SP 225Lecture 11

Introduction to Hypothesis Testing

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

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 legislator’s 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 author’s uncertain of this rank order? Why do the authors maintain it is necessary to analyze President Bush’s stated issue positions in order to interpret Senator Kerry’s 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 Journal’s liberal-to-conservative scorecard? Was the public well-served by the magazine’s publication of its analysis?

Research Questions

Are the elderly more likely to vote than the population as a whole?

Do college graduates really make more money?

Investigating Questions

Compare group statistics to population statistics

All data obtained through EPSEM sampling

Evaluating Claims

Reasons for differences between sample and population statistics:

Sampling variability Genuine differences

What CAN We Say?

We can give the probability there are genuine differences

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)

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?

Review of Scientific Method

The Wheel of Science

Hypothesis Testing5 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

Test Requirements

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

Null Hypothesis

Always a statement of ‘no difference’ The researcher’s belief is the alternative

hypothesis Null hypothesis can be disproven but

never proven

Alternative Hypothesis

Statement which is true when the null hypothesis is false

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

Decision Making Criteria

Probability of our observed statistic given the null hypothesis is true.

Exact value is called a p-value

SPSS TestUsing 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).

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)