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**preview**shows half of the first page. to view the full**3 pages of the document.**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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