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Correlation (Whenever two scores have exactly the same value, their ranks…
Correlation
Whenever two scores have exactly the same value, their ranks should also be the same. This is accomplished by the following procedure.
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- Assign a rank (first, second, etc.) to each position in the ordered list.
- When two (or more) scores are tied, compute the mean of their ranked positions, and assign this mean value as the final rank for each score.
When the Pearson correlation formula is used with data from an ordinal scale (ranks), the result is called the Spearman correlation. The Spearman correlation is used in two situations.
First, the Spearman correlation is used to measure the relationship between X and Y when both variables are measured on ordinal scales.
the Spearman correlation can be used as a valuable alternative to the Pearson correlation, even when the original raw scores are on an interval or a ratio scale. As we have noted, the Pearson correlation measures the degree of linear relationship between two variables—that is, how well the data points fit on a straight line.
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A correlation is a numerical value that describes and measures three characteristics of the relationship between X and Y. These three characteristics are as follows
- The Direction of the Relationship The sign of the correlation, positive or negative, describes the direction of the relationship.
In a positive correlation, the two variables tend to change in the same direction: as the value of the X variable increases from one individual to another, the Y variable also tends to increase; when the X variable decreases, the Y variable also decreases.
In a negative correlation, the two variables tend to go in opposite directions. As the X variable increases, the Y variable decreases. That is, it is an inverse relationship.
- The Form of the Relationship In the preceding salary and weight examples, the relationships tend to have a linear form; that is, the points in the scatter plot tend to cluster around a straight line. We have drawn a line through the middle of the data points in each figure to help show the relationship. The most common use of correlation is to measure straight-line relationships. However, other forms of relationships do exist and there are special correlations used to measure them.
3.The Strength or Consistency of the Relationship Finally, the correlation measures the consistency of the relationship. For a linear relationship, for example, the data points could fit perfectly on a straight line. Every time X increases by one point, the value of Y also changes by a consistent and predictable amount.
Perfect Correlation : A relationship where the actual data points perfectly fit the specific form being measured. For a Pearson correlation, the data points fit perfectly on a straight line.
The Pearson correlation measures the degree and the direction of the linear relationship between two variables.
Sum of products : A measure of the degree of covariability between two variables; the degree to which they vary together.
A partial correlation measures the relationship between two variables while controlling the influence of a third variable by holding it constant.
Point-biserial correlation : A correlation between two variables where one of the variables is dichotomous.
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