Business Research Methods William G' Zikmund

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Business Research MethodsWilliam G. Zikmund

• Chapter 22
• Bivariate Analysis -
• Tests of Differences

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Common Bivariate Tests
Type of Measurement
Differences between two independent groups
Differences among three or more independent groups
Interval and ratio
Independent groups t-test or Z-test
One-way ANOVA
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Common Bivariate Tests
Type of Measurement
Differences between two independent groups
Differences among three or more independent groups
Ordinal
Mann-Whitney U-test Wilcoxon test
Kruskal-Wallis test
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Common Bivariate Tests
Type of Measurement
Differences between two independent groups
Differences among three or more independent groups
Nominal
Z-test (two proportions) Chi-square test
Chi-square test
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Type of Measurement
Differences between two independent groups
Nominal
Chi-square test
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Chi-Square Test
x² chi-square statistics Oi observed
frequency in the ith cell Ei expected frequency
on the ith cell d.f.(R-1)(C-1)
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Chi-Square Test
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Awareness of Tire Manufacturers Brand
Men Women Total
Aware 50 10 60 Unaware
15 25 40 65 35
100
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Awareness of Tire Manufacturers Brand
Men Women Total
Aware 50 (39) 10 (21)
60 Unaware 15 (28) 25 (14)
40 65 35 100
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Chi-Square Test Differences Among Groups Example
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X23.84 with 1 d.f.
Since 22.161 is greater than 3.84, thus reject
the null. More men are aware of this tire brand
than women.
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Type of Measurement
Differences between two independent groups
Interval and ratio
t-test or Z-test
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Differences Between Groups when Comparing Means

• Interval or ratio scaled dependent variables
• t-test
• When groups are 30 or less
• When population standard deviation is unknown
• z-test
• When groups are greater than 30

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Null Hypothesis About Mean Differences Between
Groups
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t-Test for Difference of Means
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t-Test for Difference of Means
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Pooled Estimate of the Standard Error t-test
for the Difference of Means
S12 the variance of Group 1 S22 the variance
of Group 2 n1 the sample size of Group 1 n2
the sample size of Group 2
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Degrees of Freedom

• d.f. n - k
• where
• n n1 n2
• k number of groups

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t-Test for Difference of Means Example

• Researcher wants to test for difference between
  sociology and business majors on attitudes toward
  business.
• Business Students Sociology Students
• Mean 16.5 12.2
• S 2.1 2.6
• n 21 14

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t-Test for Difference of Means Example
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Since the calculated t-value of 5.395 is greater
than the critical value of t with an alpha of
.01, which is 2.75. Thus, reject the null.
Business students scores are significantly
higher that those of sociology students.
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Type of Measurement
Differences between two independent groups
Nominal
Z-test (two proportions)
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Comparing Two Groups when Comparing Proportions

• Percentage Comparisons
• Sample Proportion - P
• Population Proportion -

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Z-Test for Differences of Proportions
or
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Z-Test for Differences of Proportions
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Z-Test for Differences of Proportions
p1 sample portion of successes in Group 1 p2
sample portion of successes in Group 2 (p1 - p2)
hypothesized population proportion 1 minus
hypothesized population proportion 2 Sp1-p2
pooled estimate of the standard errors of
difference of proportions
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Standard Error of the Difference of Proportions
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Z-Test for Differences of Proportions
p pooled estimate of proportion of success in a
sample of both groups p (1- p) or a
pooled estimate of proportion of failures
in a sample of both groups n1 sample size for
group 1 n2 sample size for group 2
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Pooled Estimator for Differences of Proportions
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A Z-Test for Differences of Proportions
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Z-Test for Differences of Proportions
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Z-Test for Differences of Proportions
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Z-Test for Differences of Proportions
Since the absolute value of -.73 or .73 is less
than 1.96, We fail to reject the null hypothesis
of no difference with alpha .05.
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Differences between three or more independent
groups
Type of Measurement
Interval or ratio
One-way ANOVA
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Analysis of Variance

• Hypothesis when comparing three groups
• m1 m2 m3
• Utilizes F test, which is a test of variances