To this point I have been writing about what I thought people might be interested in reading, but I thought I would start taking requests… Debussy's Clair de Lune, 50 Cent, Michael Bolton, Britney Spears… okay maybe not Michael Bolton. Post what you would like to see a blog entry about and I will do my best to comply.
It seems a great number of you are interested in bivariate correlation, so here is another entry on this favorite of statistical tests. I also think I could be a bit more comprehensive on the assumptions of ANOVA, so look for that in the very near future. I also plan on covering the assumptions of bivariate correlation. In the meantime…
What is bivariate correlation?
A bivariate correlation is a statistical test that measures the association or relationship between two continuous/interval/ordinal level variables. This test will use probability and tell the researcher the nature of the relationship between the two variables, but not the direction of the relationship in the sense of describing causality…but I digress.
How to interpret bivariate correlation
To understand how to interpret a bivariate correlation, we have to first understand what the possible results are. If the correlation is significant, our correlation coefficient will be either positive or negative.
Positive Correlation Coefficients
A positive correlation coefficient means that the relationship between the two variables is positive and that the variables move in the same direction. It also means that an increase in say… height, corresponds with an increase in weight. Stated another way, "As height increases, weight also increases, or as weight increases, height also increases."
Negative Correlation Coefficients
A negative correlation coefficient means that the relationship between the two variables is negative and means that the variables move in opposite directions. Using the same example, we would say, "As height increases, weight decreases, or as weight increases, height decreases."
The sign of the correlation coefficient tells us the nature of the relationship, as in one variable decreasing as one variable is increasing, or both variables increasing or decreasing together, but does not tell us how one variable affects another variable.
Note that the sign of the correlation – negative or positive – can be interpreted two ways. With a positive correlation, as height increases, weight also increases, or as weight increases, height also increases. Both are correct. For a negative correlation, as weight increases, height decreases, or as height increases, weight decreases. I hope this isn't confusing. If any of you are having trouble, just post a comment and let me know. Better yet, let me do the correlations for you. Get help with how to interpret bivariate correlation coefficients for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.
What does the bivariate correlation coefficient mean?
Correlation coefficients range from -1 to +1. If the bivariate correlation coefficient is -1, the relationship between the two variables is perfectly negative, and if the bivariate correlation coefficient is +1, the relationship between the two variables is perfectly positive. The closer the correlation coefficient is to -1 or +1, the stronger the relationship. The closer the correlation coefficient is to 0, the weaker the relationship.
What is r2?
Often the correlation is interpreted in terms of the amount of variance explained in one variable by another variable – just remember, though, that the correlation is bidirectional and can be interpreted either way. If you are conducting a Pearson correlation, in your output, you will get a Pearson correlation coefficient or a product-moment correlation coefficient. Squaring this gives you…r2. If I have a correlation coefficient of 0.4, then r2 = 0.16 and would be interpreted as, "…16% of the variance in height is explained by weight," and vice versa. Get help with interpreting r2 for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.
How to report a Pearson correlation or a Pearson product-moment correlation?
Here is the gem of the entire post and free of charge.
There was a significant, positive relationship between height and weight, r(98) = 0.40, p < 0.01, indicating that as height increases, weight also increases. Height accounted for 16% of the variance in weight.
Of course there is more to it than this, such as determining which variable is going to be your dependent variable and which variable is going to be your independent variable, as well as how the appropriateness of the test and how it relates to the rest of your thesis or dissertation. Click here for help with writing bivariate correlations for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.
What are the degrees of freedom for a bivariate correlation?
The degrees of freedom for a bivariate correlation are n – 2, where n is the sample size. This is also the number in the parenthesis above. The number in parenthesis is not the sample size.
How do I use the bivariate correlation?
If you were interested merely in the relationship of two variables, you would use the bivariate correlation. If you are interested in the effect of one variable on another variable, you would use a regression. The regression is the same as the correlation, but will tell you the specific impact one variable has on another variable in terms of the unstandardized beta coefficient and the standardized beta coefficient. It will also tell you the equation for the best fit line. We'll cover regressions very soon. Sometimes knowing the relationship of the two variables is enough, however, and if this is the case then bivariate correlation is the statistical test for you. Get help with how to use bivariate correlation for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation. We even provide customized videos of your bivariate correlations being conducted.
