Geography 226

Lab 8


Correlation

Science! true daughter of Old Time thou art!

Who alterest all things with thy peering eyes.

Why preyest thou thus upon the poet's heart,

Vulture, whose wings are dull realities?

- Edgar Allan Poe -


 

1.   As a medical geographer, you are investigating geographic trends in mortality. You have focused your research on mortality due to lung cancer and circulatory disease on southern Vancouver Island. Ten randomly selected health areas have been ranked (from lowest to highest) for male and female deaths resulting from the two diseases. The rankings are based on the standardized mortality ratio (SMR).

 

Lung Cancer

Circulatory Disease

 

Males

Females

Males

Females

Greater Victoria

5

2

4

2

Sooke

10

8

3

6

Saanich

2

1

1

1

Gulf Islands

1

3

2

3

Cowichan

4

5

5

5

Lake Cowichan

3

6

6

8

Ladysmith

9

7

9

10

Nanaimo

8

10

10

7

Qualicum

7

9

7

4

Alberni

6

4

8

9

  1. Which correlation coefficient would you use for these data? Why?
     
  2. Enter the data into an SPSS file. Conduct a correlation analysis to determine if there are significant correlations between:

    3. Source: Foster, L and Edgell, M. 1992. The Geography of Death: Mortality Atlas of British Columbia, 1985-1989. Western Geographical Series No. 26, University of Victoria.
     

    2.   The United Nations Educational, Scientific and Cultural Organziation (UNESCO) collects data on many aspects of economic and social well being for nations around the world. The variables listed below are in the file Nations.sav.

    Nation

    - country code

    Pop_gro

    - population growth rate (% per annum)

    Life_exp

    - life expectancy at birth (years)

    Fert

    - total fertility rate (births per woman)

    Energy

    - energy use (oil equivalent - kg per capita)

     2 a.   What type of relationship (direction and strength) do you think exists between each set of variables? Briefly   explain your rationale for each set.

     

    2 b.    What type of hypotheses (directional/non-directional) will you use for each individual relationship in this correlation analysis? Explain why.
     

    2 c.  Conduct an analysis to determine which variables are significantly correlated with each other (include the p-values in your analysis). Does the analysis support your theories? 

    Table for answers

     

    Pop vs life

    Pop vs Fertility

    Pop vs Energy

    Life vs  Fertility

    Life vs Energy

    Fertility  vs Energy

    Assumptions

     

     

     

     

     

    Hypotheses

     

     

     

     

     

     

     

     

     

     

    Significance value

     

     

    Probability distribution

     

     

    Critical values

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

 

Test statistic

 

 

Decision

 

 

 

 

 

 

 

 

 

 

Inference

 

 

 

 

 

 

 

 

 

 

2 d.  Can this correlation analysis be used to infer causal relationships between the variables? Explain why or why not.
 

2 e.  Examine the scatter plots for each significant correlation. Identify any problems that may affect the results of your correlation analysis.
(Note: you do not need to fix the problems).

 

3.   Investigators are studying a possible relationship between crime rates and education levels. The file Florida.sav contains the following variables for the 67 counties of Florida:

crime - crime rate (number of crimes per 1,000 residents).
educat - percentage of residents aged 25 and older with a high school or university education.
urban - percentage of the county’s residents living in an urban environment.

 

  1. What type of relationship (positive or negative) do you expect between crime and education? Explain your rationale.  
  2. Use SPSS to calculate the correlation between the two variables. Does the correlation coefficient support your theory? (Note: you do not need to conduct a significance test for this question, just look at the correlation values). 
  3. There are many factors associated with crime rates, including size of the urban population. Describe the kind of relationship you expect between the variables crime & urban and urban & education. Explain your rationale.
    4. Use SPSS to calculate a Pearson’s r for both sets of variables to confirm your theory about the relationships (Note: you do not need to conduct significance tests, just look at the correlation values).
  4. Conduct a partial correlation analysis between crime and education, controlling for the influence of urban. Do these results support your theory? (Visit the VassarStats site to learn more about partial correlation. Click on Chapter 3a on the sidebar).
  5. Based on your experiences above, explain why it is important to have a theory about the expected relationships before conducting the analysis.

    Visit the National Institute of Justice's Mapping and Analysis for Public Safety (MAPS) program for information on the geography of crime.

 


 

Show all your steps for conducting the analyses.
For SPSS instructions, go to the SPSS Help manual

Marking Guide (Total = 38)

Question

Mark

 

Question

Mark

Q1

a

1

Q3

a

6

b

6

b

1

Q2

a

1

c

6

b

2

d

2

c

3

e

3

d

4

 

e

3