1. Chapter 8  INFERENTIAL STATISTICS: CORRELATION
Understanding Statistics for International Social Work and Other Behavioral Sciences
Serge Lee, Maria C Silveira Nunes Dinis, Lois Lowe and Kelly Anders (2015). Oxford University Press

2. THE MEANING OF CORRELATION
Correlation is used to study numerical statements about the relationship between two interval/ratio variables. It is also used to examine the strengths and variations of the relationship between two interval/ratio level variables
Pearson Correlation Coefficient (Pearson r), is the statistical test. It is also called Product-moment correlation coefficient
Correlation does not presume causation
Correlation is highly spurious
The correlation coefficient will always be ±1.0
A value of 0.00 represents a complete lack of correlation
A value of +1.0 represent a perfect positive correlation
A value of -1.0 represent a perfect negative correlation

3. DIRECTION OF PEARSON r Perfect Correlation No Correlation
Domestic violence knowledge
Likelihood one will abuse own spouse
X-axis
Y-axis
Domestic violence knowledge
Likelihood one will abuse own spouse
X-axis
Y-axis
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

4. DIRECTION OF THE PEARSON r CONTINUES
Positive Correlation
Negative Correlation
Socialization skills of children
Family size
X-axis
Y-axis
Domestic violence knowledge
Likelihood one will abuse own spouse
X-axis
Y-axis
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

5. THE COMPUTATIONAL FORMULA
The Pearson’s Product Moment Correlation Coefficient (r) r =

6. COMPUTING A SITUATION
Example. X = Family size; Y = Socialization skills
r = .8685; p = .05
At the 95% confidence interval, two-tailed hypothesis, there was a strong correlation between socialization skills of children and the size of family (r = , p < .05).

7. THE RANGE OF CORRELATION COEFFICIENT
When will terms such as weak, moderate, strong, and very strong (extremely strong) be used with regard to relationship? Possible suggestions:
Base conclusion on the p-value. Smaller p-value indicates stronger relationship.
Factor the sample size into findings. When the sample size is small, a larger coefficient is needed to reject the null hypothesis
Lee. Dinis, Lowe, Anders (2015). Understanding statistics for international social work and other behavioral sciences. Oxford University Press

8. COEFFICIENT OF DETERMINATION
When two interval/ratio variables are correlated, the variance plays a crucial role. When the correlation coefficient is squared (), and then multiply by 100%, the product becomes known as the coefficient of determination.
The result represents the proportion of variance in the dependent variable that is explained by the independent variable
The coefficient of determination represents the strength or magnitude of the variables under investigation