R², or Coefficient of Determination.
This fact of the day will be separated into two parts as this requires a bit of understanding related to statistics in order to properly interpret. It’s simple, but quite easy to misinterpret the results without understanding. I promise that this has everything to do with kava, we just need to get this understanding locked down first. There has been some previous misunderstanding that needs to be corrected regarding R values and their interpretation. It’s important to understand that correlation analysis measures a relationship or association, and does not define the explanation or its basis. It's imperative for us to understand the contents of this "fact of the day" in order to understand tomorrow's.
First we need to understand what R means. The letter “r” stands for correlation coefficient, and it is used to measure the linear relationship between two sets of data. In other words it tells us how related two sets of data are. The closer the value for “r” is to 1, or -1, the more correlated the data points are. The closer it is to zero, the less correlated the data points will be. The following are some simple graphs depicting various values for r.
As you can see by graph A, a perfect positive correlation will see all of the data points fall perfectly along the line in an ascending slope. Graph D depicts a negative perfect correlation with the slope reversed but also with all data points falling on the line. Data that we normally see in kava research will rarely have a perfect correlation and will usually look something more like graph C, F, or E.
Correlation analysis is one of the most widely used and reported methods of summarizing medical and scientific research. We’ll be applying this information to a rather current kava research paper about kava root, chips and powders. This paper deals with identifying the quality of kava by using a machine to read the absorbance spectrum. Absorbance spectrum is how much of a certain wavelength of light passes through a sample. It can identify the presence, and sometimes the quantity of different molecules. The absorbance spectra was used to identify flavokavains and kavalactones in kava in the paper we’ll be covering tomorrow. They used this information to arrive at kava quality based on a ratio of flavokavains to kavalactones.
Now that we understand what a correlation coefficient is, it’s just an easy calculation for us to come up with what is known as the “Correlation of Determination” (COD), also known as “r squared”. This is simply found by squaring the known correlation coefficient. We’ll use Figure 1A graph C as an example. In order to find the COD you would simply take “r” which equals .70 and square it. This gives you the coefficient of determination of .49 or in other words 49%.
That’s great, but what does it mean?
In statistics “r squared” is the proportion of the variance in the dependent variable (Y on the graph) that is predictable from the independent variable (X on the graph). R² gives us an understanding of how the two variables relate to each other. In graph C we see that COD comes up to .49 or 49%. This means that 49% of the variation in the dependent variable X can be explained by the independent variable or Y. This also means that 51% of the variation of X in this example cannot be explained by the variation in Y.
If you’re left scratching your head, don’t worry. Tomorrow we will apply what we’ve learned here today in order to better understand an important kava research paper.
Taylor, Richard. 1990. “Interpretation of the Correlation Coefficient: A Basic Review.” Journal of Diagnostic Medical Sonography 6 (1): 35–39.
(https://doi.org/10.1177/875647939000600106.)
(https://sci-hub.st/10.1177/875647939000600106)
Wikimedia Foundation. (2021, May 3). Coefficient of determination. Wikipedia.
(https://en.wikipedia.org/wiki/Coefficient_of_determination)
This fact of the day will be separated into two parts as this requires a bit of understanding related to statistics in order to properly interpret. It’s simple, but quite easy to misinterpret the results without understanding. I promise that this has everything to do with kava, we just need to get this understanding locked down first. There has been some previous misunderstanding that needs to be corrected regarding R values and their interpretation. It’s important to understand that correlation analysis measures a relationship or association, and does not define the explanation or its basis. It's imperative for us to understand the contents of this "fact of the day" in order to understand tomorrow's.
First we need to understand what R means. The letter “r” stands for correlation coefficient, and it is used to measure the linear relationship between two sets of data. In other words it tells us how related two sets of data are. The closer the value for “r” is to 1, or -1, the more correlated the data points are. The closer it is to zero, the less correlated the data points will be. The following are some simple graphs depicting various values for r.
Correlation analysis is one of the most widely used and reported methods of summarizing medical and scientific research. We’ll be applying this information to a rather current kava research paper about kava root, chips and powders. This paper deals with identifying the quality of kava by using a machine to read the absorbance spectrum. Absorbance spectrum is how much of a certain wavelength of light passes through a sample. It can identify the presence, and sometimes the quantity of different molecules. The absorbance spectra was used to identify flavokavains and kavalactones in kava in the paper we’ll be covering tomorrow. They used this information to arrive at kava quality based on a ratio of flavokavains to kavalactones.
Now that we understand what a correlation coefficient is, it’s just an easy calculation for us to come up with what is known as the “Correlation of Determination” (COD), also known as “r squared”. This is simply found by squaring the known correlation coefficient. We’ll use Figure 1A graph C as an example. In order to find the COD you would simply take “r” which equals .70 and square it. This gives you the coefficient of determination of .49 or in other words 49%.
That’s great, but what does it mean?
In statistics “r squared” is the proportion of the variance in the dependent variable (Y on the graph) that is predictable from the independent variable (X on the graph). R² gives us an understanding of how the two variables relate to each other. In graph C we see that COD comes up to .49 or 49%. This means that 49% of the variation in the dependent variable X can be explained by the independent variable or Y. This also means that 51% of the variation of X in this example cannot be explained by the variation in Y.
If you’re left scratching your head, don’t worry. Tomorrow we will apply what we’ve learned here today in order to better understand an important kava research paper.
Taylor, Richard. 1990. “Interpretation of the Correlation Coefficient: A Basic Review.” Journal of Diagnostic Medical Sonography 6 (1): 35–39.
(https://doi.org/10.1177/875647939000600106.)
(https://sci-hub.st/10.1177/875647939000600106)
Wikimedia Foundation. (2021, May 3). Coefficient of determination. Wikipedia.
(https://en.wikipedia.org/wiki/Coefficient_of_determination)
