# Monotonic relationship between variables

Spearman's correlation coefficient is a statistical measure of the strength of a monotonic relationship between paired data. In a sample it is denoted by and is by. Your understanding of Spearman's rank-correlation measure seems wrong. There is no monotonicity assumption in applying it. In fact it was. The term "correlation" refers to a mutual relationship or association between . shows weak association, since the data is non-monotonic.

Linear relationships are most common, but variables can also have a nonlinear or monotonic relationship, as shown below.

## Spearman's Rank-Order Correlation using SPSS Statistics

It is also possible that there is no relationship between the variables. You should start by creating a scatterplot of the variables to evaluate the relationship.

A linear relationship is a trend in the data that can be modeled by a straight line. For example, suppose an airline wants to estimate the impact of fuel prices on flight costs.

This describes a linear relationship between jet fuel cost and flight cost.

Strong positive linear relationship Plot 2: Strong negative linear relationship When both variables increase or decrease concurrently and at a constant rate, a positive linear relationship exists. The points in Plot 1 follow the line closely, suggesting that the relationship between the variables is strong.

When one variable increases while the other variable decreases, a negative linear relationship exists.

The points in Plot 2 follow the line closely, suggesting that the relationship between the variables is strong. Weak linear relationship Plot 4: Nonlinear relationship The data points in Plot 3 appear to be randomly distributed.

The Spearman's rank-order correlation is the nonparametric version of the Pearson product-moment correlation.

### Linear, nonlinear, and monotonic relationships - Minitab Express

What are the assumptions of the test? You need two variables that are either ordinal, interval or ratio see our Types of Variable guide if you need clarification. 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?

## Spearman's Rank-Order Correlation

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