Then values of x are plotted with the corresponding values of y. If the relationship between the variables is positive then a line drawn through the points will slope upward. This upward slope signifies that as the values for x increase the values corresponding values for y also increase. The opposite will be true for a negative relationship. In this case the line will slope downward and the correlation would be negative.
In interpreting the correlation coefficient there is one other factor to consider and that is the p value. The statistical program will produce a probability statistic that suggests how likely the result that is observed is the product of chance. The researcher then examines the p value and compares it to the predetermined alpha level that was set for this particular test. If the p value is less than the alpha level the researcher must make a decision to reject the null hypothesis. If however, the p value is greater than the alpha level then the researcher must accept the null hypothesis. The correct interpretation of a correlation statistic involves the consideration of the magnitude of the correlation coefficient, the sign in front of the coefficient and the p value produced by the statistical test.
This type of interpretation can be observed with the following example. If the pre-loan and post-loan expenditure on school books by students is examined a correlation can be determined.
A scatter plot of the data would suggest that the correlation between the data points would be positive.
Pre-Loan
Post-Loan
36
74
33
62
75
55
73
93
65
50
83
62
77
74
67
44
70
99
87
40
83
37
71
83
59
85
72
57
86
55
88
89
79
91
73
It is also important to remember that the presence of a correlation does not mean that the researcher has identified a cause (Creswell 1996). The change in one variable is not to be understood as causing the change in the second variable. The establishment of cause requires more than simply the demonstration of correlation between the variables. A causal relationship also requires that the researcher demonstrate that the observed relationship is non-spurious, so that a third variable does not explain the observed relationship. Additionally, the researcher must also determine which variable existed in time first. This is because the cause must of necessity exist in time before the thing it is deemed to have brought into existence. These factors are generally difficult to produce within the social sciences and consequently one never says that one thing causes another. An example of this difference is the correlation between breast implants and suicide. Loviglio (2011) noted that while the data shows that among women with breast implants there is a higher rate of suicide this is not to be taken to mean that implants cause persons to commit suicide.
Correlation provides the researcher with a useful tool to indicate in a numerical manner the degree of association between two variables. When interpreting a correlation coefficient the researcher should be careful to observe three the aspects of the coefficient, the magnitude, the direction and the p value. Additionally, it must always be remembered that even where there are strong correlations one is not to infer that cause exists.
References
Cooper, D.R. & Schindler P.S. (2011) Business research methods. New York: McGraw-Hill.
Creswell J.W. (1994).Research Design: Qualitative and Quantitative approaches.
London: Sage
Publications.
Howell, D.C. (2011). Fundamental Statistics for the behavioral sciences. New York: Cengage learning.
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