Related Samples
T-Test
Quantitative Methods in HPELS
HPELS 6210
Agenda
Introduction
 The t Statistic for Related-Samples
 Hypothesis Tests with Related-Samples tTest
 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 tTest
 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 = SD / 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
M
O
X
O

Δ
O

Δ
Agenda
Introduction
 The t Statistic for Related-Samples
 Hypothesis Tests with Related-Samples tTest
 Instat
 Assumptions

Hypothesis Test: Repeated-Samples
t-Test

1.
Recall  General Process:
State hypotheses

State relative to the two samples
 No effect  samples will be equal
2.
3.
4.
Set criteria for decision making
Sample data and calculate statistic
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
Degrees of Freedom:
Non-Directional
df = (n – 1) df = 5 – 1 = 4
H0: µD = 0
H1: µD ≠ 0
Directional
H0: µD ≤ 0
H1: µD > 0
Critical Values:
Non-Directional  2.776
Directional  2.132
Step 2: Set Criteria
Alpha (a) = 0.05
2.132
Step 3: Collect Data and Calculate Statistic
Mean Difference (MD):
Sum of Squares (SS):
Variance (s2)
MD = SD/n
SS = SD2 – [(SD)2 / n]
s2 = SS / df
MD = -16 / 5
SS = 66 – [(-16)2 / 5]
s2 = 14.8 / 4
MD = -3.2
SS = 66 – 51.2
s2 = 3.7
SS = 14.8
SEM (sMD):
sMD = √s2 / n
t-test:
Step 4: Make Decision
sMD = √3.7 / 5
t = MD – µD / sMD
Accept or Reject?
sMD = √0.74
t = -3.2 - 0 / 0.86
sMD = 0.86
t = -3.72
Agenda
Introduction
 The t Statistic for Independent-Measures
 Hypothesis Tests with IndependentMeasures 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

Parameter Menu:
 Choose

variable of interest
“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 IndependentMeasures 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