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

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

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

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?

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

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)

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

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

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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

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

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

Applet Exploration Go to the website www.whfreeman.com/ips Register as a student Make sure to enter instructor’s email kdbrad2@uky.edu