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Chapter 11 t -Test for Two Related Samples

Chapter 11 t -Test for Two Related Samples. PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J Gravetter and Larry B. Wallnau. Chapter 11 Learning Outcomes. Concepts to review. Introduction to the t Statistic

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Chapter 11 t -Test for Two Related Samples

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  1. Chapter 11t-Test for Two Related Samples PowerPoint Lecture SlidesEssentials of Statistics for the Behavioral SciencesSeventh Editionby Frederick J Gravetter and Larry B. Wallnau

  2. Chapter 11 Learning Outcomes

  3. Concepts to review • Introduction to the t Statistic • Estimated standard error • Degrees of freedom • t Distribution • Hypothesis test with t statistic • Independent Measures Design

  4. 11.1 Introduction to Repeated-Measures Designs • Repeated measures design • Also known as within-subjects design • Two separate scores are obtained for each individual in the sample • Same subjects are used in all treatment conditions • No risk of the treatment groups differing from each other significantly.

  5. Matched-Subjects Design • Approximates the advantages of a repeated-measures design • Two separate samples are used • Each individual in a sample is matched one-to-one with an individual in the other sample. • Matched on relevant variables • Participants are not identical to their match • Ensures that the samples are equivalent with respect to some specific variables.

  6. Related-samples Designs • Related (or correlated) sample designs • Repeated measures • Matched sample • Statistically equivalent methods • Use different number of subjects • Matched sample has twice as many subjects as a repeated-measures design.

  7. 11.2 t-Statistic for Repeated- Measures Research Design • Structurally similar to the other t statistics • Essentially the same as the single-sample t • Based on difference scores (D) rather than raw scores (X) • Difference score = D = X2—X1 • Mean Difference

  8. Hypotheses for Related Samples Test • H0: μD = 0 • H1: μD ≠ 0

  9. Figure 11.1 Populations of Difference Scores

  10. t- statistic for Related Samples

  11. Figure 11.2 Sample of Difference Scores

  12. Learning Check • For which of the following would a repeated-measures study be appropriate? A matched-subjects?

  13. Learning Check - Answer • For which of the following would a repeated-measures study be appropriate? A matched-subjects?

  14. Learning Check • Decide if each of the following statements is True or False.

  15. Answer

  16. 11.3 Hypothesis Tests and Effect Size for Repeated-Measures Design • Numerator of t statistic measures actual difference between the data MD and the hypothesis μD • Denominator measures the standard difference that is expected if H0 is true • Same four-step process as other tests.

  17. Figure 11.3 Critical region for t with df = 8 and α = .01

  18. Effect size for Related Samples

  19. Variability as measure of consistency • When treatment has consistent effect • Difference scores cluster together • Variability is low • When treatment effect is inconsistent • Difference scores are more scattered • Variability is high • Treatment effect may be significant when variability is low, but not significant when variability is high

  20. Figure 11.4 Sample difference scores from Example 11.1

  21. Figure 11.5 Sample of differences scores with high variability

  22. Directional Hypotheses and One-Tailed Tests • Researchers often have specific predictions for related samples designs • Null hypothesis and research hypothesis are stated directionally, e.g. • H0: μD ≤ 0 • H1: μD > 0 • Critical region is located in one tail

  23. 11.4 Uses and assumptions for related samples t tests • Advantages of repeated measures design • Requires fewer subjects • Able to study changes over time • Reduces or eliminates influence of individual differences • Disadvantages of repeated measures design • Factors besides treatment may cause subject’s score to change • Participation in first treatment may influence score in the second treatment (order effects)

  24. Assumptions of the related samples t Test • Observations within each treatment condition must be independent. • Population distribution of difference scores must be normal. • This assumption is not a concern unless the sample size is small. • With relatively large samples (n > 30) this assumption can be ignored.

  25. Learning Check • Assuming that the sample mean difference remains the same, which of the following sets of data is most likely to produce a significant t statistic?

  26. Learning Check • Assuming that the sample mean difference remains the same, which of the following sets of data is most likely to produce a significant t statistic?

  27. Learning Check TF • Decide if each of the following statements is True or False.

  28. Answer TT

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