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Correlation - Correlation Describing the Relationship...

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Correlation Describing the Relationship between Two Variables The descriptive statistics we have studied so far have been univariate . That is, we use them to describe the shape, center and spread of scores we have for a single variable. It is rare to study just one variable. Often we study numerous variables, and we want to understand how a variable is related to another variable. Example: What is the relationship between optimism and depression? Perhaps we propose that those who are more optimistic tend to be less depressed. We would need to do some research to see if this is true. Let’s say we have a sample of 11 people and each one completes a questionnaire measuring depression and a separate questionnaire measuring optimistic thinking. Optimism Depression Subject Score Score 1 2 13 2 6 14 3 3 17 4 7 14 5 10 18 6 12 12 7 14 5 8 17 12 9 20 3 10 24 8 11 21 9 M = 12.36 M = 11.36 s = 7.50 s = 4.70 Techniques for Describing a Bivariate Relationship: Graphing and Correlation Coefficient Graphing Scatterplot: Graph used to show the relationship between 2 variables Scatterplot for optimism and depression 0 5 10 15 20 0 5 10 15 20 25 30 Optimism Depression A. Constructing a scatterplot 1. Horizontal axis is used for independent variable (X) 2. Vertical axis is used for the dependent variable (Y) 3. Draw axes approximately same length 4. Plot a point for each pair of scores
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Page 2 of 8 B. What to look for in a scatterplot 1. Form of relationship: Linear or curvilinear Curvilinear 0 10 20 30 40 50 60 70 80 0 20 40 60 80 IV DV Linear 0 10 20 30 40 50 60 70 80 0 20 40 60 80 IV DV Linear 0 10 20 30 40 50 60 70 80 0 20 40 60 80 IV DV 2. Strength or degree of relationship: The closer the points are to forming a single line, the stronger the relationship Perfect 0 10 20 30 40 50 60 70 80 0 20 40 60 80 IV DV Strong 0 10 20 30 40 50 60 70 80 0 20 40 60 80 IV DV Moderate 0 10 20 30 40 50 60 70 80 0 20 40 60 80 IV DV Weak 0 10 20 30 40 50 60 70 0 20 40 60 80 IV DV
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Page 3 of 8 3. Direction of relationship: Positive or negative a. Positive: scores on one variable are associated with scores at a similar level on the other variable High scores on X are associated with high scores on Y Low scores on X are associated with low scores on Y b. Negative: scores on one variable are associated with scores at the opposite level on the other variable High scores on X are associated with low scores on Y Low scores on X are associated with high scores on Y Positive Relationship 0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 IV DV Negative Relationship 0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 IV DV Note: With weak relationships, it may be hard to discern the direction of the relationship from the scatterplot.
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