# Relationship between ordinal and continuous variable

The test is used for either ordinal variables or for continuous data that has failed Assumption #2: There is a monotonic relationship between the two variables. For two continuous variables you can perform a Pearson or Spearman's correlation .. can a correlation be done between a continuous and an ordinal variable?. As the correlation coefficient value goes towards 0, the relationship between the two variables will be weaker. Continuous data: Data that is interval or ratio level. analysis when the variables are measured on a scale that is at least ordinal.

**Scales of Measurement - Nominal, Ordinal, Interval, Ratio (Part 1) - Introductory Statistics**

Other relationships are possible. This relationship forms a perfect line. However, the real value of correlation values is in quantifying less than perfect relationships. Finding that two variables are correlated often informs a regression analysis which tries to describe this type of relationship more.

### What is the difference between categorical, ordinal and interval variables?

Other nonlinear relationships Pearson correlation coefficients measure only linear relationships. Spearman correlation coefficients measure only monotonic relationships.

So a meaningful relationship can exist even if the correlation coefficients are 0. Examine a scatterplot to determine the form of the relationship.

### Understanding the different types of variable in statistics

Just remember that if you do not test these assumptions correctly, the results you get when running a Spearman's correlation might not be valid. This is why we dedicate a number of sections of our enhanced Spearman's correlation guide to help you get this right.

You can find out about our enhanced content as a whole hereor more specifically, learn how we help with testing assumptions here. Spearman's correlation determines the degree to which a relationship is monotonic. Put another way, it determines whether there is a monotonic component of association between two continuous or ordinal variables.

As such, monotonicity is not actually an assumption of Spearman's correlation. However, you would not normally want to pursue a Spearman's correlation to determine the strength and direction of a monotonic relationship when you already know the relationship between your two variables is not monotonic.

## A comparison of the Pearson and Spearman correlation methods

Instead, the relationship between your two variables might be better described by another statistical measure of association. Say we assign scores 1, 2, 3 and 4 to these four levels of educational experience and we compare the difference in education between categories one and two with the difference in educational experience between categories two and three, or the difference between categories three and four.

The difference between categories one and two elementary and high school is probably much bigger than the difference between categories two and three high school and some college.

In this example, we can order the people in level of educational experience but the size of the difference between categories is inconsistent because the spacing between categories one and two is bigger than categories two and three. If these categories were equally spaced, then the variable would be an interval variable.

Interval An interval variable is similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced.

Why does it matter whether a variable is categorical, ordinal or interval? Statistical computations and analyses assume that the variables have a specific levels of measurement.

For example, it would not make sense to compute an average hair color. An average of a categorical variable does not make much sense because there is no intrinsic ordering of the levels of the categories.

Moreover, if you tried to compute the average of educational experience as defined in the ordinal section above, you would also obtain a nonsensical result. Because the spacing between the four levels of educational experience is very uneven, the meaning of this average would be very questionable.