SP 225 Lecture 11

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SP 225Lecture 11

• Introduction to Hypothesis Testing

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The Most Liberal Senator

• Article by the National Journal rated Senator
  Kerry as the most liberal member of the Senate
  during the 2004 Presidential Election
• Aid decision-making by simplifying large amounts
  of data
• Can be misapplied
• Can be an essential tool for interest groups

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Questions

• Explain the National Journal's methodology for
  determining its scores. What method do the
  authors use to reexamine the roll call data used
  by the National Journal?
• From a statistical point of view, what is the
  importance of the absentee data presented in
  Table 1 for the analysis of legislators voting
  records?
• What factors influence a legislators voting
  decisions? How do these issues complicate the
  interpretation of voting records?
• Explain the format and the purpose of the
  graphing technique employed in figures 1-4.
• According to Figure 3, where does President Bush
  stand in comparison with the members of the
  Senate for those 62 votes? What makes the
  authors uncertain of this rank order? Why do the
  authors maintain it is necessary to analyze
  President Bushs stated issue positions in order
  to interpret Senator Kerrys voting record
  properly?
• Using the results shown in figure 4, explain how
  selecting a larger set of voting decisions over a
  longer period of time results in a different rank
  ordering.
• What was your overall assessment of the validity
  of the National Journals liberal-to-conservative
  scorecard? Was the public well-served by the
  magazines publication of its analysis?

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Research Questions

• Are the elderly more likely to vote than the
  population as a whole?
• Do college graduates really make more money?

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Investigating Questions

• Compare group statistics to population statistics
• All data obtained through EPSEM sampling

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Evaluating Claims

• Reasons for differences between sample and
  population statistics
• Sampling variability
• Genuine differences

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What CAN We Say?

• We can give the probability there are genuine
  differences

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Making Probability Statements

• We are 95 confident there is a difference in
  income between men and women
• Benadryl makes patients more drowsy than Claritin
  (95 confident)

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Example of Mean Test

• Nationally, the population as a whole watches 6.2
  hours of TV per day. A random sample of 1,017
  senior citizens reports watching an average of
  5.9 hours per day with a standard deviation of
  .7. Is the there a difference between the amount
  of television senior citizens watch as compared
  to the population as a whole?

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Review of Scientific Method
The Wheel of Science
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Hypothesis Testing

• 5 Step Process
• Making assumptions about meeting test
  requirements
• Stating the null and alternative hypothesis
• Selecting the sampling distribution and
  establishing the critical region
• Making a decision and interpreting the test
  results

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Test Requirements

• Randomly collected data
• Interval-ratio data
• Normally distributed or large sample size

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Null Hypothesis

• Always a statement of no difference
• The researchers belief is the alternative
  hypothesis
• Null hypothesis can be disproven but never proven

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Alternative Hypothesis

• Statement which is true when the null hypothesis
  is false

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Selecting a Distribution

• Currently, only use the normal distribution
• Size of the critical region determines the level
  of certainty desired
• Rejection region is the range of z-scores where
  the null hypothesis is rejected
• Alpha is the level of uncertainty

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Decision Making Criteria

• Probability of our observed statistic given the
  null hypothesis is true.
• Exact value is called a p-value

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SPSS Test

• Using SPSS and GSS test the following claims
• Extreme liberals sampled in the GSS share the
  opinion of the general population when asked if
  homosexuals should be allowed to become teachers
  (colhomo).
• Extreme conservatives sampled in the GSS share
  the opinion of the general population when asked
  if homosexuals should be allowed to become
  teachers (colhomo).

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Essay

• In the GSS, respondents are asked to rank their
  ideological beliefs (polviews)on a scale from 1
  to 7, where 1 represents extremely liberal and 7
  represents extremely conservative. Choose one
  ideology, either extremely liberal or extremely
  conservative, and write an essay describing the
  difference in beliefs between people sampled in
  GSS rating themselves as extremely ideological
  and the general population. Use any three
  measures that show a significant difference.
  Complete a full hypothesis test for each variable
  including the hypotheses, result and conclusion.
  Staple all SPSS output and calculations to your
  final essay. (1-2 pages. Due in 1 week)