in only one tail:
- Thus the null
hypothesis can be rejected at .05 with a
smaller absolute critical value of t,
for example, 1.65 is less than 1.96
- Assuming a two-tailed
test, the observed t-value of plus or minus
3.03 has .0015 in each tail of the distribution
- Because we are
making a one-tailed test, we are interested
only in the .005 associated with the critical
value, 3.03
- Thus, we divide
the stated probability for a two-tailed test by 2
for a one-tailed test
- The important thing
to note is that a one-tailed test makes it "easier"
to reject your null hypothesis by requiring a smaller
critical value to reject, and, by implication, tests
statistics calculated for a two-tailed test are
twice as significant (i.e., the associated
probabilities are divided by two and therefore 1/2 the
size)
- Suppose your data are
proportions rather than means?
- A proportion is
simply the mean of a dichotomized
variable, measured 0 for one category, and 1 for the
other
- The "mean" for this
variable is simply the proportion of those in
category 1 (or percent, if multiplied by 100)
.
- In the special case
of proportions, the standard error of a sampling
distributions can use simplifications in
computation:
- The
variance of a dichotomous variable when p =
proportion in one category and q = proportion in
the other is simply, variance =
pq
- so the standard
deviation is the square root of pq for
dichotomous proportions
- the standard
deviation becomes square root of pq
divided by N
- Thus, one can use the
T-Test to test for differences in
proportions, as well as in means.
Go here for an example using the
Paired Sample T-Test.
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