# Test for relationship between two ordinal variables

### chi-square with ordinal data

How can you take that ordinal information and make it part of your analysis? At first glance we might be tempted to apply a standard Pearson's chi-square test to these data, Notice that Trauma represents an ordered variable. The Pearson correlation between those two measures is , which has. This page shows how to perform a number of statistical tests using SPSS. . Using the hsb2 data file, let's see if there is a relationship between the type of one independent variable with two or more levels and an ordinal dependent variable. Test of Association Between Two Ordinal Variables While Adjusting for two multinomial models and then tests for correlation between these.

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.

Instead, the relationship between your two variables might be better described by another statistical measure of association.

## Announcement

For this reason, it is not uncommon to view the relationship between your two variables in a scatterplot to see if running a Spearman's correlation is the best choice as a measure of association or whether another measure would be better.

If your two variables do not appear to have a monotonic relationship, you might consider using a different statistical test, which we show you how to do in our Statistical Test Selector N. This data file contains observations from a sample of high school students with demographic information about the students, such as their gender femalesocio-economic status ses and ethnic background race.

It also contains a number of scores on standardized tests, including tests of reading readwriting writemathematics math and social studies socst.

### How to calculate the correlation between two ordinal variables? - Statalist

You can get the hsb data file by clicking on hsb2. One sample t-test A one sample t-test allows us to test whether a sample mean of a normally distributed interval variable significantly differs from a hypothesized value. For example, using the hsb2 data filesay we wish to test whether the average writing score write differs significantly from We can do this as shown below.

The mean of the variable write for this particular sample of students is We would conclude that this group of students has a significantly higher mean on the writing test than One sample median test A one sample median test allows us to test whether a sample median differs significantly from a hypothesized value.

We will use the same variable, write, as we did in the one sample t-test example above, but we do not need to assume that it is interval and normally distributed we only need to assume that write is an ordinal variable. Binomial test A one sample binomial test allows us to test whether the proportion of successes on a two-level categorical dependent variable significantly differs from a hypothesized value.

### What statistical analysis should I use? Statistical analyses using SPSS

Chi-square goodness of fit A chi-square goodness of fit test allows us to test whether the observed proportions for a categorical variable differ from hypothesized proportions. We want to test whether the observed proportions from our sample differ significantly from these hypothesized proportions.

What we want is a statistic that does take order into account. A Correlational Approach There are several ways we can accomplish what we want, but they all come down to assigning some kind of ordered metric to our independent variables. Dropout is not a problem because it is a dichotomy.

**Lambda Measure of Association for Two Nominal Variables in SPSS**

We could code dropout as 1 and non-dropout as 2, or dropout as 1 and non-dropout as 0, or any other two values we like. The result will not be affected by our choice of values.

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

When it comes to the number of traumatic events, we could simply use the numbers 0, 1, 2, 3, and 4. Alternatively, if we thought that 3 or 4 traumatic events would be much more important than 1 or 2, we might use 0, 1, 2, 4, 6.

In practice, as long as we chose numbers that are monotonically increasing, and are not very extreme, the result will not change much as a function of our choice. I will choose to use 0, 1, 2, 3, and 4.