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Chapter 13

Chapter 13 – Relationships between variables

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MKT 500
Helene Moore

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 2 o Chi-squared = Sum of (observed – ixpected) /eipected i 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 - Covariation – defined as the amount of change in one varia
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