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Intro to Stats

Intro to Stats. Independent t-tests. Independent t-tests. Use when: You are examining differences between groups Each participant is tested once Comparing two groups only. What does it mean?. Mean Group 1 - Mean Group 2 ___________________________________

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Intro to Stats

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  1. Intro to Stats Independent t-tests

  2. Independent t-tests • Use when: • You are examining differences between groups • Each participant is tested once • Comparing two groups only

  3. What does it mean? 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

  4. Assumptions • 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

  5. Calculating t = X1 – X2 (n1-1) s12 + (n2 – 1)s22 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

  6. Example 1 • 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)

  7. Example 1 • 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

  8. Example 1 t = X1 – X2 (n1-1) s12 + (n2 – 1)s22 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

  9. The Numerator X1 – X2 • Prep group: 1400, 1450, 1200, 1350, 1300 • Noprep group: 1400,1200, 1050, 1100, 1200

  10. Degrees of Freedom • 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)

  11. Example 1 • **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

  12. Example 1 • 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

  13. Example 1 • 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.

  14. An interpretation should include: • 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

  15. Significance • 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

  16. Effect Sizes • A measure of the magnitude of the difference between groups ES = X1 – X2 SD

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