Assessing Hypotheses: Means

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Assessing HypothesesMeans Graphs
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Lecture plan

• Hypotheses
• Cross-tabs, means, or graphs?
• Comparing means
• Creating and interpreting graphs

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Hypotheses

• What are hypotheses?
• Testable statements about empirical relationships
• Derived from theory.
• Examples
• The more religious are more Republican.
• Democratic states do not go to war with one
  another.
• Droughts depress the vote of the Democratic
  party.
• How do we test hypotheses?
• It depends on the data.

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Continuous DV

• Crosstabs works for nominal and ordinal dependent
  and independent variables
• But what do we do when the dependent variable is
  interval and the independent variable is nominal?
• Compare means Bar chart (more on this later).
• What do you do when the dv is interval and the iv
  is ordinal?
• Line graph (more on this later).
• When both are interval?

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Continuous v. Nominal

• Lets start with a question that has puzzled
  social scientists for centuries
• Do Canadians have more fun than Brits and
  Americans?
• So we hypothesize Canadians will report higher
  levels of fun than Brits and Americans.
• Validity problems?

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Do Canadians Have More Fun?

• Fortunately, you have a thermometer measuring
  the self-reported fun experienced by Canadians,
  Brits, and Americans (technically called the
  Fun-O-Meter).
• What is your (continuous) DV?
• What is your (nominal) IV?
• How would you test the hypothesis that Canadians
  have more fun than Brits or Americans?

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Comparing Means

• Right-O!
• Compare the mean of the dependent variable across
  values of the independent variable.
• This is how you do it

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Comparing Means

• Who has more fun?

Nationality Mean N Std. Deviation
Canadians 98.50 3 4.163
British 75.750 4 13.744
Americans 91.667 2 .70711
Total 86.111 9 13.37
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Graphical Comp of Means Bar Chart
TV hours per week

• Continuous v. categorical (nom, ord)
• This is not a frequency bar chart!

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Howd that happen?

• Graphs ? Bar
• Simple
• Summaries
• Define

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Bye Bye Nominal Hello Line Graphs

• Works for all levels of measurement except
  nominal data
• Continuous v. nominal (ordinal) Complements
  means comparison.
• Ordinal v. Ordinal (numerically coded)
• Continuous v. Continuous
• Lets look at ourselves again
• Two ordinal variables
• 7-category Dem Party L-R Placement Variable
• 5-category Religious Attendance Variable
• Do more religiously observant students view the
  Dem Party differently than less observant
  students?

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Line Graph Dem L-R v. Religious

• Negative Relationship

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Line Graph Rep L-R v. Religious

• positive
• or
• curvilinear

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Howd that happen?

• Graphs ? lines
• Simple
• Summaries for groups of cases
• Define
• Next
• Other summary function
• Enter variables
• OK

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Continuous v. Continuous?

• Hmm what if BOTH the dependent and independent
  variables are continuous?
• DV Hours spent exercising and playing sports.
• IV Hours spent watching TV.
• What would happen if we just line graphed TV
  against exercise???

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Hmm
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• This rolling average takes the mean of the
  original observation and those two hours before
  and after.

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• Or, we can categorize one of the variables.