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# How to Analyze Correlation between Ratio and Ordinal Scale Variables (Different Measurement Scales)

In correlation analysis, we often use Pearson correlation to test the relationship between variables measured on a ratio/interval scale. Variables measured on a ratio/interval scale have a greater potential to meet the normality assumption for data testing.

Recently, some students asked me how to test the relationship between variables with different measurement scales. For instance, they were curious about examining the correlation between competence measured on an ordinal scale and income measured on a ratio scale. This prompted me to write this article, addressing the appropriate tests for variables with different measurement scales. But before that, let’s delve into the basic concepts of correlation analysis.

## Basic Theory of Correlation Analysis

Correlation analysis is an associative test aiming to elucidate the relationship between variables. In correlation analysis, the tested variables are bidirectional. For example, if we test the relationship between competence and income, a positive and significant result implies that competence correlates with income, and vice versa.

This is different from linear regression analysis, where the associative relationship is one-way. An independent variable significantly affects the dependent variable, but the reverse is not necessarily true.

Therefore, correlation analysis does not use independent and dependent variables but focuses on how variables correlate with each other. It’s essential to understand that correlation analysis includes partial correlation and simultaneous correlation. In this article, I will focus on discussing partial correlation, widely used by researchers.

## Understanding Data Measurement Scales

In the previous paragraph, I mentioned discussing correlation tests for variables with different measurement scales. In statistics, variable measurement scales can be divided into four categories: nominal, ordinal, interval, and ratio scales. Parametric variables generally use interval and ratio scales, while non-parametric variables use nominal and interval scales.

For a detailed explanation of the differences between nominal, ordinal, interval, and ratio scales, refer to my previous article titled “How to Differentiate between Nominal, Ordinal, Interval, and Ratio Data Measurement Scales in Research.”

Variables measured on an ordinal scale have levels or ranks within their categories, such as educational attainment or competence measured using a Likert scale. In contrast, variables measured on a ratio scale have numerical data, intervals, and an absolute zero, such as production, consumption, and income.

## Correlating Ratio and Ordinal Scale Variables

If both variables are measured on a ratio scale, Pearson Product Moment correlation can be used. But what if you want to correlate a ratio scale variable with a non-parametric ordinal scale variable?

Consider a researcher investigating the relationship between competence and employee income. In this case, income is measured on a ratio scale, while competence is measured on an ordinal Likert scale.

In such cases, we can use the Spearman rank correlation test. The criterion is based on the lower scale of the variables being correlated. In this example, the ordinal scale is lower than the ratio scale when ranked from lowest to highest: nominal, ordinal, interval, and ratio.

If Pearson correlation is used, competence may not meet the normality assumption. Hence, it’s more appropriate to consider the Spearman rank correlation test, which does not require the data to be normally distributed.

## Conclusion

In conclusion, when conducting correlation tests, it’s crucial to consider the measurement scale of the variables. If the correlated variables have different measurement scales, focus on the lower measurement scale. I hope this article provides insights and proves beneficial. Until next week’s educational article from Kanda Data, thank you and see you soon.

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