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 Samples are DEPENDENT/RELATED

Dependent or Related samples due to:Repeated measures designMatched pairs design

Either case is handled with same statisticRelated-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 = 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 = D / n

sMD: Estimated SEM

Related-Samples t-Test Formula Considerations:

t = MD – µD / sMD

Estimated SEM (sMD): sMD = √s2 / n where:

s2 = SS / df

Related-Samples Designs

One-Group Pretest Posttest Design: Administer pretest to sample Provide treatement Administer posttest to sample Compare means

O X O

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

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 making3. Sample data and calculate statistic4. Make decision

Hypothesis Test: Repeated-Samples t-Test

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

H0: µD = 0

H1: µD ≠ 0

Directional

H0: µD ≤ 0

H1: µD > 0

Step 2: Set Criteria

Alpha () = 0.05

Degrees of Freedom:

df = (n – 1) df = 5 – 1 = 4

Critical Values:

Non-Directional 2.776

Directional 2.132

2.132

Step 4: Make Decision

Accept or Reject?

Step 3: Collect Data and Calculate Statistic

Mean Difference (MD):

MD = D/n

MD = -16 / 5

MD = -3.2

Variance (s2)

s2 = SS / df

s2 = 14.8 / 4

s2 = 3.7

t-test:

t = MD – µD / sMD

t = -3.2 - 0 / 0.86

t = -3.72

Sum of Squares (SS):

SS = D2 – [(D)2 / n]

SS = 66 – [(-16)2 / 5]

SS = 66 – 51.2

SS = 14.8

SEM (sMD):

sMD = √s2 / n

sMD = √3.7 / 5

sMD = √0.74

sMD = 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 0.1095% = 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 designScale of measurement assumption violation:

Ordinal data

Normality assumption violation: Regardless of scale of measurement

Textbook Assignment

Problems: 1, 15, 21, 25