Related Samples T-Test Quantitative Methods in HPELS HPELS 6210

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  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

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

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

Related-Samples t-Test Statistical Notation:  D = X 2 – X 1 : Difference score Post – pre Matched subject #1 – Matched subject #2  µ D : Population mean of difference scores  M D : Sample mean of difference scores M D =  D / n  s MD : Estimated SEM

Related-Samples t-Test Formula Considerations:  t = M D – µ D / s MD Estimated SEM (s MD ):  s MD = √s 2 / n where:  s 2 = SS / df

Related-Samples Designs One-Group Pretest Posttest Design:  Administer pretest to sample  Provide treatement  Administer posttest to sample  Compare means OXOOXO

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 MOXO  Δ MOO  Δ

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

Recall  General Process: 1. State hypotheses  State relative to the two samples  No effect  samples will be equal 2. Set criteria for decision making 3. Sample data and calculate statistic 4. Make decision 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

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?

Step 1: State Hypotheses Non-Directional H 0 : µ D = 0 H 1 : µ D ≠ 0 Directional H 0 : µ D ≤ 0 H 1 : µ D > 0 Step 2: Set Criteria Alpha (  ) = 0.05 Degrees of Freedom: df = (n – 1) df = 5 – 1 = 4 Critical Values: Non-Directional  Directional 

Step 4: Make Decision Accept or Reject? Step 3: Collect Data and Calculate Statistic Mean Difference (M D ): M D =  D/n M D = -16 / 5 M D = -3.2 Variance (s 2 ) s 2 = SS / df s 2 = 14.8 / 4 s 2 = 3.7 t-test: t = M D – µ D / s MD t = / 0.86 t = Sum of Squares (SS): SS =  D 2 – [(  D) 2 / n] SS = 66 – [(-16) 2 / 5] SS = 66 – 51.2 SS = 14.8 SEM (s MD ): s MD = √s 2 / n s MD = √3.7 / 5 s MD = √0.74 s MD = 0.86

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

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”

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

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!!!

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)

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

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

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

Textbook Assignment Problems: 1, 15, 21, 25