1. 4/4/2019
Correlations

2. Distinguishing Characteristics of Correlation
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Distinguishing Characteristics of Correlation
Correlational procedures involve one sample containing all pairs of X and Y scores
Neither variable is called the IV or DV
Use the individual pair of scores to create a scatterplot

3. Correlation Coefficient
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Correlation Coefficient
Describes three characteristics of the relationship:
Direction
Form
Degree

4. What Is A Large Correlation?
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What Is A Large Correlation?
Guidelines:
0.00 to <±.30 – low
±.30 to <±.50 – moderate
>±.50 – high
While 0 means no correlation at all, and 1.00 represents a perfect correlation, we cannot say that .5 is half as strong as a correlation of 1.0

5. 4/4/2019
Pearson Correlation
Used to describe the linear relationship between two variables that are both interval or ratio variables
The symbol for Pearson’s correlation coefficient is r
The underlying principle of r is that it compares how consistently each Y value is paired with each X value in a linear manner

6. Calculating Pearson r There are 3 main steps to r:
4/4/2019
Calculating Pearson r
There are 3 main steps to r:
Calculate the Sum of Products (SP)
Calculate the Sum of Squares for X (SSX) and the Sum of Squares for Y (SSY)
Divide the Sum of Products by the combination of the Sum of Squares

7. 4/4/2019
1) Sum of Products
To determine the degree to which X & Y covary (numerator)
We want a score that shows all of the deviation X & Y have in common
Sum of Products (also known as the Sum of the Cross-products)
This score reflects the shared variability between X & Y
The degree to which X & Y deviate from the mean together
SP = ∑(X – MX)(Y – MY)

8. Sums of Product Deviations
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Sums of Product Deviations
Computational Formula
n in this formula refers to the number of pairs of scores

9. 4/4/2019
2) Sum of Squares X & Y
For the denominator, we need to take into account the degree to which X & Y vary separately
We want to find all the variability that X & Y do not have in common
We calculate sum of squares separately (SSX and SSY)
Multiply them and take the square root

10. 4/4/2019
2) Sum of Squares X & Y
The denominator: =

11. Hypothesis testing with r
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Hypothesis testing with r
Step 1) Set up your hypothesis
Step 2) Find your critical r-score
Alpha and degrees of freedom

12. Hypothesis testing with r
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Hypothesis testing with r
Step 3) Calculate your r-obtained
Step 4) Compare the r-obtained to r-critical, and make a conclusion
If r-obtained < r-critical = fail to reject Ho
If r-obtained > r-critical = reject Ho

13. Coefficient Of Determination
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Coefficient Of Determination
The squared correlation (r2) measures the proportion of variability in the data that is explained by the relationship between X and Y
Coefficient of Non-Determination (1-r2): percentage of variance not accounted for in Y

14. Correlation in Research Articles
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Correlation in Research Articles
Coleman, Casali, & Wampold (2001). Adolescent strategies for coping with cultural diversity. Journal of Counseling and Development, 79,

15. Other Types of Correlation
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Other Types of Correlation
Spearman’s Rank Correlation
variable X is ordinal and variable Y is ordinal
Point-biserial correlation
variable X is nominal and variable Y is interval
Phi-coefficient
variable X is nominal and variable Y is also nominal
Rank biserial
variable X is nominal and variable Y is ordinal