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Find the best survey software for you!
(Along with a checklist to compare platforms)
Take a peek at our powerful survey features to design surveys that scale discoveries.
Explore Voxco
Need to map Voxco’s features & offerings? We can help!
We’ve been avid users of the Voxco platform now for over 20 years. It gives us the flexibility to routinely enhance our survey toolkit and provides our clients with a more robust dataset and story to tell their clients.
Steve Male
VP Innovation & Strategic Partnerships, The Logit Group
Explore Regional Offices
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The correlation coefficient is a statistical analysis method that is used to measure the strength and the direction of the relationship between two variables. Or, it can also be said that correlation analysis in research helps us to measure the change in one variable caused by the change in other variables.
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A Positive correlation means that when the value of one variable increases the value of the second variable also increases.
A negative correlation means that when the value of one variable increases, the value of the second variable decreases.
A zero correlation indicates that there is no relationship between the two variables.
You can use a scatter plot to graphically display the strength and direction of the relationship between two variables. The pair of values are plotted along the axes – x and y – to study the pattern that emerges.
The relation between the values is determined by how far the data points fall from the regression line. The correlation coefficient indicates how closely the data fit on the line.
The regression line is the best fitting line in a scatter plot, which takes all the data points into account. When your data points are closer to the straight line, the absolute value is higher and the linear relationship is stronger.
Perfect correlation: all the data points are on the regression line
High correlation coefficient: all data points are closer to the straight line
Low correlation coefficient: all data points are spread far away from the line
There are many approaches suggested for the interpretation of the correlation coefficient. Descriptors like “strong”, “moderate”, or “weak” are used to translate the relationship. As a guideline, you can use the table to interpret the strength of the relationship from the value of the correlation coefficient.
Correlation Coefficient  Strength  Type 
0.7 to 1.0  Very Strong  Positive 
0.5 to 0.7  Strong  Positive 
0.3 to 0.5  Moderate  Positive 
0 to 0.3  Weak  Positive 
0  None  Zero 
0 to – 0.3  Weak  Negative 
0.3 to 0.5  Moderate  Negative 
0.5 to 0.7  Strong  Negative 
0.7 to 1.0  Very Strong  Negative 
The value of the correlation coefficient ranges between +1.0 to – 1.0. The value is an indicator of the strength of the relationship between two variables.
The sign – positive and negative – indicates whether the change in the variables is in the same or opposite direction.
Absolute value: is the number without its sign. It reflects the magnitude of correlation. If the absolute is greater, then the correlation is stronger.
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There are several correlation coefficients you can choose from depending on the linearity of the relationship, the level of measurement, and the distribution of data.
Correlation Coefficient  Relationship  Levels of Measurement  Distribution 
Pearson’s r  Linear  Two Quantitative variables – interval or ratio  Normal distribution 
Spearman’s rho  Nonlinear  Two Ordinal Variables – interval or ratio  Any distribution 
Cramer’s V  Nonlinear  Two Nominal Variables  Any distribution 
Kendall’s tau  Nonlinear  Two Ordinal Variables  Any distribution 
The most common correlation coefficient used in research is Pearson’s r. It is parametric, allows for strong inferences, and measures linear correlation. However, there are certain assumptions in Pearson’s r. The data for your research needs to meet these assumptions, and in case it doesn’t you need to use a nonparametric test.
Spearman’s rho or Kendall’s tau can be used for nonparametric tests. Kendall’s tau is a preferred choice for small samples. Spearman’s rho is used for wide samples.
Pearson’s r is used to interpret the relationship between two quantitative variables. It cannot be used if your variables have a nonlinear relationship.
There are certain assumptions that the data needs to meet in order to use Pearson’s r:
The formula of Pearson’s r is:

Most software can quickly work out the formula and generate the correlation coefficient from your data.
To calculate the “r”, first the covariance of the variables is determined. Then, the resulting quantity is divided by the product of the standard deviation of those variables.
When you have decided to use the formula of Pearson’s r, you also need to decide upon whether you are working with data from a sample or from the population. Both the sample and population have a different formula with different symbols and inputs.
“r” is used for the formula of sample correlation coefficient
“rho” or Greek letter “ρ” is used for the population correlation coefficient
Sample correlation coefficient

The formula uses the sample covariance between the variables and the sample standard deviation.
Population correlation coefficient

It uses the population covariance between the variables and the population standard deviation.
Spearman’s rho, also called Spearman’s rank correlation coefficient, is used for nonparametric tests. It is the commonly used alternative of Pearson’s r.
It is called a rank correlation coefficient because instead of using the raw data, it uses the ranking of the data from each variable. Spearman’s rho is generally used when one of the variables is on an ordinal level of measurement or when the variables do not follow a normal distribution.
Spearman’s rho examines the monotonicity of relationships. It is used when the relationship between the variables is nonlinear. The characteristic of a monotonic relationship is that each variable changes in one direction but not at the same rate.
Positive Monotonic indicates that when one variable increase the second variable also increases
Negative Monotonic indicates that one variable increases the other variable decreases
In the case of Spearman’s rank correlation coefficient

“ρ” is used for population coefficient
“rs “ is used for sample coefficient
To calculate Spearman’s rho, you first need to rank the data from each variable in the order of lowest to highest. Next, you need to measure the difference between the ranks of the variables for each pair of data and use that as the main input in the formula.
Correlation coefficient +1: means all the ranks for each variable match for each data pair
Correlation coefficient 1: means the rankings for one variable are the exact opposite of the rankings of the other variable.
Correlation coefficient near 0: means there is no monotonic relationship
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Correlation coefficients can be used for surveys such as employee satisfaction/ engagement, customer satisfaction, and other types of surveys.
In market research, the aim of the researcher is to analyze the quantitative data collected from surveys. The researcher uses a correlation coefficient to identify and understand the relationship and trends between two variables.
A Correlation Coefficient “r” describes the strength and direction of the relationship between two variables. The value always ranges between +1 to – 1.
A Positive correlation means that when the value of one variable increases the value of the second variable also increases.
A Negative correlation means that when the value of one variable increases, the value of the second variable decreases.
Zero correlation reflects that there is no relationship between the two variables
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