Difference Between Correlation and Association (With Table)

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People these days use the terms correlation and association interchangeably both in everyday life and in statistics. A person who uses them should be clear with the differences between the terms and their meaning. Correlation and association have various similarities but are still different concepts in statistics and English.

Correlation vs Association

The difference between correlation and association is that correlation defines the linear relationship between two variables, and it quantifies this relationship with the use of numbers between -1 and 1. The association defines any general relationships between two random variables, and it is not quantifiable.

Correlation is a relationship between 2 or more objects in English. It is an exact term consisting of one meaning. In statistics, it measures a linear relationship between variables while quantifying it with numbers. It is useful in both statistics and science.

On the other hand, the association is the act of associating various variables. It is a vague term that doesn’t have an exact meaning to it. In statistics, it measures a general relationship between two or more variables. It is a concept that is hardly used in science, but it is used in psychology.

Comparison Table Between Correlation and Association

Parameters of ComparisonCorrelationAssociation
StatisticsIt can measure the linear relationship between random variablesIt can measure linear or non-linear relationships between random variables.
MeaningIt is a measurement of association.It is a concept.
Scientific UsageIt is used in statistics and science.It is hardly ever used in science, but it is used in psychology.
QuantificationIt quantifies a relationship amongst 2 variables with the help of a number between -1 and 1.It doesn’t use any numbers to quantify a relationship between variables.
EnglishAn exact term with one meaning.A vague term that doesn’t have an exact definition but can describe different things.
General DefinitionIt is a relationship between 2 or more objects.It is the act of associating.

What is Correlation?

Correlation is a statistical measure between two random variables having a linear relationship. Correlation quantifies the relationship but does not reveal whether x causes y or vice versa—or whether the association is the result of a third component.

Correlation can quantify the relationships using numbers between -1 and +1. The most common correlation between 2 variables is PPMCC which stands for Pearson product-moment Correlation Coefficient.

In mathematics, it is considered as the precision of the least-squares fit to the original information. It is computed by dividing the covariance ratios of different variables in the quantitative dataset by their square roots. In English, it is defined as a mutual relationship between 2 or more things.

Correlation has 3 possible results. These are positive correlation, negative correlation, and zero correlation. A positive correlation is a relationship in which the 2 different variables both move in the same direction, which means that an increase in one variable causes an increase in the other and vice versa.

When one variable increases, the other variable decreases. This is referred to as a negative correlation. A zero correlation indicates that no relationship exists between the two variables being assessed.

A correlation can visually be expressed by drawing a scattergram. This helps indicate the strength and direction of correlation between the variables.

What is Association?

In English, the association is a vague term that doesn’t have just one exact meaning. It can also mean a group of people with a common goal or similar interests. It is an act of associating.

In statistics, association indicates a relationship between 2 variables. It generally refers to a relationship without elaborating on it, and it does not have to be a causative tie.

In statistics, association indicates a relationship between 2 variables.

It defines a general relationship that can be both linear and non-linear. A few examples of association in statistics are Goodman’s and Kruskal’s Lambda and Spearman’s rho, distance correlation, etc.

Association can be determined with the help of various different analyses, like correlation analysis, regression analysis, etc. Which method you use to determine the association between variables and the strength of association is dependent on the characteristics of the variable’s data.

The most common ways to analyze association are Spearman rank-order correlation coefficient, relative risk and odds ratio, serial correlation, Pearson’s correlation coefficient, etc.

In psychology, an association is a mental link formed by specific encounters connecting concepts, events, or mental states. Associations can be found in a lot of different schools of thought like behaviorism, psychoanalysis, structuralism, social psychology, etc.

Main Differences Between Correlation and Association

  1. Correlation measures the linear relationship between 2 random variables. On the other hand, association measures a general relationship between 2 random variables, which means that it can be measure both linear and non-linear relationships.
  2. Correlation can be explained as a measurement of association with various tools that can help measure the magnitude. Association, however, is a concept.
  3. Correlation can be used in science and statistics. Association is hardly used in science, but it is fairly used in psychology in various schools of thought.
  4. Correlation quantifies a relationship among two variables with the help of a number between -1 and +1, whereas association can’t quantify a relationship between variables using a number.
  5. From this point of view, correlation is an exact term with proper meaning, whereas association means an act of associating.
  6. Correlation is a relationship between 2 or more objects, and association is the act of associating.

Conclusion

Correlation can be seen as a technical term, while association can’t. Association indicates the mere presence of relation, whereas correlation aims to quantify this relationship using various methods.

Statistically speaking, correlation measures the linear relationship between variables, whereas association measures the general relationships (including both linear and non-linear).

Correlation quantifies the relationship between variables using a numerical value between -1 and +1, whereas association uses no numerical value to quantify a relationship.

References

  1. https://www.nature.com/articles/nmeth.3587
  2. http://search.ebscohost.com/login.aspx?direct=true&profile=ehost&scope=site&authtype=crawler&jrnl=15487091&AN=110030895&h=1vpmMT%2BldAwaS10UlDyO0h8jP8TYWEWEXQf8Qt5Qozk1S4Sk%2BTDKi3RkHv9nGK5cC36K82Xb4r0F47bJlGDccA%3D%3D&crl=c
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