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Correlation and Regression in Research

 Applications to research: Field: "Determinants of Abortion Policy in Developed Nations"?

What accounts for variations across nations in abortion policies?
Proposed ten explicit hypotheses, Examples:
The greater the proportion of Catholics in a country, the more conservative the abortion policy.
The greater the strength of leftist, non-communist parties, the more liberal the abortion policies.
Your research papers should contain hypotheses which are equally explicit in FORM as Field's.
Field's tests of her hypotheses:
Used data from 29 nations.
Created abortion policy scale according to legal grounds for abortion:
1 = No acceptable reasons
2 = life-saving only
3 = life-saving and health-preserving
4 = medical/social circumstances allowable
5 = Social reasons other than age and number of births
6 = Simply on request of the woman
Treated ordinal data as interval
Scale scores varied from Ireland (1) to East Germany (6)
Findings for all 29 nations and for 22 non-Communist nations:
ALL 29 Nations: correlation between % Catholic and abortion scale: r = -.47
NON-COMMUNIST: correlation between % Catholic and abortion scale: r = -.80
NON-COMMUNIST: correlation between % Socialist in govt and scale: r = .51

Earlier versions of SPSS contained a simple PLOT procedure that also produced regression statistics. SPSS 10 has dropped that simple procedure, but one can get a plot with regression statistics. As described by Ms. Wuyi Wang at SPSS, Inc., this is the procedure, with illustrations from me:

  • Go to Graphs->Interactive->Scatterplot
  • drag and drop the variables to the vertical axis and horizontal axis.
  • It should look like this:
  • Right-click on each variable to make sure that Scale is selected
    • [SPSS interprets data without decimals as "Ordinal"]
    • (if the variable is tagged as Ordinal no regression line will be shown).
  • Click on the Fit tab. Select Regression from the drop-down list (the default is None).
  • Leave all other settings as default.

Click OK. A scatterplot made this way has the regression line and R-squared.

Assumptions about the distributions of variables involved in correlational analysis

For maximum utility in analysis, correlation and regression assumes that both variables have unimodal, symmetrical distributions -- at least that one or the other variable is not highly skewed in either direction
In a technical sense -- and using a term to be defined explicitly later -- both variables are assumed to approximate a normal distribution, which looks like this:
Problems arise if either variable departs from a normal distribution
If one variable is skewed away from a normal distribution, and the other is not, the correlation can never equal 1.
If both variables are skewed away from normal, the relationship is likely to be artificially high.

How to convert skewed distributions to one that are more "normal"

Use the COMPUTE command in SPSS to transform the variable by pulling in the outliers
See the transformation of a variable on "CIVIL DISORDER" computed for nations across the world