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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 5: Comparing Two Sample Means
Lesson 1: The Paired Samples t Test
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
To Reject or Not to Reject?
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University of North Texas Dr. J. Kyle Roberts © 2004
Paired Samples t Test
The same people measured on the same construct on two different occasions
Pre-test ↔ Post-test
(a.k.a., Dependent Samples t Test)
Assessing the effectiveness of a reading intervention with 8 students in a single classroom
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University of North Texas Dr. J. Kyle Roberts © 2004
Null Hypothesis
postpre XXH :0
0:0 postpre XXH
0:0 DiffXH
Pre Post Diff
5 8 -3
6 9 -3
7 8 -1
7 9 -2
6 8 -2
4 7 -3
5 7 -2
4 6 -2
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University of North Texas Dr. J. Kyle Roberts © 2004
Paired Samples t Test in SPSSAnalyzeCompare MeansPaired-Samples T Test
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University of North Texas Dr. J. Kyle Roberts © 2004
Paired Samples t Test in SPSS
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University of North Texas Dr. J. Kyle Roberts © 2004
SPSS OutputPaired Samples Statistics
5.5000 8 1.19523 .42258
7.7500 8 1.03510 .36596
READPRE
READPOST
Pair1
Mean N Std. DeviationStd. Error
Mean
Paired Samples Correlations
8 .808 .015READPRE & READPOSTPair 1N Correlation Sig.
Paired Samples Test
-2.2500 .70711 .25000 -2.8412 -1.6588 -9.000 7 .000READPRE - READPOSTPair 1Mean Std. Deviation
Std. ErrorMean Lower Upper
95% ConfidenceInterval of the
Difference
Paired Differences
t df Sig. (2-tailed)
Mean of the difference scores
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University of North Texas Dr. J. Kyle Roberts © 2004
Comparing Studies
Study 1
Pretest Posttest
Mean = 80 Mean = 90
SD = 10 SD = 10
N = 20 N = 20
Study 2
Pretest Posttest
Mean = 80 Mean = 90
SD = 10 SD = 10
N = 121 N = 121
t-crit = 2.093on
19 df
Which study is more likely to produce results that are statistically significant?
t-crit = 1.980on
120 df
Study 2
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University of North Texas Dr. J. Kyle Roberts © 2004
Comparing Studies
Study 1
Pretest Posttest
Mean = 80 Mean = 90
SD = 10 SD = 10
N = 20 N = 20
Study 2
Pretest Posttest
Mean = 80 Mean = 90
SD = 10 SD = 2
N = 20 N = 20
t-crit = 2.093on
19 df
Which study is more likely to produce results that are statistically significant?
Study 2
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University of North Texas Dr. J. Kyle Roberts © 2004
Comparing Studies
Study 1
Pretest Posttest
Mean = 80 Mean = 90
SD = 10 SD = 10
N = 20 N = 20
Study 2
Pretest Posttest
Mean = 80 Mean = 85
SD = 10 SD = 10
N = 20 N = 20
t-crit = 2.093on
19 df
Which study is more likely to produce results that are statistically significant?
Study 1
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University of North Texas Dr. J. Kyle Roberts © 2004
Factors Affecting t-calc
1. The magnitude of the difference between the two means
2. The “spreadoutness” of the scores
3. The number of people in the study
4. The level at which α is set
Just like the Single-Sample t Test
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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 5: Comparing Two Sample Means
Lesson 1: The Paired Samples t Test
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
To Reject or Not to Reject?
