# MKT 500 Chapter Notes - Chapter 13: Null Hypothesis, Bar Chart, Contingency Table

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12 Nov 2012
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Wk. 9 Chapter 13 Relationships between variables
Lecture on: November 6, 2012
What is a relationship between two variables?
- Relationship consistent and systematic linkage between the levels or labels for two
variables
Boolean relationships and cross-tabulation analysis
- Boolean relationship one in which the presence of one’s variable’s label is systematically
related to the presence of another variable’s label
- Characterizing a Boolean relationship with a graph:
o Stacked bar graph two variables are shown simultaneously on the same bar graph
each bar in the stacked bar chart stands for 100% and it is divided proportionately
by the amount of relationship that one variable shares with the other variable
- Cross-tabulation analysis analytical technique that assesses the statistical significance of
Boolean or categorical variable relationships
o Frequencies table contains the raw counts of the various Boolean relationships
found in the complete data set
o Chi-squared analysis examination of frequencies for two categorical variables in
the cross-tabulation table to determine whether the variables have a significant
relationship
o Observed frequencies raw counts
o Expected frequencies if there was no significant relationship
Expected frequency = (Cell column total*Cell row total)/Grand total
o Chi-squared = Sum of (observedi expectedi)2/expectedi
o How to interpret a significant cross-tabulation finding:
Set up cross-tab table with observed frequencies
Calculate expected frequencies
Calculate chi-square value
Determine critical chi-square using (#rows 1)*(#columns 1) = degrees of
freedom (using this number, find it in the critical value table)
Evaluate whether or not the null hypothesis of no relationship is supported
when the computed value is greater than the table value, reject null
hypothesis because there is a relationship
Liner relationships and correlation analysis
- Y= a+bx
- Correlation coefficient index number falling between the range of -1.0 and +1.0
o Communicates the strength and the direction of the linear relationship between two
metric variables
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## Document Summary

9 chapter 13 relationships between variables. Relationship consistent and systematic linkage between the levels or labels for two variables. Boolean relationship one in which the presence of one"s variable"s label is systematically related to the presence of another variable"s label. Characterizing a boolean relationship with a graph: stacked bar graph two variables are shown simultaneously on the same bar graph. Each bar in the stacked bar chart stands for 100% and it is divided proportionately by the amount of relationship that one variable shares with the other variable. Cross-tabulation analysis analytical technique that assesses the statistical significance of. Expected frequency = (cell column total*cell row total)/grand total: chi-squared = sum of (observedi expectedi)2/expectedi, how to interpret a significant cross-tabulation finding: Set up cross-tab table with observed frequencies. Determine critical chi-square using (#rows 1)*(#columns 1) = degrees of freedom (using this number, find it in the critical value table) Evaluate whether or not the null hypothesis of no relationship is supported.

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