Independent t-tests
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Use when:
You are examining differences between
groups
Each participant is tested once
Comparing two groups only
Mean Group 1 - Mean Group 2
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Spread of the groups' data points
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t is larger (more likely significant) when:
◦ Two groups’ means are very different
◦ When spread (variance) is very small
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Observations are independent
Samples are normally distributed
Samples should have equal variance
◦ There is a “fix” for violations of this assumption that
will be discussed in lab
t=
X 1 – X2
(n1-1) s12 + (n2 – 1)s22
n1 + n 2 - 2
X1 = mean for group 1
X2 = mean for group 2
n1 = number of participants in group 1
n2 = number of participants in group 2
s12 = variance for group 1
s22 = variance for group 2
n1+n2
n1 n 2
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Study:
◦ Effects of GRE prep classes on test scores
◦ One group given prep classes
 (1400, 1450, 1200, 1350, 1300)
◦ One group given no classes
 (1400, 1200, 1050, 1100, 1200)
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1. State hypotheses
◦ Null hypothesis: there is no difference between test
scores in the groups with or without prep classes
 μprep = μnoprep
◦ Research hypothesis: there is a difference in test
scores between the groups with and without prep
classes
 Xprep ≠ Xnoprep
t=
X 1 – X2
(n1-1) s12 + (n2 – 1)s22
n1 + n 2 - 2
X1 = mean for group 1
X2 = mean for group 2
n1 = number of participants in group 1
n2 = number of participants in group 2
s12 = variance for group 1
s22 = variance for group 2
n1+n2
n1 n 2
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X1 – X2
Prep group: 1400, 1450, 1200, 1350, 1300
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Noprep group: 1400,1200, 1050, 1100, 1200
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Degrees of freedom ( df ): Describes
number of scores in sample that are free to
vary (without changing value of descriptive
statistic).
Needed to identify the critical value
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df = (n1 - 1) + (n2 – 1) (for t-test only)
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**if dfs are bigger than biggest value in chart,
use infinity row
**if precise dfs are not listed, use the next
smallest to be conservative
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6. Determine whether the statistic exceeds the
critical value
◦ 2.03 < 2.31
◦ So it does not exceed the critical value
◦ THE NULL IS REJECTED IF OUR STATISTIC IS BIGGER
THAN THE CRITICAL VALUE – THAT MEANS THE
DIFFERENCE IS SIGNIFICANT AT p < .05!!
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7. If not over the critical value, fail to reject the
null
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& conclude that there was no effect of GRE
training on test scores
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In results
◦ There was no significant difference in test scores
between participants given the GRE prep course (M
= 1340, SD = 96.18) and those given no GRE prep
course (M = 1190, SD = 134.16), t(8) = 2.03, n.s.
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If it had been significant:
◦ Participants given the GRE prep course had
significantly higher test scores (M = 1340, SD =
96.18) than those given no GRE prep course (M =
1190, SD = 134.16), t(8) = 2.80, p < .05.
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Whether the effect/difference was
significant or not
The outcome in the study
The different groups or categories being
compared in the study
The mean and SD for each group or
category
The t statistic and p-value, as shown in
examples
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Remember: Just because means are
different, it does not mean they are
meaningfully different
Need to examine significance
◦ i.e., likelihood that the differences are due to
chance
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A measure of the magnitude of the difference
between groups
ES = X1 – X2
SD