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Understanding Correlations-- Sample answers

This practice exercise was distributed in class on Fri., Sept. 3.  To go back to the questions, click on the answers.

Correlational studies show relationships between variables.   If high scores on one variable predict high scores on the other, the correlation is positive.  Likewise, low scores on one predicting low scores on the other would still reflect a positive correlation because the change in one is in the same direction as the other.

pos_corr.jpg (10269 bytes)

A negative corelation is found when change in one variable is accompanied by change in the opposite direction in the other variable.neg_corr.jpg (10138 bytes)

Showing that two variables are related does not justify claiming that a causal relationship exists.  There may be a causal relationship, but other explanations usually exist.  For example, the variables may be related because both have a causal relationship with a third variable.  So, if you find that A is correlated with B, any of the following may explain the cause underlying that relationship:cause.jpg (4988 bytes)

For each of the correlational studies described below, decide whether the correlation is positive or negative and give two alternative explanations for each finding.

1.  A study of married couples showed that the longer they had been married, the more similar their opinions on social  and political issues were.

Positive or negative?   Positive

Explanation 1:

Couples that have been married longer could become more similar or being more similar may lead to more longevity in marriage.

Explanation 2:

Having had similar life experiences may have made them develop similar beliefs and made them more likely to stay together.

2.    An intelligence test was given to all the children in an orphanage.  The results showed that the longer children had lived in the orphanage, the lower their IQ scores.

Positve or negative?   Negative

Explanation 1:

Orphanage   environment has an adverse effect on cognitive development.

Explanation 2:

More intelligent children are more likely to be adopted.

3.    In a study of American cities, a relationship was found between the number of violent crimes and the number of stores selling violence-depicting pornography.

Positive or negative?   Positive

Explanation 1:

Violent pornography stimulates violent behavior or  people with violent tendencies are attracted to violent pornography.

Explanation 2:

Both the violent crime and the number of stores selling violent pornography are related to the size of the city.

4.    A college professor found that the more class absences students have, the lower their grade in the course tends to be.

Positive or negative?   Negative

Explanation 1:

Absent students miss important course information.

Explanation 2:

Students with multiple responsibilities (jobs, family obligations) find it dificult making it to classes and also have trouble finding time to study.

5.    A politician running against a candidate who had been in office for eight years pointed out that violent crime had increased during those eight years even though the administration appropriated more and more money to fight crime.

Positive or negative? Positive

Explanation 1:

The money appropriated to control crime was poorly spent or  the rising crime rates forced the increase in spending.

Explanation 2:

The city grew requiring increased spending on policing but also resulting in increased crime (both due, therefore, to the increase in population and not related to each other.)

 

(Adapted from V. Diehl (1999).  New York: Longman.)

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