# Monotonic relationship definition in science

### Concepts: Linear and Nonlinear | NECSI

This tutorial provides examples of how to determine three main correlation types — Pearson, Spearman, and Data Science . In the first example, there is a clear monotonic (always increasing) and non-linear relationship. Some nonlinear relationships are monotonic, meaning they always increase or decrease, but not both. Monotonic relationships differ from. I'm not sure where you read that a relationship must already be monotone So yes, the value you calculated has meaning independent of any.

Although you would normally hope to use a Pearson product-moment correlation on interval or ratio data, the Spearman correlation can be used when the assumptions of the Pearson correlation are markedly violated. However, Spearman's correlation determines the strength and direction of the monotonic relationship between your two variables rather than the strength and direction of the linear relationship between your two variables, which is what Pearson's correlation determines.

What is a monotonic relationship? A monotonic relationship is a relationship that does one of the following: Examples of monotonic and non-monotonic relationships are presented in the diagram below: Join the 10,s of students, academics and professionals who rely on Laerd Statistics.

• Concepts: Linear and Nonlinear
• Linear, nonlinear, and monotonic relationships
• Spearman's Rank-Order Correlation

Spearman's correlation measures the strength and direction of monotonic association between two variables. Monotonicity is "less restrictive" than that of a linear relationship.

For example, the middle image above shows a relationship that is monotonic, but not linear. A monotonic relationship is not strictly an assumption of Spearman's correlation.

### Monotonic | Definition of Monotonic by Merriam-Webster

That is, you can run a Spearman's correlation on a non-monotonic relationship to determine if there is a monotonic component to the association. When there is very little information to determine what the relationship is, assuming a linear relationship is simplest and thus, by Occam's razor, is a reasonable starting point. However, additional information generally reveals the need to use a nonlinear relationship. Many of the possible nonlinear relationships are still monotonic.

This means that they always increase or decrease but not both. Monotonic changes may be smooth or they may be abrupt. For example, a drug may be ineffective up until a certain threshold and then become effective.

Testing the Assumptions for Spearman's Rank-Order Correlation in SPSS

However, nonlinear relationships can also be non-monotonic. For example, a drug may become progressively more helpful over a certain range, but then may become harmful.

Thus the degree of help increases and decreases and this is a non-monotonic, as well as a nonlinear, relationship. Even when a relationship is monotonic, and the changes in one quantity are smoothly related to the changes in the other quantity a linear relationship is not always the best approximation. It is often useful to generalize to a power law relationship.