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# The Fundamental Differences of Pearson Correlation, Spearman Rank, Kendall tau, and Chi-Square

The associative correlation test between variables is currently the most frequently chosen by researchers, lecturers, and students to answer research hypotheses. There are several choices of correlation tests that can be chosen, but the selection of correlation tests must follow statistical rules.

The purpose of the correlation test is to determine the significance of the relationship between variables. In addition, the correlation test can also be seen sign and correlation coefficient.

The coefficient value is in the range of zero to one. The correlation coefficient whose value is closer to one, the higher the closeness of the relationship on the variables tested.

A positive sign on the correlation coefficient indicates a unidirectional relationship between variables. Then the negative sign on the correlation coefficient indicates the opposite relationship.

The correlation analysis that is often chosen is a partial correlation. The partial correlation analysis examines the relationship between two variables. For simultaneous correlation analysis, we will discuss this on another occasion.

When you read scientific journals, you can find different correlation analysis options. For example, in a scientific article, you find a researcher using the Pearson correlation.

But in other scientific articles, you can also find researchers using Spearman’s rank correlation analysis. You may also find researchers who test relationships using chi-square or contingency coefficients.

Well, on this occasion, Kanda Data will discuss the basic differences between several choices of correlation analysis. Researchers can choose correlation analysis options consisting of Pearson correlation analysis, Spearman’s rank, Kendall’s tau, chi-square, and contingency coefficients.

On this occasion, we will discuss when we can use Pearson correlation, Spearman’s rank, Kendall’s tau, and chi-square? The selection of each of these correlation analyses is adjusted to the type of measurement data.

In a previous article, I have stated that the type of data measurement scale consists of 4 scales, namely nominal, ordinal, interval, and ratio data scales. For those who haven’t read it yet, please visit Kanda Data’s article entitled: “Nominal, Ordinal, Interval, and Ratio Scales | Types Of Data Measurement.”

If you have read the article with the title above, you will find it easy to understand the choice of using correlation analysis which we will discuss. Let’s discuss the correlation tests one by one.

## Pearson Correlation

Pearson correlation is used to test the relationship between two variables with a ratio data scale. Variables with ratio data scales already have numerical data that can be directly analyzed.

In Pearson correlation, you need to test whether the data is normally distributed or not. One of the assumptions required is that the data is normally distributed.

Thus, you need to test the normality of the data. You can do a normality test using the Kolmogorov-Smirnov normality test, scatter plot, or other tests that you think are easy to do.

## Spearman’s Rank Correlation

Spearman rank correlation is intended to test the relationship between two variables with ordinal data scales. The ordinal data scale is non-parametric, so you need to convert the variables into scores.

Qualitative variables, such as entrepreneurial competence, producer behavior, learning motivation, etc., cannot be obtained directly with numerical data. You can use a Likert scale or create question items on the questionnaire to obtain a score.

The sum of the scores from the statement/question items for each variable represents your observed variables. In the Spearman’s rank correlation, you do not need to test the normality of the data.

## Kendall’s Tau Correlation

In principle, the Kendall’s tau correlation test is almost the same as the Spearman’s rank correlation. The Kendall’s tau correlation test can test the relationship between variables with a minimal scale of ordinal data.

The Kendall’s tau correlation is used to measure conformity, namely, whether there is a difference in the level of ranking suitability between the two observed variables.

Example: correlation of two interviewers selecting prospective employees, correlation of performance on practical and theoretical exams in one course at university.

## Chi-Square

Chi-square was used to measure the difference between the observed and expected frequencies of variables. The chi-square test can be used as an alternative to testing the relationship between variables with a nominal data scale.

Therefore, if you want to test the relationship between two variables but both variables are on a nominal scale, you can consider using the chi-square test.

## Conclusion

You can choose to use correlation analysis according to the measurement scale of the variable. For example, ratio scale data can use Pearson correlation, then ordinal scale data can use Spearman’s rank correlation, and nominal scale data can use chi-square.

Maybe you want to know the relationship between variables that have different data scales at some point. For example, you will observe the relationship between entrepreneurial competence and income.

The income variable was measured using a ratio data scale, and the entrepreneurial competence variable was measured using an ordinal data scale. The next question is, which correlation to choose?

In principle, you need to look at the lowest data scale of your variable. In the example above, the lowest variable scale is the ordinal scale. The selection of the correlation test uses the lowest data scale of the correlated variables.

Therefore, in the example above, we can use the Spearman’s rank correlation test. With the same principle, you can use it for other case examples.

This time, that’s our discussion about the fundamental differences between Pearson Correlation, Spearman’s Rank, Kendall’s tau, and Chi-Square. See you in the following article!

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