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Intro to Stats

This guide introduces independent t-tests, a statistical method used to compare means between two distinct groups. Suitable for studies where participants are tested once, it explores when to use this test, its underlying assumptions, and an example involving GRE prep classes. Key calculations such as the t statistic and degrees of freedom are explained. Understanding the significance of findings, including null and research hypotheses, is crucial for interpreting results. This resource is essential for anyone looking to comprehend group comparisons in statistical analyses.

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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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