1. Variables Dependent variable: measures an outcome of a study
Independent variable: explains or causes changes in the response variables

2. Bivariate Data
We often make two observations on each subject. We call such data bivariate data.
Examples:
beliefs on abortion, political preference
height of a person, weight
dosage of drug, subject’s response
SAT score, first year college GPA

3. Case 1: Both variables qualitative
Cross tabulation table
Rows represent categories of 1st variable
Columns represent categories of 2nd variable
Count the number of observations falling into each combination of categories

4. Case 2: One qualitative variable, one quantitative variable
Side by side presentation of dot plots, box plots, 5 number summaries
How do the results differ?

5. Case 3: Two quantitative variables
Plot observed data on a graph
Horizontal (X) axis, one variable
Vertical (Y) axis, other variable

6. Scatterplots
A scatterplot shows the relationship between two quantitative variables measured on the same individuals.
If applicable,
Independent variable placed on horizontal axis (So, usually labeled as X)
Dependent variable place on vertical axis (So, usually labeled as Y)

7. Examining a Scatterplot
Form
Linear relationships, where the points show a straight-line pattern
Curved relationships
Clusters
Direction
Positive association
Negative Association
Strength
Determined by how close points in the scatterplot lie to a simple form such as a line

8. Examining a Scatterplot
In any graph of data, look for the overall pattern and for deviations from that pattern.
Two variables are positively associated when above-average values of one tend to accompany above-average values of the other and below-average values also tend to occur together
Two variables are negatively associated when above-average values of one accompany below-average values of the other and vice-versa

9. Let’s give it a try!

10. Correlation
Measures the direction and strength of the linear relationship between 2 quantitative variables.
Positive r suggests large values of X and Y occur together and that small values of X and Y occur together
Negative r suggests large values of one variable tend to occur with small values of the other variable

11. r = 1; all data on straight line with positive slope
r = -1; all data on straight line with negative slope
r = 0; no linear relationship
The stronger the linear relationship, the larger |r|
Existence of correlation does not imply cause/effect

12. Correlation: Need to Know(s)
No distinction between independent and dependent variable
Both variables must be quantitative
Correlation uses standardized values, so it does not change when we change the unit of measurement
Measures only the linear relationship
Correlation is strongly affected by a few outlying observations, so it should be used with caution when outliers appear in scatterplots

13. Applet Exploration Go to the website www.whfreeman.com/ips
Register as a student
Make sure to enter instructor’s