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Chapter 8  INFERENTIAL STATISTICS: CORRELATION

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Presentation on theme: "Chapter 8  INFERENTIAL STATISTICS: CORRELATION"— Presentation transcript:

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


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