Correlation analysis aims to determine the relationship between variables. Partial correlation analysis is the analysis most often used by researchers.
In the correlation analysis, we must choose the right analysis according to the variable measurement scale. Correlation analysis for nonparametric variables is different from correlation analysis for parametric variables.
Examples of correlation analysis that researchers often use include Pearson correlation analysis, Spearman rank correlation, Kendall Tau, Contingency, Lambda correlation, Cramer correlation, and others. The choice of correlation analysis has the required assumptions.
Before discussing further, it would be better for us to understand the differences between the variables included in parametric statistics and those included in nonparametric statistics.
The difference between parametric and nonparametric statistics
In statistics, we know about parametric statistics and nonparametric statistics. The selection of both is generally based on the variable measurement scale. Based on the measurement scale, the data is divided into nominal, ordinal, interval, and ratio scales.
Which variables are included in parametric statistics, and which variables are included in nonparametric statistics? Variables measured using interval and ratio measurement scales fall into parametric statistics. The variables measured using nominal and ordinal scales are included in nonparametric statistics.
Characteristics of parametric variables can be obtained in numerical values. As for nonparametric variables, instruments are needed so that the variables measured using nominal and ordinal scales can be converted into numeric and further analysis can be carried out.
Correlation analysis assumptions
As I wrote before, there are several correlation analysis choices in both parametric and nonparametric statistics. Next, we need to understand that several correlation analysis options use nonparametric variables.
In this article, the nonparametric variables are measured using nominal and ordinal scales. The difference between the two is that the variables measured using a nominal scale are categorized, aiming only to differentiate (without level) so that their meaning can be understood.
As for the variables measured using an ordinal scale, the categorization, besides aiming to differentiate, also includes levels. Variables measured using a nominal scale and those measured using an ordinal scale have different choices for correlation analysis.
Correlation of ordinal scale vs ordinal scale variables
The first analysis we discuss is correlation analysis for variables measured using an ordinal scale. Examples of variables are education level, perception, behaviour, motivation, competence, and others. For these variables, you can use the Likert scale approach.
Furthermore, what correlation analysis can we choose if the variables measured use an ordinal scale? We can use Spearman and Kendall tau rank correlation in the variables measured using an ordinal scale.
For example, a researcher observed the relationship between employee competency and performance. These two variables are measured using a Likert scale. The researcher can consider one of them using the Spearman rank correlation.
Correlation of nominal scale vs nominal scale variables
The variables measured using a nominal scale are indicated by the categorization of variables which only aims to differentiate. Examples are gender, type of work, place of residence, and so on.
Variables measured using a nominal scale may consider using Chi-square, contingency coefficients, and others. For example, a researcher wants to know the relationship between gender and type of work. Both are measured using a nominal scale, so one of these researchers can consider using chi-square.
Conclusion
In conclusion, I will underline that the correlation analysis on nonparametric variables does not require the assumption that the data must be normally distributed. The second thing to note, the variable measurement scale will determine the right choice of correlation analysis.
One of the variables analyzed using an ordinal scale can be considered using Spearman’s rank correlation. As for the variables measured using a nominal scale, we can consider using a chi-square.
The interpretation of the results in the correlation analysis for nonparametric variables is the same as in the correlation analysis for parametric variables. Researchers need to look at the correlation coefficient’s significance value to determine whether or not the relationship is significant.
In addition, researchers need to look at the magnitude of the correlation coefficient and the direction of the correlation coefficient. These three things are useful to assist in the interpretation of the results and concluding the research that has been done.
Well, this is an article that I can write on this occasion. Hopefully useful and add new insight related to statistics and data analysis. See you in the educational article next week. Thank You!
