In statistics, correlation tests are frequently used by researchers to examine associations. The purpose of conducting a correlation test is to determine the relationship between two observed variables. However, many people still ask me about one specific correlation test for variables measured on an ordinal scale.
As I have discussed in a previous article, there are several types of correlation tests to choose from. Of course, selecting the appropriate correlation test must follow scientific principles. One key factor in determining the correct correlation test is understanding the measurement scale of the data in statistics.
Several correlation tests are commonly used, including the Pearson product-moment correlation, Spearman rank correlation, and correlation tests for variables measured using a nominal scale. To select the appropriate test, it is essential to consider the measurement scale of the data.
In this article, I will focus on Spearman rank correlation analysis, providing a case study example for practical analysis along with result interpretation. Before starting the correlation analysis, let’s first understand the theoretical concept of Spearman rank correlation.
Basic Theory of Correlation Analysis
According to its fundamental theory, Spearman rank correlation is a non-parametric statistical technique used to estimate the relationship between two variables measured on an ordinal scale. Additionally, Spearman rank correlation can be applied when the data do not meet the assumption of normal distribution.
There is an important aspect to understand when using Spearman rank correlation analysis. In this analysis, we do not use the actual values of the data; instead, we use the rank values of the data. Therefore, Spearman rank correlation is applicable for variables measured on an ordinal scale or for data that contain extreme outliers.
The Spearman rank correlation coefficient ranges from -1 to 1. In Spearman rank correlation analysis, it is crucial to understand the significance of positive and negative signs when interpreting the results.
A positive correlation coefficient indicates a direct relationship, meaning that if one variable increases, the other variable tends to increase as well. Conversely, a negative correlation coefficient indicates an inverse relationship, meaning that as one variable increases, the other variable decreases.
In Spearman rank correlation analysis, the prerequisite assumptions are not as strict as those of parametric methods. Since Spearman correlation is a non-parametric method, its assumptions are more flexible compared to Pearson correlation.
The primary assumption of Spearman rank correlation is that the data must be paired, meaning that each observation has a corresponding pair with another observation. Additionally, the data collected for correlation testing can be in the form of ordinal scale data or numerical data that can be converted into ranks without losing the meaning of their relationship.
One of the key points in Spearman rank correlation is that it does not assume that the data must be normally distributed. Therefore, even if a variable is measured using an interval or ratio scale but is not normally distributed, Spearman rank correlation can still be used for the analysis.
Case Study Example: The Relationship Between Education Level and Employee Performance
As I promised at the beginning of this article, I will provide a case study on the relationship between education level and employee performance. Based on this case study, we can identify that the two variables we are examining are measured using an ordinal scale.
In this case study, data was collected from 40 respondents using a simple random sampling technique. The education level variable is categorized into four levels: Score 1 for elementary school graduates, Score 2 for middle school graduates, Score 3 for high school graduates, Score 4 for university graduates.
Meanwhile, the employee performance variable is categorized into three levels: Score 1 for low performance, Score 2 for medium performance, and Score 3 for high performance. The detailed data from the 40 respondents can be seen in the table below:
Based on the table above, the next step is to conduct a Spearman rank correlation analysis. For the practical analysis in this article, I will use SPSS software.
Steps for Spearman Rank Correlation Test
The first step is to set up the variables in the Variable View window in SPSS. Enter the variable name as “Education” in the Name column, and provide a full description “Education Level” in the Label column. In the Measure column, select Ordinal.
Similarly, for the second row, enter “Performance” in the Name column, provide the label “Employee Performance Level”, and ensure the Measure is set to Ordinal.
After setting up the variables in Variable View, the next step is to switch to the Data View window in SPSS. Copy the data from Excel and paste it into SPSS, ensuring that both the education level and employee performance variables are correctly entered before proceeding with the Spearman rank correlation analysis.
The steps for conducting the analysis are as follows:
- Click the “Analyze” ribbon, then select “Correlate” and choose “Bivariate”.
- In the Bivariate Correlations window, move the education level and employee performance variables from the left box to the right box.
- Ensure that Spearman is checked under Correlation Coefficients and uncheck Pearson.
- Under Test of Significance, select Two-tailed and check Flag Significant Correlations to mark significant correlations with an asterisk.
- You can also add additional statistics such as the mean and standard deviation by clicking “Options”.
- After completing the analysis setup, click “OK”, and the output will appear in a new SPSS window.
Interpretation of Results
Based on the analysis results, the output will be displayed as shown in the image below:
From the analysis, the correlation coefficient between education level and employee performance is 0.986. In correlation analysis, there are three key aspects to consider: the strength of the relationship, the direction of the relationship, and the significance of the relationship.
The correlation coefficient of 0.986 is very close to 1, indicating a strong correlation. Additionally, the correlation is positive, meaning that the relationship between the two variables is in the same direction.
The p-value of 0.000 is smaller than 0.05, meaning that we reject the null hypothesis. Since the null hypothesis is rejected, we can conclude that education level has a significant relationship with employee performance.
The positive correlation coefficient indicates that higher education levels tend to be associated with higher employee performance levels. Conversely, employees with lower education levels tend to have lower performance levels.
This case study serves as a learning example based on sample data. However, in real-world applications, you should verify your findings with actual data collected from your research.
That concludes this article, I hope it is useful and provides insight for those who need it. Stay tuned for updates from Kanda Dara in future articles!
