Pearson’s Correlation Coefficient
Pearson’s Correlation Coefficient
Pearson’s correlation coefficients are the most widely used method of measuring the degree of relationship between two variables. This coefficient assumes the following: That there is a linear relationship between the two variables; That the two variables are casually related which means that one of the variables is independent and the other one is dependent; and A large number of independent causes are operating in both the variables so as to produce a normal distribution. Pearson’s correlation coefficients = (∑(x 1 - x) (y 1 - Ӯ))/(n .σx.σy)
Xi= ‘i’th value of X variable
X = mean of X
Y1 = value of Y variable
Ӯ = mean of Y n = number of pairs of observations of X and Y σx = Standard deviation of X σy = Standard deviation of Y
The Pearson’s correlation coefficient has several important properties. First, as the methodology has demonstrated, it is independent of sample size and units of measurement. Second, it lies between 1 and +1. Thus, the interpretation is intuitively reasonable.
How is it calculated for a population?
If the correlation coefficient is calculated for the entire population, it is denoted by p, the population correlation coefficient. Like the case of the sample mean being an estimator of the population mean, the simple correlation coefficient r is an estimate of the population correlation coefficient p.
How is it calculated for a sample?
The first step in understanding how Pearson correlation coefficients are calculated is to notice that we are concerned with a samples score on two variables at the same time. Returning to our example of study time and test scores, suppose that we randomly select a sample of five students and measure the time they spent studying for the exam and their exam scores. For these data to be used in a correlation analysis, it is critical that the scores on the two variables are paired. That is, for each student in my
Pearson’s correlation coefficients are the most widely used method of measuring the degree of relationship between two variables. This coefficient assumes the following: That there is a linear relationship between the two variables; That the two variables are casually related which means that one of the variables is independent and the other one is dependent; and A large number of independent causes are operating in both the variables so as to produce a normal distribution. Pearson’s correlation coefficients = (∑(x 1 - x) (y 1 - Ӯ))/(n .σx.σy)
Xi= ‘i’th value of X variable
X = mean of X
Y1 = value of Y variable
Ӯ = mean of Y n = number of pairs of observations of X and Y σx = Standard deviation of X σy = Standard deviation of Y
The Pearson’s correlation coefficient has several important properties. First, as the methodology has demonstrated, it is independent of sample size and units of measurement. Second, it lies between 1 and +1. Thus, the interpretation is intuitively reasonable.
How is it calculated for a population?
If the correlation coefficient is calculated for the entire population, it is denoted by p, the population correlation coefficient. Like the case of the sample mean being an estimator of the population mean, the simple correlation coefficient r is an estimate of the population correlation coefficient p.
How is it calculated for a sample?
The first step in understanding how Pearson correlation coefficients are calculated is to notice that we are concerned with a samples score on two variables at the same time. Returning to our example of study time and test scores, suppose that we randomly select a sample of five students and measure the time they spent studying for the exam and their exam scores. For these data to be used in a correlation analysis, it is critical that the scores on the two variables are paired. That is, for each student in my