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Introduction
The Pearsons correlation coefficient r is a statistic that shows the degree to which the values of two variables x and y are in the linear correlation; r takes values from -1 to 1, with r = 1 when the correlation can be described with the linear function (y = ax + b), r = -1 when the correlation is linear and negative (-y = ax + b), and r = 0 when there is no correlation (Field, 2013). This statistic can be provided when conducting a simple linear regression in SPSS. Furthermore, for the results of a simple linear regression to be adequate, it is important that the independent and dependent variables are in a linear relationship, and not in any type of non-linear relationship (Warner, 2013). Because Pearsons r can be used to assess the degree of the linear relationship, it is of particular importance for a study employing simple linear regression. The simple linear regression will be utilized in the future study of the relationship between perceived social support and HIV treatment compliance among African American females who are infected with HIV, which is why Pearsons r is discussed in this paper. Furthermore, knowing Pearsons r between the variables of the current study can also provide additional insights into the researched problem (Frankfort-Nachmias & Nachmias, 2015).
The Assumptions for Pearsons r, and the Situations in Which It Is Appropriate to Use It
There are a number of assumptions for Pearsons r test. The violation of these assumptions leads to an inadequate estimation of this statistic. The assumptions are as follows (Field, 2013; Statistics Solutions, n.d.):
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Both variables need to be measured on a continuous scale. Pearsons r for nominal or ordinal scales cannot be adequately computed.
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Normality of distributions.
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There should be no (extreme) outliers.
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Each case (participant) in the sample needs to have values for both variables.
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Linearity and homoskedasticity.
Pearsons r is appropriate to use if it is needed to see whether or not two phenomena often occur together, roughly speaking. It should only be used when there is no need to assess the causal relationship, for this statistic cannot show whether there is a causal relationship.
The Number of Dependent and Independent Variables Involved
Pearsons r can only assess the correlation between two variables. However, if there are more than two variables, Pearsons r can still be supplied as part of SPSS output for some statistical tests; the program will usually provide a table showing the value of Pearsons r for every two variables used in the test.
Social Change Implications
If Pearsons r between perceived social support (higher values=more support) and HIV treatment compliance (higher values = higher compliance) is close to 1, then it might be hypothesized that higher perceived social support can help achieve higher treatment compliance. If Pearsons r is close to -1, it might be assumed that lower support can help achieve higher treatment compliance. Pearsons r=0 will show that the phenomena are uncorrelated. However, it is important that these assumptions will only remain assumptions, and that another research design will be needed to establish a causal relationship.
For researchers, Pearsons r may indicate in which direction further research should proceed. For practitioners, it will help to understand whether or not it may be fruitful to increase or decrease the level of perceived social support in order to stimulate treatment compliance (but further studies will be needed). For social change, it may also be helpful to know whether greater perceived social support is often accompanied by higher treatment compliance.
References
Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.
Frankfort-Nachmias, C., & Nachmias, D. (2015). Research methods in the social sciences (8th ed.). New York, NY: Worth.
Statistics Solutions. (n.d.). Pearson correlation assumptions. Web.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.
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