Correlation Types and Their Uses Essay

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Statistical MethodWhat the Statistical Method DoesType of Research Question Applicable
Pearson correlationAssesses the strength and direction of the linear correlation between two variables.
Produces the number ranging from -1 to 1. The closer the value is to 1 or -1, the stronger the correlation. If the value is -1 or 1, then the relationship can be expressed as a linear function; if the value is 0, there is no correlation (Field, 2013)
Questions exploring the linear relationship between two continuous variables that are not correlated in a non-linear way (e.g., the scatter plot does not show a curvilinear correlation)
Spearman correlationEstimates whether a relationship between two variables is monotonic, and the direction of that relationship.
Produces the number ranging from -1 to 1; values of 1 or -1 indicate that the variables are perfectly monotonic functions of one another (Warner, 2013)
Questions which explore the relationship between two ordinal, interval, or ratio variables to assess whether this relationship is monotonic (Warner, 2013)
Kendall rank correlationAssesses whether a relationship between two variables is monotonic, and the direction of that relationship. An alternative to Spearman correlation if there are many tied ranks in the data (i.e., many scores have the same rank) (Field, 2013)Questions that assess whether there is a monotonic relationship between two ordinal, interval, or ratio variables which have many tied ranks (Warner, 2013)
Point-biserial correlationEstimates the strength and direction of a relationship between two variables; an alternative for Pearson correlation for cases when one variable is dichotomous (Field, 2013)Questions assessing the strength of the relationship between two variables, one of which is dichotomous, whereas the other is interval/ratio (Field, 2013)

On the whole, the four correlation coefficients in question are used to assess the relationship between two variables. All these analyses produce a number ranging from -1 to 1, where -1 denotes a perfect negative correlation (a linear or monotonic function), 1 indicates a perfect positive correlation (a linear or monotonic function), and 0 indicates no correlation; the closer the coefficient is to -1 or 1 and the farther it is from 0, the more the relationship approaches the function (Warner, 2013).

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Which correlation coefficient to use depends on the properties of the variables to be analyzed. Often, a Pearson correlation coefficient will be used. However, it requires several assumptions to be met, namely: (1) interval/ratio levels of measurement of both variables; (2) a linear relationship between the variables (and not, e.g., curvilinear); (3) the absence of significant outliers; and (4) approximately normal distribution of each of the variables (Field, 2013; Warner, 2013).

If only the first assumption is not met, namely, in the case when one of the variables is dichotomous, then the point-biserial correlation should be used. It should be noted that in this case, the direction of the relationship will depend on the coding of the dichotomous variable (Field, 2013).

If the first assumption is not met, and at least one of the variables is at least ordinal; or if there are many significant outliers in the data and it is not desired to remove them; or if the distribution is not normal – then, Spearman correlation will often be used. It is a non-parametric version of the Pearson correlation; it ranks the data and then calculates the Pearson correlation coefficient for that ranked data (Field, 2013). However, due to the ranking, part of the information is lost, and the Spearman correlation coefficient only shows how close the relationship is to some monotonic function (instead of just a linear function).

Finally, Kendall rank correlation should be used in circumstances similar to those when a Spearman correlation ought to be utilized, but when, in addition to that, a ranking of the data produces many tied ranks (i.e., many values in the data have the same rank). The interpretation of this coefficient is similar to that of the Spearman correlation coefficient (Field, 2013).

References

Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications. Web.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications. Web.

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IvyPanda. 2020. "Correlation Types and Their Uses." July 27, 2020. https://ivypanda.com/essays/correlation-types-and-their-uses/.

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IvyPanda. "Correlation Types and Their Uses." July 27, 2020. https://ivypanda.com/essays/correlation-types-and-their-uses/.

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