Independent t-tests. Use when: You are examining differences between groups Each participant is...
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Transcript of Independent t-tests. Use when: You are examining differences between groups Each participant is...
![Page 1: Independent t-tests. Use when: You are examining differences between groups Each participant is tested once Comparing two groups only.](https://reader035.fdocuments.us/reader035/viewer/2022072010/56649dc35503460f94ab5d98/html5/thumbnails/1.jpg)
Intro to StatsIndependent t-tests
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Use when:
You are examining differences between groups
Each participant is tested once Comparing two groups only
Independent t-tests
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Mean Group 1 - Mean Group 2___________________________________ Spread of the groups' data points
t is larger (more likely significant) when: ◦ Two groups’ means are very different◦ When spread (variance) is very small
What does it mean?
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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
Assumptions
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t = X1 – X2
(n1-1) s12 + (n2 – 1)s2
2 n1+n2
n1 + n2 - 2 n1n2
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
Calculating
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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)
Example 1
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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
Example 1
![Page 8: Independent t-tests. Use when: You are examining differences between groups Each participant is tested once Comparing two groups only.](https://reader035.fdocuments.us/reader035/viewer/2022072010/56649dc35503460f94ab5d98/html5/thumbnails/8.jpg)
t = X1 – X2
(n1-1) s12 + (n2 – 1)s2
2 n1+n2
n1 + n2 - 2 n1n2
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
Example 1
![Page 9: Independent t-tests. Use when: You are examining differences between groups Each participant is tested once Comparing two groups only.](https://reader035.fdocuments.us/reader035/viewer/2022072010/56649dc35503460f94ab5d98/html5/thumbnails/9.jpg)
X1 – X2
Prep group: 1400, 1450, 1200, 1350, 1300
Noprep group: 1400,1200, 1050, 1100, 1200
The Numerator
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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
df = (n1 - 1) + (n2 – 1) (for t-test only)
Degrees of Freedom
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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
Example 1
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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!!
7. If not over the critical value, fail to reject the null
& conclude that there was no effect of GRE training on test scores
Example 1
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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.
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.
Example 1
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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
An interpretation should include:
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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
Significance
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A measure of the magnitude of the difference between groups
ES = X1 – X2
SD
Effect Sizes