Exam 1 Study Guide Answers

Bring paper, a calculator, and pencils with erasers. 

It will cover all material from the class and homework on univariate statistics.

It will not involve any SPSS use.

It will include:

• short answer questions  
• short essay questions  
• hand calculation questions  

The last two true/false questions do not have wrong answers.  (4 free points). 

I will provide the formulas on the exam.  You can bring in your Univariate Analysis Chart.

Each question on the exam identifies the number of points it is worth. 

The following topics are covered on the exam.

• hypotheses
• sampling (generally)
• causality
• level of measurement
• spuriousness
• frequency tables
• univariate statistics
• outliers

1.  Identify the level of measurement of the variables below:  2 points each                                       

a.       fear of crime; measured as no fear, some fear, a great deal of fear     (ordinal) 

b.       # of visits to a psychiatrist      (interval)

c.       grade in a statistics course; measured as A, B, C, D (ordinal)

d.       amount due/owed on federal tax form (interval or ratio)

e.       race   (nominal)                                                      

2.  Recently Self magazine summarized a study that found children of divorced couples get lower grades in school after the divorce than before the divorce.  Based on this research, Self advised their readers to track their children’s grades as a way of predicting future problems in their marriages.  Does this advice follow from the research findings?  Why or why not? 

This advice does not follow the research.  The research looked at divorce as an independent variable and grades as a dependent variable.  The advice makes grades an independent variable.  The causality is wrong.  Children's grades do not cause/influence parents' divorce.

3.  A social psychological theory posits that people with lower perceived social status marry earlier than people with higher perceived social status.   State the hypothesis that follows from this statement. 

Research Hypothesis: avg. marital age among people with lower perceived status  < avg. marital age among people with higher perceived status 

or

mean 1 < mean 2

mean 1 = avg. lower perceived status age at marriage
mean 2 = avg. higher perceived status age at marriage

4.  I think men with traditional beliefs about gender and men with more progressive beliefs about gender differ in the number of crimes they commit.   I ask a sample of men about their gender beliefs and how many crimes they committed last year.  State the hypothesis that follows from this statement. 

Research Hypothesis: The average crime rate of men with traditional gender beliefs does not equal the average crime rate of men with progressive gender beliefs

or

mean 1 ≠ mean 2

mean 1 = avg. crime rate of men with traditional gender beliefs
mean 1 = avg. crime rate of men with progressive gender beliefs

5.  How might a sample be biased?  How would that affect your statistical analyses?

It may over-represent Caucasians, and under-represent  African-Americans and Latino- Americans. Hence any of the findings that are influenced by race (most social science variables) may not be generalizable to the entire country or to minority groups.  The data could only be used to discuss what Caucasian Americans think.  

6. What is a spurious relationship? Give an example not used in class or in a homework assignment.  Be sure to identify the spurious variable and why it is a spurious variable.  

A spurious relationship is a relationship that appears to exist between an independent and dependent variable, but which is really caused by a third variable that influences both the independent and dependent variables and which is not being included in the analysis.

Examples from student exams:

• food intake influences weight (spurious variable = exercise)

• employment status influences poverty (spurious variable = the health of the economy, housing costs, number of children)

• gender influences income (spurious variable = education)

• race influences whether someone commits crime (spurious variable = poverty)

• moving influences whether or not you smoke (spurious variable = stress)

7.  Below is data on the number of pounds lost among participants in a health program.   
                                                                        

                        20, 10, 5, 0, 5, 10, 1                                                     

a.      Create a frequency table for this data. 

b.       What univariate statistics are appropriate for this data?  

All univariate statistics are appropriate because this variable is measured on an interval scale.  Mode, median, mean, range, standard deviation, variance (though the variance doesn't have much meaning as a summary statistic)

c.       Calculate the univariate statistics identified above.  

mode = 5 and 10  (2 points)
median = 5  (2 points)
range =  0-20 = 20  (2 points)

mean = 51/7 = 7.29  

standard deviation = 6.824 (see board for calculation) 

range =  20

d.  Are there any outliers in this data?  Indicate which method you choose to identify outliers and the value of the outlier(s).  

Using the 3 standard deviation below and above the mean rule, there are no outliers.

7.29 + and - 3(6.824) = -13.18 to 27.76

e.  Based on your answer to d, which measure of central tendency should you use to summarize this data?       Why?     

If you used the 2 or 3 standard deviation rule to identify outliers, there are no outliers. So you should use the mean as your measure of central tendency.

If you used the 99% percentile rule to identify outliers, there is one outlier so you should use the median as your measure of central tendency.

8.  Below is a frequency table and univariate statistics from SPSS on how often respondents have felt depressed in the last 4 weeks. This data is from the General Social Survey, year 2000.

Write a sentence about the meaning of the above statistics.  Do you find these results about depression in the U.S. surprising? Why or why not?

The mean has no meaning for ordinal (or nominal) data, nor does the standard deviation or the variance.

The median is 5, which means that half of Americans feel depressed rarely or never, and half of Americans feel depressed some to all of the time. 

The mode is 5, which means that the most common amount that Americans are depressed is a little bit of the time.

The range is 5, which means that across all Americans vary a great deal in how frequently they feel depressed. People feel depressed between none of the time to all of the time. 

These findings are surprising in that most Americans (66%) feel depressed. What does that say about American society?  Is our culture oppressive?  Or are we very sensitive?