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

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

## 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.