related samples t-test
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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Related Samples T-Test
Quantitative Methods in HPELS
440:210
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Agenda
Introduction The t Statistic for Related-Samples Hypothesis Tests with Related-Samples t-
Test Instat Assumptions
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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
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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
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Agenda
Introduction The t Statistic for Related-Samples Hypothesis Tests with Related-Samples t-
Test Instat Assumptions
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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
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Related-Samples t-Test Formula Considerations:
t = MD – µD / sMD
Estimated SEM (sMD): sMD = √s2 / n where:
s2 = SS / df
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Related-Samples Designs
One-Group Pretest Posttest Design: Administer pretest to sample Provide treatement Administer posttest to sample Compare means
O X O
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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
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Agenda
Introduction The t Statistic for Related-Samples Hypothesis Tests with Related-Samples t-
Test Instat Assumptions
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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
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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
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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?
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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
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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
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Agenda
Introduction The t Statistic for Independent-Measures Hypothesis Tests with Independent-
Measures t-Test Instat Assumptions
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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”
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Instat
Data Column Menu:Choose variable of interest
Parameter Menu:Choose “Mean (t-interval)”
Confidence Level:90% = alpha 0.1095% = alpha 0.05
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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!!!
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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)
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Agenda
Introduction The t Statistic for Independent-Measures Hypothesis Tests with Independent-
Measures t-Test Instat Assumptions
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Assumptions of Repeated-Samples t-Test
Independent observations Normal Distribution of Difference Scores
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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
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Textbook Assignment
Problems: 1, 15, 21, 25