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Pearson correlation in r.
Posted on October 26, 2021 by Statistical Aid in R bloggers | 0 Comments
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The Pearson correlation coefficient, sometimes known as Pearson’s r, is a statistic that determines how closely two variables are related. Its value ranges from -1 to +1, with 0 denoting no linear correlation, -1 denoting a perfect negative linear correlation, and +1 denoting a perfect positive linear correlation . A correlation between variables means that as one variable’s value changes, the other tends to change in the same way.
Creating or Importing data into R
Let’s import data into R or create some example data as follows:
If we want to calculate the Pearson’s correlation of x and y in data, we can use the following code:
From the above result, we get that Pearson’s correlation coefficient is 0.90, which indicates a strong correlation between x and y.
Interpretation of Pearson Correlation Coefficient
The value of the correlation coefficient (r) lies between -1 to +1. When the value of –
- r=0; there is no relation between the variable.
- r=+1; perfectly positively correlated.
- r=-1; perfectly negatively correlated.
- r= 0 to 0.30; negligible correlation.
- r=0.30 to 0.50; moderate correlation.
- r=0.50 to 1 highly correlated.
A common misconception about the Pearson correlation is that it provides information on the slope of the relationship between the two variables being tested. This is incorrect, the Pearson correlation only measures the strength of the relationship between the two variables. To illustrate this, consider the following example:
The Pearson correlation coefficient of these two sets of x and y values is exactly the same:
However, when we plot these x and y values on a chart, the relationship looks very different:
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COMMENTS
The Pearson correlation of the sample is r. It is an estimate of rho (ρ), the Pearson correlation of the population. Knowing r and n (the sample size), we can infer whether ρ is significantly different from 0. Null hypothesis (H 0): ρ = 0; Alternative hypothesis (H a): ρ ≠ 0
Pearson’s product moment correlation coefficient, or Pearson’s r was developed by Karl Pearson (1948) from a related idea introduced by Sir Francis Galton in the late 1800’s.
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The following examples show how to report Pearson’s r in APA format in various scenarios. Example 1: Hours Studied vs. Exam Score Received. A professor collected data for the number of hours studied and the exam score received for 40 students in his class. He found the Pearson correlation coefficient between the two variables to be 0.48 with ...
This thesis looks at working status with particular emphasis on how it may correlate with measures of success among college students. After a literature review, I supplied explanations of my proposed hypotheses, procedures, and methods. When I started this project, the main goal of my thesis was to point out the underappreciated
Pearson correlation measures the existence (given by a p-value) and strength (given by the coefficient r between -1 and +1) of a linear relationship between two variables (Samuels, & Gilchrist,...
The Pearson correlation coefficient, sometimes known as Pearson’s r, is a statistic that determines how closely two variables are related. Its value ranges from -1 to +1, with 0 denoting no linear correlation, -1 denoting a perfect negative linear correlation, and +1 denoting a perfect positive linear correlation.
When using the Pearson correlation coefficient formula, you’ll need to consider whether you’re dealing with data from a sample or the whole population. The sample and population formulas differ in their symbols and inputs. A sample correlation coefficient is called r, while a population correlation coefficient is called rho, the Greek ...
Research Hypothesis: Knowing that store owners are often over-worked, the researcher hypothesized that stores with fewer fish would have healthier fish (thus predicting a negative or inverse relationship between these variables in this population).
Test statistic T = r * √(n-2) / (1-r2) where n is the number of pairs in our sample, r is the Pearson correlation coefficient, and test statistic T follows a t distribution with n-2 degrees of freedom. Let’s walk through an example of how to test for the significance of a Pearson correlation coefficient.