chapter 9. we want to test whether the means of two samples are statistically significantly...
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Two Sample t testChapter 9
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We want to test whether the means of two samples are statistically significantly different from each other
Example: Student-motivation data
Test whether the ‘males and females in the study have similar mean academic ability score?’
t test
Two sample t test
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Two independent samples◦ Samples drawn randomly from different
populations Hypothesis : Population means are same
Where S is the standard deviation
Student t test for 2 samples
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If both population are found to have equal variance◦ Pooled variance estimate is computed
If both population are found to have unequal variance◦ An exact t cannot be estimated◦ Only an approximation can be computed
First test if population variance are equal
Two independent Sample t test
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Testing for equality of population variance
F statistics is computed from sample variance
Known as Levene’s test for equality of variance
F test for population variance
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SF nn
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Test whether the ‘males and females have similar mean academic ability score?’
Academic ability score = OLTS
Testing the mean value of OLTS grouped by gender variable
Testing mean for our example
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Analyze > Compare means > Independent sample t test
Test variable : OLTS Grouping variable : Gender
◦ Click on Define groups
Two independent sample t test: SPSS
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Two independent sample t test: SPSS
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First part of the table gives the Levene’s test
Decision Rule: P value < 0.05◦ Reject the H0
Two independent sample test: SPSS Output
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H0: Samples are from population with equal variance
In our example P value = 0.56 > 0.05 Hence we cannot reject the H0
The samples are drawn from populations with equal variances
P value: level of significance
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Independent Samples TestLevene's Test for
Equality of Variances
t-test for Equality of Means
F Sig. t df Sig. (2-tailed)
Online Test Score
Equal variances assumed .345 .560 -.286 48 .776
Equal variances not assumed -.286 45.174 .776
SPSS output
The Significance level (P value) > 0.05We cannot reject the H0 that the mean OLTS for Male and Females are same
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Exercise 2, 3 and 5
Exercise on Pg 73
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Paired t test
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The sample relate to same set of respondents
Before After test
Test whether mean performance of a set of respondents before and after a treatment is same◦ Set of employees undergoing training◦ Students undergoing MBA course work
Paired t test
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Test performance over time
Test the performance of an organization from the response of same set respondents over time
Feedback about the institute from same set of students in their 1st year and 2nd year of MBA
Paired t test
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Example on pg69 Scores of 20 individuals before and after the
training programme
H0: There is no difference in the mean performance of individuals before and after the training programme
H1: There is difference in the mean performance of individual before and after the training programme
Paired t test
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Hypothesis
Analyze > Compare means > Paired t test Select both the variables
Paired t test: SPSS
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SPSS output
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Results for the t test
Significance level (P value) = 0.000 < 0.05 (α)
Hence we reject the null hypothesis at 5% level of significance
There is a significant difference in the mean performance of individuals before and after the training.
Paired t test: SPSS
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Independent Samples
Paired Samples Independent
SamplesPaired
Samples* Two-Group t
test* Z test
* Paired t test * Chi-Square
* Mann-Whitney* Median* K-S
* Sign* Wilcoxon* McNemar* Chi-Square
A Classification of Hypothesis Testing Procedures for Examining Differences
Hypothesis Tests
One Sample Two or More Samples
One Sample Two or More Samples
* t test* Z test
Chi-Square * K-S * Runs* Binomial
Parametric Tests (Metric Tests)
Non-parametric Tests (Nonmetric Tests)
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Exercise 1 on pg 72 Exercise 4 on Pg 73
Exercise