Correlation Analysis is a cornerstone of data science. It unlocks the hidden relationships between variables in your data, revealing the strength and direction of these connections and empowering you to make informed decisions and accurate predictions.
The analytical field of Data science relies heavily on correlations. Correlation Analysis is essential for understanding the relationships between data points, and the two most common types of correlation—Spearman and Pearson—are widely used in data science. Understanding the differences between Spearman vs Pearson correlation and when to use each one is a key part of data analysis.
This article will explore the difference between the Spearman and Pearson correlations, understand the strengths, weaknesses, and use cases of each type of correlation, and discuss the coefficients of Spearman and Pearson in detail.
What is Correlation?
Correlation is a statistical tool that quantifies the relationship between two variables. It describes how two parameters vary from one another. In statistics, it mostly refers to the degree to which two parameters are linearly related or vary linearly.
There are three types of correlations in data science:
- Positive: Two parameters vary in the same direction.
- Negative: Two variables vary in the opposite direction.
- No correlation: Parameters do not vary in any specific direction.
Correlation is useful to know how one parameter varies according to another, which in turn is used to predict the behavior of that parameter. For example, as the temperature increases, people consume more electricity through fans and ACs. So, there is a correlation between temperature increase and electricity use.
The commonly used correlations in data science are “Spearman and Pearson.” The difference between Spearman and Pearson is that Spearman uses rank variables while Pearson uses interval or ratio variables.
Knowing which one to use depends on the parameters under consideration. Understanding correlations can help you understand how certain factors influence each other and make better predictions.
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What is Pearson’s Correlation (P)?
Pearson’s Correlation (P) measures the strength and direction of a linear relationship between two variables. It ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation). The closer P is to 0, the weaker the relationship between the two variables.
P can be used to test whether one variable influences another. For example, does gender affect height? It can also be used to determine how well-defined a linear relationship is between two variables.
When interpreting correlation, it is critical to consider the magnitude and direction of its value. It is important as even if there is only a small difference in value, it could still have an important practical implication. For example, a correlation of -0.3 may not seem significant, but it could mean that the two variables are significantly more related than if they correlated 0.1
It is also important to remember that P does not imply causation. It measures the direction and strength of a linear relationship between two variables. Therefore, researchers must conduct additional tests and analysis to draw meaningful conclusions about cause-and-effect relationships.
Finally, researchers can use the Pearson Correlation with other statistical tests, such as t-tests or regression analysis, to provide further insight into the data. Understanding how to use Pearson’s Correlation with other statistical methods can help uncover deeper insights from the data.
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Pearson Correlation Coefficient
The Pearson Correlation Coefficient, developed by an English mathematician named Karl Pearson, is a statistical measure of the strength of a relationship between two variables.
It measures the covariance ratio between two variables divided by the product of their standard deviation. It is denoted by the letter “r.” Its values always lie in the range of -1 to +1. -1 is a strong negative correlation, and +1 is a strong positive correlation. If the value is 0, then there is no correlation.
The mathematical formula is:
r = Pearson correlation coefficient
x = first dataset
y = second data set
The Pearson coefficient can only be used if both variables are quantitative, normally distributed, and have no outliers and if the relationship is linear.
Examples of Pearson Coefficient
The Pearson Coefficient is useful for understanding the relationship between two variables. It can provide insight into whether changes in one variable result in corresponding changes in another variable and the strength of this correlation.
For example, if you wanted to measure the relationship between height and weight in a population, you could use the Pearson Coefficient. The calculation would involve comparing each individual’s height to their corresponding weight.
A positive result would indicate that taller individuals tend to be heavier than shorter individuals; a negative result would indicate that taller individuals tend to be lighter.
- A strong positive linear relationship with r>0.5
- A strong negative linear relationship with r<-0.5
What is Spearman Correlation (S)?
Spearman Correlation (S) measures the strength and direction of the linear relationship between two variables. It measures how well two variables are associated, regardless of their units or scales.
Spearman Correlation values range from -1 to +1; a value of 1 means that the two variables have a perfect positive correlation, while a value of -1 indicates a perfect negative correlation. The closer the S value is to zero, the weaker the linear relationship is between the two variables.
It is a statistic especially useful when outliers in your data may be skewing it. It can provide more accurate results because it is not affected by extreme values as much as Pearson’s Correlation Coefficient.
Spearman Correlation (S) is a valuable tool for data scientists and researchers, as it can provide more accurate results than the Pearson Correlation Coefficient in certain scenarios.
Researchers often use the Spearman Coefficient in psychology, sociology, and economics to analyze relationships between variables that may not necessarily follow a linear relationship. Knowing how to use this statistic can give you the necessary insights to further your research.
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Spearman Correlation Coefficient
The Spearman Correlation Coefficient, also known as the Spearman Rank Coefficient, was formulated by Charles Spearman, a British psychologist renowned for his contributions to statistical analysis. It is denoted by the Greek alphabet “rho.”
Spearman Coefficient can be used for monotonic relationships where Pearson coefficients are present. It is a statistical measure of whether a relationship is linear or not and how strong the correlation is between the two variables. Spearman’s Coefficient is useful for both continuous and discrete ordinal variables. It is a correlation between ranked variables.
The mathematical formula is:
Examples of Spearman Coefficient
The Spearman Coefficient is useful for measuring the strength of an association between two variables. The comparison allows for measuring the success of one variable. It also provides insight into what changes need to be made or how improvements can be made.
For example, we can use the Spearman Coefficient to analyze the relationship between reading skills and test scores. Calculating a Spearman rank-order Correlation Coefficient between these two factors will help examine how well a student’s score on a standardized reading test correlates with their overall literacy level.
The results can provide insight into how well-prepared a student is for college entrance exams and how much improvement could be made by additional studying.
- Positive Spearman Coefficient with an increasing monotonic relationship:
- Negative Spearman Coefficient with a decreasing monotonic relationship:
Comparative Analysis of Pearson vs Spearman Correlation
Pearson Correlation works with linear relationships only, while Spearman Correlation can work with monotonic relationships. Monotonic means that when one variable increases, the other increases, but not at a constant rate.
Hence, the difference between Pearson and Spearman Coefficients is that they yield different values for monotonic relationships.
Let’s see the Spearman Correlation vs Pearson Correlation through a few examples:
- Pearson = +1, Spearman = +1
In the above picture, the relationship is linearly increasing. Hence, both coefficients are +1.
An example of this is the relationship between age and height. As a person’s age increases, so does their height. Therefore, the Pearson Correlation Coefficient will be +1, while the Spearman Correlation Coefficient will be +1 since this is a monotonically increasing relationship.
- Pearson = +0.851, Spearman = +1
In the above picture, the relationships are monotonically increasing, i.e., increasing but not constantly. Hence, the Spearman Coefficient is +1, but the Pearson Coefficient is less than one. So, we can see that monotonic relationships do not affect the Spearman Coefficient.
An example of this is when we consider the height of a group of people. Even though their heights may vary, if one person is taller than another, then it will be true for any two people in the group.
This means there is a difference between Pearson and Spearman Correlations, as there will be a monotonic relationship between people’s different heights. Hence, the Spearman Coefficient would be +1, while the Pearson coefficient would be less than one.
Thus, the example helps to explain how increasing relationships can yield different results for Pearson and Spearman Correlation Coefficients. It also illustrates why Spearman’s Correlation Coefficient can often better indicate a monotonic relationship between two variables in a Spearman Correlation vs Pearson Correlation.
- Pearson = -1, Spearman = -1
In the above picture, the relationship is linearly decreasing. Hence, both coefficients are -1.
An example is the relationship between gas consumption and air pollution. As more gasoline is consumed, air pollution increases exponentially, decreasing Pearson and Spearman’s Correlation Coefficient.
Numerous studies conducted worldwide have shown that increased car traffic has increased ground-level ozone concentration and other pollutants from vehicles. Thus, the example illustrates a linear correlation coefficient decrease with Pearson and Spearman equal to -1.
It is important to remember that Pearson’s and Spearman’s Coefficients measure a dataset’s degree of linearity or monotonicity. However, depending on which one you use will depend on how strong or weak that relationship may be.
Additionally, both coefficients may be lower or higher than -1 when dealing with datasets involving non-linear relationships. We must also remember that there are other ways to measure the Pearson vs Spearman Correlation, such as Kendall’s Tau, which may better suit certain scenarios.
By understanding the differences between Spearman Correlation and Pearson Correlation when measuring correlations and how they work in different situations, researchers can make informed decisions about choosing the appropriate one for their data and analysis goals.
Furthermore, this knowledge can help inform discussion about the implications of a particular relationship on the research questions being explored. Understanding how the Pearson vs Spearman Coefficient works differently can lead to more meaningful insights from any dataset.
- Pearson = -0.799, Spearman = -1
In the above picture, the relationships are monotonically decreasing, i.e., decreasing but not constantly. Hence, the Spearman Coefficient is -1, but the Pearson Coefficient is less than 0. Here, we can see that monotonic relationships do not affect the Spearman Coefficient.
An example is when we consider the relationship between an individual’s age and height. Here, the taller individuals are usually older than the shorter ones, but not necessarily in a linear proportion.
Hence, when we calculate the Spearman Coefficient for this data set, it will be -1 (perfect monotonic decreasing correlation), whereas the Pearson Coefficient would be less than 0. The Pearson Coefficient only considers linear correlations, whereas the Spearman Coefficient considers any monotonic relationship.
Therefore, when there is a non-linear relation between two variables, like in our example above, the Spearman Correlation can help capture it better than the Pearson Correlation.
In conclusion, Spearman Correlation vs. Pearson Correlation helps better understand any monotonic relationships between two variables. However, Pearson Correlation only looks for linear relationships.
- Pearson = -0.093, Spearman = -0.093
The above picture shows no relationship between the two variables; hence, both coefficients have -0.093 values. There is no correlation between the two variables.
An example is a student scoring in an exam and the hours he spent studying for it. Even if the student puts in more hours, his score may not improve as there is no correlation between the two variables.
The Pearson and Spearman Coefficients will remain at -0.093, indicating no relationship. Thus, even if one variable increases or decreases, the other variable will not change. In this scenario, other factors, such as the student’s aptitude and the difficulty level of questions, are also important to consider. This means that these variables, too, cannot be used to predict the score obtained by a student in an exam.
Therefore, it explains how Spearman vs Pearson Correlation Coefficients can help interpret relationships between two variables or datasets. Understanding and interpreting their values helps draw meaningful conclusions from data analysis results and make better decisions. It demonstrates the importance of these coefficients in research and analytical tasks.
Pearson vs Spearman Correlation: Key Differences
Choosing between Pearson and Spearman depends on the nature of your data and the type of relationship you want to examine. They both assess the strength and direction of the relationship between two variables but have certain differences:
Conclusion
Spearman and Pearson’s Correlations are powerful methods for measuring the strength of relationships between variables. While researchers commonly use both, understanding their differences is important for deciding when to apply each.
Researchers can use the Spearman Correlation Coefficient, a non-parametric measure, for rank data or data that does not follow a normal distribution. In comparison, the Pearson Correlation Coefficient is a parametric measure that works best for interval data with an approximately normal distribution.
Understanding which type of method provides the most accurate values for your data set will help you make informed decisions about your research findings. By applying these methods appropriately, data scientists can gain valuable insight into their work and use this knowledge to inform future studies.
FAQs
- What is the difference between Pearson and Spearman correlation?
The Pearson coefficient works well with only linear relationships, while the Spearman coefficient can also work with monotonic relationships. Pearson coefficients vary considerably for monotonic relationships, while monotonic relationships do not affect Spearman coefficients. The Pearson coefficient is preferred when data is numeric and quantitative, while the Spearman coefficient is preferred when data is qualitative and ordinal.
- Why is Pearson correlation better than Spearman?
Pearson correlation measures the relationship’s strength, whether linearly increasing or decreasing. It also tells us how tightly packed a scatter plot is about the linear line. It helps us deduce the strength of a relationship and determine if there is a correlation between the two variables. Hence, Pearson’s correlation is better than Spearman’s.
- Why is the Pearson correlation preferred?
Most of the time, the data we get is quantitative. The Pearson coefficient works well with quantitative data. We prefer the Pearson coefficient for linear relationships because we can determine whether the data is bivariate normal and conduct various tests to check its correlation.
