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Published byHarry Blake Modified over 9 years ago
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Independent t-tests
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Use when: You are examining differences between groups Each participant is tested once Comparing two groups only
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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
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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
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t = X 1 – X 2 (n 1 -1) s 1 2 + (n 2 – 1)s 2 2 n 1 +n 2 n 1 + n 2 - 2 n 1 n 2 X 1 = mean for group 1 X 2 = mean for group 2 n 1 = number of participants in group 1 n 2 = number of participants in group 2 s 1 2 = variance for group 1 s 2 2 = variance for group 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 μ prep = μ noprep ◦ Research hypothesis: there is a difference in test scores between the groups with and without prep classes X prep ≠ X noprep
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t = X 1 – X 2 (n 1 -1) s 1 2 + (n 2 – 1)s 2 2 n 1 +n 2 n 1 + n 2 - 2 n 1 n 2 X 1 = mean for group 1 X 2 = mean for group 2 n 1 = number of participants in group 1 n 2 = number of participants in group 2 s 1 2 = variance for group 1 s 2 2 = variance for group 2
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X 1 – X 2 Prep group: 1400, 1450, 1200, 1350, 1300 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 df = (n 1 - 1) + (n 2 – 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!! 7. If not over the critical value, fail to reject the null & 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. 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 = X 1 – X 2 SD
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