Understanding Variables and Correlation: Bivariate Data Analysis, Slides of Statistics

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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 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

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

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

 1  r  1