Welcome to the Class of Bivariate Data Analysis

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Welcome to the Class of Bivariate Data Analysis
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Bivariate Analysis

• Correlation Interval or Ratio vs. I or R
• e.g. GPA(i) vs. SAT(i)
• T-test of mean Interval or Ratio vs. Binary
  Nominal
• e.g. GPA(i) by Gender(n)
• Cross tabulation Nominal or Ordinal vs. N or O
• e.g. Gender(n) by Major(n)

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Cross Tabulations

• Relationship among and between variables
• Sample divided into subgroups
• gender
• age
• student status
• How dependent variables vary by subgroup

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Gender by Favorite Type of Soft Drink
Soft Drink Type
Gender

• Marginal totals
• 65 people prefer diet soft drink, while 35 prefer
  regular.
• Note sample is near to representative of the
  population with 54 males and 46 females.
• Does soft drink type depend on gender?
• It would seem so from the table.
• Need to compute percentages.

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Gender by Preference Preference
by Gender

• Mathematically equivalent, different messages.
• Soft drink preference is affected by gender.
• 83 of females preferred diet soft drink, while
  only 50 of males preferred diet soft drink.
• Gender is affected by soft drink preference.
• 58 of people who preferred diet soft drink were
  females, while only 42 of people who preferred
  diet soft drink were males.
• Does this mean that preference produces gender?

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Rule Percentage Calculations

• Calculate s in the direction of the causal
  factor, or across the effect factor.
• In this case
• Gender is logically the cause or independent
  variable
• Independent of whether the person drinks diet or
  regular pop
• Preference for diet or regular pop, is logically
  the effect or dependent variable
• Dependent on gender

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Correct Calculation of Percentage
Cross tabulation of gender by type of soft drink
(n100).
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Conditional Probability

• Probability of one event occurring given that
  another event has occurred or will occur.
• Be careful of past and present behavior.
• Probability that a person prefers to drink diet
  pop GIVEN that they are female makes sense.
• Notion that a person is female GIVEN that she
  drinks pop does not.

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What about this one?

• Preference for soft drink type
• Perception of weight
• Last soft drink purchased
• Perception of weight

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Soft Drink Type
Soft Drink Type

• Marginal Totals
• 65 people prefer to drink diet pop, while 35
  prefer to drink regular pop (as before).
• Cross tabulation
• 88 of people who think they are overweight
  prefer to drink diet pop, while only 25 of
  people who think they are underweight drink diet
  pop.
• Only 12 of people who think they are overweight
  drink regular pop, while 75 of people who think
  they are underweight drink regular pop.

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Multivariate Analysis

• Regression
• Dependent variable Interval or Ratio
• Independent variable Interval, Ratio, and Binary
• e.g. GPA(i) on SAT(i), Gender(n)
• ANOVA
• Dependent variable Interval or Ratio
• Independent variable Nominal or Ordinal
• e.g. GPA(i) on Major(n), Gender(n)

Plus, Discriminant, Factor, Correspondence,Canonic
al, SEM