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Related Samples T-Test

Related Samples T-Test. Quantitative Methods in HPELS 440:210. Agenda. Introduction The t Statistic for Related-Samples Hypothesis Tests with Related-Samples t-Test Instat Assumptions. Introduction. Recall  There are two scenarios when comparing two samples: Samples are INDEPENDENT

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Related Samples T-Test

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  1. Related Samples T-Test Quantitative Methods in HPELS 440:210

  2. Agenda • Introduction • The t Statistic for Related-Samples • Hypothesis Tests with Related-Samples t-Test • Instat • Assumptions

  3. Introduction • Recall  There are two scenarios when comparing two samples: • Samples are INDEPENDENT • Samples are DEPENDENT/RELATED • Dependent or Related samples due to: • Repeated measures design • Matched pairs design • Either case is handled with same statistic • Related-Samples t-Test

  4. Introduction • Repeated Measures Design: • Two sets of data from same sample • Pre-post • Matched pairs Design: • Two sets of data from two samples • Subjects from one sample deliberately matched with subjects from second sample • Identical twins • One or more variables can be used for matching

  5. Agenda • Introduction • The t Statistic for Related-Samples • Hypothesis Tests with Related-Samples t-Test • Instat • Assumptions

  6. Related-Samples t-Test • Statistical Notation: • D = X2 – X1: Difference score • Post – pre • Matched subject #1 – Matched subject #2 • µD: Population mean of difference scores • MD: Sample mean of difference scores • MD = SD / n • sMD: Estimated SEM

  7. Related-Samples t-Test • Formula Considerations: • t = MD – µD / sMD • Estimated SEM (sMD): • sMD = √s2 / n where: • s2 = SS / df

  8. Related-Samples Designs • One-Group Pretest Posttest Design: • Administer pretest to sample • Provide treatement • Administer posttest to sample • Compare means O X O

  9. Related-Samples Designs • Two-Groups Matched-Samples Design: • Match subjects • Administer pretest to both groups • Provide treatment to one group • Administer posttest to both groups • Compare delta scores M O X O  Δ M O O  Δ

  10. Agenda • Introduction • The t Statistic for Related-Samples • Hypothesis Tests with Related-Samples t-Test • Instat • Assumptions

  11. Hypothesis Test: Repeated-Samples t-Test • Recall  General Process: • State hypotheses • State relative to the two samples • No effect  samples will be equal • Set criteria for decision making • Sample data and calculate statistic • Make decision

  12. Hypothesis Test: Repeated-Samples t-Test • Example 11.1 (p 348) • Overview: • It is believed that stress can increase asthma symptoms • Can relaxation techniques reduce the severity of asthma symptoms? • Sample (n = 5) patients is selected

  13. Hypothesis Test: Repeated-Samples t-Test • Pretest: Researchers observe the severity of their symptoms • Number of medicine doses needed throughout the week recorded • Treatment: Relaxation training • Posttest: Researchers observe severity of symptoms again • Questions: • What is the experimental design? • What is the independent variable? • What is the dependent variable?

  14. Step 1: State Hypotheses Non-Directional H0: µD = 0 H1: µD≠ 0 Directional H0: µD≤ 0 H1: µD > 0 Degrees of Freedom: df = (n – 1) df = 5 – 1 = 4 Critical Values: Non-Directional  2.776 Directional  2.132 Step 2: Set Criteria Alpha (a) = 0.05 2.132

  15. Step 3: Collect Data and Calculate Statistic Mean Difference (MD): MD = SD/n MD = -16 / 5 MD = -3.2 Sum of Squares (SS): SS = SD2 – [(SD)2 / n] SS = 66 – [(-16)2 / 5] SS = 66 – 51.2 SS = 14.8 Variance (s2) s2 = SS / df s2 = 14.8 / 4 s2 = 3.7 SEM (sMD): sMD = √s2 / n sMD= √3.7 / 5 sMD = √0.74 sMD= 0.86 t-test: t = MD – µD / sMD t = -3.2 - 0 / 0.86 t = -3.72 Step 4: Make Decision Accept or Reject?

  16. Agenda • Introduction • The t Statistic for Independent-Measures • Hypothesis Tests with Independent-Measures t-Test • Instat • Assumptions

  17. Instat • Type data from sample into a column. • Label column appropriately. • Choose “Manage” • Choose “Column Properties” • Choose “Name” • Choose “Statistics” • Choose “Simple Models” • Choose “Normal, Two Samples” • Layout Menu: • Choose “Two Data Columns”

  18. Instat • Data Column Menu: • Choose variable of interest • Parameter Menu: • Choose “Mean (t-interval)” • Confidence Level: • 90% = alpha 0.10 • 95% = alpha 0.05

  19. Instat • Check “Significance Test” box: • Check “Two-Sided” if using non-directional hypothesis • Enter value from null hypothesis (usually zero) • Check the “paired” box • Click OK • Interpret the p-value!!!

  20. Reporting t-Test Results • How to report the results of a t-test: • Information to include: • Value of the t statistic • Degrees of freedom (n – 1) • p-value • Examples: • There was no significant difference from pretest to postest (t(25) = 0.45, p > 0.05) • The posttest score was significantly greater than the pretest score (t(25) = 4.56, p < 0.05)

  21. Agenda • Introduction • The t Statistic for Independent-Measures • Hypothesis Tests with Independent-Measures t-Test • Instat • Assumptions

  22. Assumptions of Repeated-Samples t-Test • Independent observations • Normal Distribution of Difference Scores

  23. Violation of Assumptions • Nonparametric Version  Wilcoxon (Chapter 17) • When to use the Wilcoxon Test: • Repeated-Samples design • Scale of measurement assumption violation: • Ordinal data • Normality assumption violation: • Regardless of scale of measurement

  24. Textbook Assignment • Problems: 1, 15, 21, 25

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