What are Spearman's rho and Pearson's r for ordinal categories?

To get these statistics, choose Stat > Tables > Cross Tabulation and Chi-Square, click Other Stats, and select Correlation coefficients for ordinal categories.

Use Spearman's rho and Pearson's r to assess the association between two variables that have ordinal categories. Ordinal categories have a natural order, such as small, medium, and large.

The coefficient can range in value from -1 to +1. The larger the absolute value of the coefficient, the stronger the relationship between the variables. An absolute value of 1 indicates a perfect relationship, and a value of zero indicates the absence of an ordinal relationship. Whether an intermediate value is interpreted as a weak, medium, or strong correlation depends on your goals and requirements.

Example of Spearman's rho and Pearson's r

For example, you analyze customer satisfaction for a car dealership that offers three levels of ongoing service for new cars: no service, standard service, and premium service. You take a random sample of customers and ask them whether they are unsatisfied, neutral, or satisfied with customer service. Your data includes two ordinal variables: service package and customer satisfaction. You want to determine whether an association exists between the level of service customers receive and their overall satisfaction. You enter the data in the following two-way table:
No service Standard service Premium service
Unsatisfied 162 104 36
Neutral 99 91 93
Satisfied 39 105 171

Spearman's rho and Pearson's r for this table are both 0.424. You conclude there is a positive association between level of service and customer satisfaction: customers who choose a higher service plan tend to express more satisfaction with this business.

Important considerations for Spearman's rho and Pearson's r

Remember that correlation does not imply causation. For example, if ice cream sales are positively correlated with shark attacks on swimmers, it does not mean that ice cream consumption somehow causes sharks to attack. Another variable, such as warm weather, may cause an increase in both ice cream sales and oceanic swimming.

The Pearson statistic calculated with Cross Tabulation and Chi-Square is only for ordinal data. For example, the continuous values of 22, 37, and 53 are analyzed as the ordinal values 1, 2, and 3. To calculate the Pearson correlation coefficient for two or more columns of continuous data, use Stat > Basic Statistics > Correlation instead.

Note

For text values, you should change the default value order if necessary, to show the natural order of the categories. For example, unless you change the value order for a column with the text values "narrow", "medium", and "wide", these values will be ordered alphabetically and analyzed as the ordinal values 2, 1, and 3.

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