1. Summarising and presenting data - Bivariate analysis
LIS 570
Summarising and presenting data -
Bivariate analysis

2. Association Example: gender and voting
Are gender and party supported associated (related)?
Are gender and party supported independent (unrelated)?
Are women more likely than men to vote labor? Are men more likely to vote Liberal?

3. Association Correlation Cross Tabulation Coefficient
Association in bivariate data means that
certain values of one variable tend to occur
more often with some values of the second
variable than with other variables
of that variable (Moore p.242)
Correlation
Coefficient
Cross Tabulation

4. Cross Tabulation Tables
Designate the X variable and the Y variable
Place the values of X across the table
Draw a column for each X value
Place the values of Y down the table
Draw a row for each Y value
Insert frequencies into each CELL
Compute totals (MARGINALS) for each column and row

5. Determining if a Relationship Exists
Compute percentages for each value of X (down each column)
Base = marginal for each column
Read the table by comparing values of X for each value of Y
Read table across each row
Terminology
strong/ weak; positive/ negative; linear/ curvilinear

6. Cross tabulation tables
Occupation
Calculate
percent
Vote
Read
Table
(De Vaus pp )

7. Cross tabulation
Use column percentages and compare these across the table
Where there is a difference this indicates some association

8. Describing association
Strong - Weak
Direction
Strength
Positive - Negative
Nature
Linear - Curvilinear

9. Describing association
Two variables are positively associated when larger values of one tend to be accompanied by larger values of the other
The variables are negatively associated when larger values of one tend to be accompanied by smaller values of the other
(Moore, p. 254)

10. Describing association
Scattergram
a graph that can be used to show how two interval level variables are related to one another Y Y
Variable N
Shoe
size
Age X
Variable M X

11. Description of Scattergrams
Strength of Relationship
Strong
Moderate
Low
Linearity of Relationship
Linear
Curvilinear
Direction
Positive
Negative

12. Description of scatterplotsY Y X X
Strength and direction Y Y X X

13. Description of scatterplotsY Y
Nature X X
Strength and direction Y Y X X

14. Correlation Correlation coefficient
number used to describe the strength and direction of association between variables
Very strong = .80 through 1
Moderately strong = .60 through .79
Moderate = .50 through .59
Moderately weak = .30 through .49
Very weak to no relationship 0 to .29
-1.00
Perfect Negative
Correlation
0.00
No relationship
1.00
Perfect Positive
Correlation

15. Correlation Coefficients
Nominal
Phi (Spss Crosstabs)
Cramer’s V (Spss Crosstabs)
Ordinal (linear)
Gamma (Spss Crosstabs)
Nominal and Interval
Eta (Spss Crosstabs)

16. Correlation: Pearson’s r (SPSS correlate, bivariate)
Interval and/or ratio variables
Pearson product moment coefficient (r)
two interval normally distributed variables
assumes a linear relationship
Can be any number from
0 to -1 : 0 to 1 (+1)
Sign (+ or -) shows direction
Number shows strength
Linearity cannot be determined from the coefficient r = .8913

17. Summary Bivariate analysis crosstabulation Correlation and scattergram
X - columns
Y - rows
calculate percentages for columns
read percentages across the rows to observe association
Correlation and scattergram
describe strength and direction of association