Variables

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Variables

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

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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, subjects response
• SAT score, first year college GPA

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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

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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?

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Case 3 Two quantitative variables

• Plot observed data on a graph
• Horizontal (X) axis, one variable
• Vertical (Y) axis, other variable

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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)

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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

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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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Lets give it a try!
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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

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• 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

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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

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Applet Exploration

• Go to the website
• www.whfreeman.com/ips
• Register as a student
• Make sure to enter instructors email
• kdbrad2_at_uky.edu