Correlation: what is it and how to interpret it?
Correlation is a statistical measure that expresses the relationship between two variables. The value of the correlation coefficient tells us whether and how strong the relationship between the variables is and whether the relationship is direct or indirect.
Types of correlation coefficient
- Pearson’s correlation coefficient (r): used to measure the linear relationship between two quantitative variables. The values of r range from -1 to +1.
- Spearman’s correlation coefficient (r_s): Used to measure a monotonic relationship between two ordinal variables. The values of r_s also range from -1 to +1.
- Kendall’s tau (τ): Another measure of monotonic dependence for ordinal variables. The values of τ range from -1 to +1.
Interpretation of the correlation coefficient value
- -1: Absolute indirect linear dependence
- 0: No dependence
- +1: Absolute direct linear dependence
Strength of the correlation coefficient
- 0.00 – 0.20: Weak correlation
- 0.20 – 0.40: Moderate correlation
- 0.40 – 0.60: Strong correlation
- 0.60 – 1.00: Very strong correlation
The correlation coefficient does not indicate a causal relationship between the variables. The value of the correlation coefficient may be affected by outliers. The interpretation of the correlation coefficient depends on the context and the type of variables.
Example:
Suppose we are investigating the relationship between student height and weight. We find that the Pearson correlation coefficient is r = 0.65. This means that there is a strong direct correlation between height and weight. This means that as the height of the students increases, their weight also increases.
Correlation is a useful tool for:
- Establishing the existence and strength of dependence between variables
- Predicting one variable from another
- Identifying trends and patterns in the data
Practical use of correlation in various fields
Correlation, as a statistical measure of the relationship between two variables, finds wide application in a variety of fields:
Project management
Risk management: correlation can help to identify the relationships between different risks in a project. For example, delays in one activity can lead to delays in other activities. Understanding these correlations can help with better risk mitigation strategies.
Prediktívna analýza: Koreláciu možno použiť na predpovedanie výsledkov projektu na základe historických údajov. Napríklad, ak existuje silná pozitívna korelácia medzi úspešnosťou projektu a úrovňou zapojenia zainteresovaných strán, môže byť výhodné investovať viac do činností riadenia zainteresovaných strán.
Production processes
Identification of efficiency: correlation can help to identify the efficiency of the production process. For example, if models show that the use of a certain material increases production costs, correlation can lead managers to try to identify substitute supplies that reduce production costs.
Quality control: Correlation can be used to identify factors that affect the quality of the final product. For example, if there is a strong negative correlation between machine temperature and product quality, it may be advantageous to maintain machines at lower temperatures.
Business services
Performance measurement: correlation can be used to measure the performance of different business services. For example, a positive correlation between customer satisfaction and speed of service can indicate that faster service leads to happier customers.
Predictive analysis: Correlation can be used to predict future business trends. For example, if there is a strong positive correlation between market demand and sales of a particular service, it may be profitable to invest more in that service when market demand is predicted to increase.
Economics
Stock market analysis: correlation analysis is used to measure the relationship between the prices of different stocks to identify investment opportunities and risks.
Market forecasting: Correlation between economic indicators such as GDP and inflation rates allows predicting the future development of the market and the economy.
Science and research
Medical research: correlation analysis is used to investigate the relationship between various factors and diseases, for example between diet and cancer incidence.
Psychology: Correlation is used to study the relationships between different psychological traits, such as intelligence and personality traits.
Marketing and business
Customer Behavior Analysis:Correlation analysis is used to examine the relationship between buying behavior and various factors such as demographics and marketing campaigns.
Correlation analysis helps to identify the most effective marketing channels and strategies.
Education
Educational research: correlation analysis is used to investigate the relationship between various factors and student achievement, for example, between teaching methods and test scores.
Personalisation of education: Correlation analysis enables the identification of optimal learning strategies for different students.
Computer Science
Recommender systems: correlation analysis is used in recommender systems to predict what products a user might like based on their previous preferences.
Data analysis: Correlation analysis is an important tool in data analysis to identify hidden patterns and relationships.
In addition to these examples, correlation is also used in many other fields such as meteorology, sociology, political science and environmental science.
It is important to note that correlation does not imply causation. That is, even if we find a strong correlation between two variables, it does not mean that one variable causes the other. Correlation analysis is just one of the tools that help us learn about the world around us.
