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Objectives

Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 11: Between-Subjects Designs. Objectives. t -test for independent groups Hypothesis testing Interpreting t and p Statistical power. t -test for Independent Groups. Basic inferential statistic

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Objectives

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  1. Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 11: Between-Subjects Designs

  2. Objectives • t-test for independent groups • Hypothesis testing • Interpreting t and p • Statistical power

  3. t-test for Independent Groups • Basic inferential statistic • Ratio of two measures of variability = Difference between two group means Standard Error of the difference between group means • Allows us to consider effect, relative to error

  4. Standard Error of the Difference between Means

  5. t-test • Larger |t-ratio| = greater difference between means • Based on this we can decide whether to reject Ho • Usually Ho= µ1 = µ2 • Sampling error may account for some difference, but when t is “large” enough…

  6. Hypothesis Testing: t-tests • Based on estimates of probability • When α = .05, there is a 5% chance of rejecting Ho when we should not (Type I error) • See Figure 11.2 (each tail = 2.5%) • Region of rejection • If t falls within the shaded ranges, we reject Ho because probability is so low

  7. Figure 11.2

  8. Hypothesis Testing Steps • State Ho and H1 • Before collecting or examining the data • Identify appropriate statistical test(s) • Based on hypotheses • Often multiple approaches are possible • Depends on how well data meet the assumptions of specific statistical tests

  9. Hypothesis Testing Steps • Set the significance level (α) • α = p(Type I error) • Risk of false alarm • You control • 1 – α = p(Type II error) • Risk of miss • Careful, you might “overcontrol”

  10. Hypothesis Testing Steps • Determine significance level for t-ratio • Use appropriate table in Appendix B, df for the test and your selected alpha (α) level to determine tcritical • If your observed |t ratio| > tcritical reject Ho • If your observed p-level is less than α you can also reject Ho

  11. Hypothesis Testing Steps • Interpreting t-ratio • Is it statistically significant? • Is it practically/clinically significant? • Does the effect size matter, really? • Book mentions d-statistic

  12. Hypothesis Testing Steps • Interpreting t-ratio • Magnitude of the effect • Degree of variance accounted for by the IV • Omega squared = % of variance accounted for by IV in the DV • Is there cause and effect? • Typically requires manipulated IV, randomized assignment, and careful pre- / post- design

  13. Correct Interpretation of t and p • If you have a significant t-ratio: = statistically significant difference between two groups = IV affects DV = probability of a Type I error is α

  14. Errors in p Interpretation • Changing αafter analyzing the data • Unethical • We cannot use p to alter α • Kills your chances of limiting Type I error risk • p only estimates the probability of obtaining at least the results you did if the null hypothesis is true, and it is based on sample statistics  not fully the case for α

  15. Errors in p Interpretation • Stating that p = odds-against chance • p = .05 does not mean that the probability of results due to chance was 5% or less • p is not the probability of committing a Type I error • Recommended interpretation: • If p is small enough, I reject the null hypothesis in favor of the alternative hypothesis.

  16. Errors in p Interpretation • Assuming p = probability that H1 is true (i.e., that the results are “valid”) • p does not confirm the validity of H1 • Smaller p values do not indicate a more important relationship between IV and DV • Effect size estimates are required for this

  17. Errors in p Interpretation • Assuming p = probability of replicating results • The probability of rejecting Ho is not related to the obtained p-value • A new statistic, prep is getting some attention for this purpose (see Killeen, 2005)

  18. Statistical Tests & Power • β = p(Type II error) or p(miss) • 1 – β = p(correctly rejecting false Ho) = power • Four main factors influence statistical power

  19. Power: Difference between µ • Power increases when the difference between µ of two populations is greater

  20. Power: Sample Size • Issue of how well a statistic estimates the population parameter (Fig. 10.5) • Larger N  smaller SEM • As SEM decreases  overlap of sampling distributions for two populations decreases  power increases • Don’t forget about cost

  21. Power: Variability in Data • Lots of variability  variance in the sampling distribution and greater overlap of two distributions • Reducing variability reduces SEM  overlap decreases  power goes up • Techniques: Use homogeneous samples, reliable measurements

  22. Power: α • Smaller α lower Type I probability  lower power • As p(Type I) decreases, p(Type II) increases (see Figure 11.6) • As αincreases, power increases • Enlarges the region of rejection

  23. Estimating Sample Size • Based on power • Tables in Appendix B can give you estimates for t-ratios • Effect size is sub-heading • Cost / feasibility considerations • Remember that sample size is not the only influence on statistical power

  24. What is Next? • **instructor to provide details

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