Understanding Correlation Analysis
Correlation analysis is a statistical technique that quantifies the degree of association between two or more variables. This is accomplished by computing a correlation coefficient that demonstrates how much one variable changes when the other one does. In case you are looking for help to do correlation analysis, our experts provide personalized data analysis services for students, researchers, and organizations in any field of research.
A correlation coefficient, denoted by r, is a statistical measure of the strength of a relationship between two variables that range from -1 to +1. The signs (-,+) of the coefficient illustrate the strength of the association. For example, a correlation of r= -0.8 shows a negative association between two variables, whereas a correlation of r= 0.6 demonstrates a positive association. A correlation close to zero or zero signifies no association between the variables.
This post explains the types of correlation analysis, how to do correlation analysis, gives a comparison of regression and correlation analysis, and gives an example of a case scenario of the procedure.
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Our experts apply the advanced analytic capabilities of software such as the Statistical Package for the Social Sciences (SPSS), R, Excel, and Python to identify interdependencies between data sets. They apply correlation techniques such as Kendall’s Tau rank correlation test to measure the strength of dependence between two variables. In this section, we demonstrate the types of correlation analysis performed by our experts, how we conduct the process and give a comparison of two similar but distinct processes, regression and correlation analysis.
Types of Correlation Analysis
(1). Canonical Correlation Analysis
Canonical correlation analysis is a technique that aims to acquire information from two data tables measuring quantitative variables on the same set of observations. For each data table, canonical analysis extracts a set of linear combinations of the variables of the table called latent variables and combines it with another variable from the other table. This ensures no overlapping between the set of variables and enables the analyst to identify variables with maximal correlation. The results of the analysis are then interpreted using graphic displays.
(2). Pearson Correlation Analysis
Pearson’s correlation analysis is used for examining linear relationships between variables measured on interval scales. The Pearson’s correlation coefficient is detonated by r. It is given by the equation:
r= Ν∑XY - ( ∑X) (XY) ⁄ √ [N∑X²- ( ∑X )²] [N∑Y² - ( ∑Y )²
Where:
N is the number of data points.
X and Y are the pairs in the data set.
∑X, Y is the sum of the product of the x and y values for each point in the data set.
(3). Bivariate Correlation Analysis
Bivariate correlation analysis is the measure of a relationship between two variables. It measures the strength and direction of their relationship on a scale of 1-0. The stronger the relationship the closer the value it is to 1 and the weaker the relationship, the closer it is to 0.
(4). Spearman Correlation Analysis
Spearman correlation analysis is a non-parametric correlation measure proposed by Charles Spearman that measures the degree of association between two variables. It is the most appropriate analysis method for variables measured on an ordinal scale. The formula for calculating the Spearman’s rank correlation coefficient is given by:
ρ = 1- [6∑di² ⁄ n (n²-1)]
Where:
ρ is the Spearman rank correlation coefficient
di is the difference between ranks of corresponding values Xi and Yi.
n is the number of values in each data set.
Regression Analysis Vs. Correlation
The table below illustrates the differences between regression and correlation analysis.
How to Do Correlation Analysis
Step 1: Calculate the Mean of Each Series
The mean is the mathematical average of a set of two or more numbers. We calculate the mean because the correlation coefficient, r, depends on the relationship of the variable of interest and its values. The mean formula is given by:
x̄ = ∑x ⁄ n
Where:
x̄ is the mean
∑x is the summation of all values
n is the total number of values.
Step 2: Calculate the Variance and Standard Deviation of the Variables
The variance is the measurement of the spread of numbers in a data set. Standard deviation is the measure of the amount of variation of the values of a data set from its mean. These factors account for the spread of the points in a data set. To calculate the variance and standard deviation:
(a). Variance Formula
σ² = ∑in [×i-x̄ ⁄ n]
Where:
σ² is the variance
n is the number of observations.
×i is the observation.
x̄ is the mean of the population.
(b). Standard Deviation Formula
The standard deviation is the square root of variance.
σ = √σ²
Step 3: Determine the Covariance
The covariance is the measure of the relationship between two random variables. It demonstrates the extent to which the variables change with each other. The formula for calculating the covariance is given by:
cov= ∑ (xi - x̄) ( yi - ȳ) ⁄ n-1
Where:
xi is the data value of x.
yi is the data value of y.
x̄ is the mean of x.
ȳ is the mean of y.
n is the number of data values.
Step 4: Calculate the Correlation Coefficient
The final step is calculating the correlation coefficient depending on the type of correlation analysis method chosen. This includes Spearman’s correlation coefficient, Pearson’s correlation coefficient, or the biserial coefficient. The results of the analysis are interpreted on a scatterplot where it can show a positive, negative, or no correlation.
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Correlation Analysis Example
A professor collected data from college students on the number of films watched per week and the number of hours they spent studying within the same period. They wanted to identify the degree of association between the two variables, so they calculated the Pearsons’ correlation coefficient based on the hours as shown in the table below:
Using the formula for calculating the Pearson’s correlation coefficient:
r= Ν∑XY - (∑X) (XY) ⁄ √[N∑X²- (∑X)²] [N∑Y² -(∑Y)²
r= (9) (278)- (36)(150)⁄ √ [(9)(228)- (36)²] [(9) (4278)- (150)²]
r= 2502-5400 ⁄ (2052-1296)(38502-22500)
r= -2898⁄ √12,097,512
r= -.83
This signifies a strong negative relationship between the two variables.
Summary
This article discusses the basics of correlation analysis highlighting its types, how to conduct the procedure, gives a comparison of regression analysis and correlation analysis, and gives an example. Correlation analysis is a statistical technique that quantifies the degree of association between two or more variables. If you are looking for experts to conduct correlation analysis on your data sets, our services apply advanced software analysis to get accurate insights from your data. Get help to do correlation analysis today from our expert analysts. Request a free quote now to get started!
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