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Correlations - Information and Exercises! (Chapter Two)

Before you begin the correlations exercises, here is a quick review:

Characteristics of Correlations

  1. Indication of a relationship between variables
    1. Positive correlation - high variables of one variable are associated with high values of the other; low values of one variable are associated with low values of the other
    2. Negative correlation - high values of one variable are associated with low values of the other
    3. Uncorrelated - a correlation coefficient of zero would mean there is no relationship between the variables
  2. Strength of relationship between the two variables expressed as correlation
    1. Possible range of correlation coefficients is -1 to +1
      1. -1 ==> a strong negative relationship
      2. +1 ==> indicated a strong positive relationship
      3. 0 ==> indicated no relationship
    2. The closer to either +1 or -1, the stronger the relationship
    3. The closer to 0, the weaker the relationship

Exercises

  1. Which of the following coefficients indicates the strongest correlation?
    1. -0.8
    2. +0.5
    3. +0.7
    4. -0.2
  2. Which of the following coefficients indicated the weakest correlation?
    1. -0.9
    2. +0.8
    3. -0.2
    4. +0.1
  3. A researcher finds that the more alcohol a student drinks the morning of an important exam, the lower that student's exam grade will be. Is this a positive or negative correlation?
  4. A researcher finds that as men decrease their intake of foods high in cholesterol, their chance of having a heart attack decreases. Is this a positive or negative correlation?
  5. A study of married couples showed that the longer they had been married, the more similar their opinions on social and political issues were. Is this a positive or negative correlation?
  6. A researcher is conducting a study investigating the relationship between ring size and IQ. In some subjects, as ring size increases, so does IQ. But in other subjects, as ring size decreases, IQ increases. And still in other subjects, as ring size increases, IQ decreases. And still in other subjects, as ring size decreases, IQ decreases. Is this a positive or negative correlation?

 

Answers

1. The strongest correlation is -0.8. Remember, the number indicates the strength of the relationship. The sign just indicated the direction. Sign does not indicate strength.

2. The weakest correlation is +0.1.

3. This is a negative correlation. As alcohol consumption increases, grade decreases. They each move in a different direction: as one goes up, the other goes down.

4. This is a positive correlation: both variables are moving in the same direction. As cholesterol consumption decreases, heart attacks decrease.

5. Positive correlation - they are both moving in the same direction. As years of marriage increase, opinion similarity also increases.

6. Trick question! Ha Ha! There is no relationship. (Sorry, had to thrown one in).

And remember: all this information is purely supplemental. It cannot replace coming to class, taking notes, and reading your text!!!!