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# How to Interpret the Output of Correlation Analysis | Hypothesis Testing, Sign, Size, and Direction

Correlation analysis is an associative test commonly used by many researchers to understand the relationship between variables. Before discussing how to interpret the results of correlation analysis, it is essential to understand the basic theory of correlation analysis.

The selection of correlation analysis is determined based on the measurement scale of the variables. In statistics, the measurement scale of variables can be divided into four types: nominal data scale, ordinal data scale, interval data scale, and ratio data scale.

Pearson correlation analysis is the most frequently used partial correlation analysis by researchers. When applying correlation analysis, some fundamental assumptions need to be met.

These assumptions include having normally distributed data. The commonly used measurement scales are interval or ratio data scales to achieve normally distributed data based on the normality test results.

Next, what if the measurement scale uses nominal or ordinal data scales, which fall under non-parametric types?

Generally, the measurement scale for non-parametric variables is not normally distributed, so that we can choose an appropriate alternative correlation analysis. For example, when the data scale is ordinal, we can consider using Spearman’s rank correlation analysis or Kendall’s tau.

On the other hand, if the measurement scale used for the variables is at the nominal scale, we may consider using the Chi-square test.

Once we have a better understanding of the basic theory of correlation analysis, we can proceed to discuss how to interpret the results of correlation analysis.

## Interpretation Method for Hypothesis Testing

The first thing we will discuss regarding result interpretation is hypothesis testing in correlation analysis. This hypothesis testing refers to statistical hypothesis testing.

It is crucial as it relates to research hypotheses. As we already know, we can formulate hypotheses to be tested when we use inferential statistical analysis.

For example, when a researcher tests “The relationship between employee motivation and employee performance.” Based on this example, we know that employee motivation and performance are measured using ordinal scales. Therefore, in this example, we use Spearman’s rank correlation analysis.

The research hypothesis states: “Employee motivation has a significant relationship with employee performance.” We can conduct research activities to prove this hypothesis, including data collection and analysis.

Next, to test this research hypothesis, we can formulate it into statistical hypotheses consisting of the null and alternative hypotheses.

For example:

Ho: Employee motivation does not have a significant relationship with employee performance.

Ha: Employee motivation has a significant relationship with employee performance.

We will test the null hypothesis to interpret the analysis results and determine whether we will accept or reject the null hypothesis. If we reject the null hypothesis, it means we accept the alternative hypothesis.

Based on the example above, if the correlation coefficient is 0.875, how do we decide on the statistical hypothesis testing?

To test this statistical hypothesis, we can use two criteria. The first criterion is to compare the correlation coefficient value with the critical value in the R-table. The second criterion involves looking at the probability value of the alpha error.

If we perform the calculations manually, we need to find the value in the R-table. However, if we use data analysis software, the probability value for the error level is readily available. Usually, this probability value is denoted as “sig” (p-value).

The next step is to conclude, for example, with a correlation coefficient value of 0.875 and a known “sig” value of 0.0012. Based on this value, we can conclude that the “sig” value is less than 5% alpha. Therefore, based on the analysis results, we reject the null hypothesis.

Since we reject the null hypothesis, we accept the alternative hypothesis. Consequently, it can be concluded that employee motivation has a significant relationship with employee performance.

## Interpreting the Direction of Relationship

Based on the example of a study on the relationship between employee motivation and performance, the correlation coefficient is 0.875. Thus, it can be concluded that the correlation is positive, meaning that the two variables have a positive relationship.

If we interpret this, an increase in employee motivation is estimated to improve employee performance. Conversely, a decrease in employee motivation is estimated to result in a decline in performance.

Therefore, we can understand that a positive correlation coefficient indicates a positive direction of the relationship, while a negative correlation coefficient indicates an inverse direction.

## Interpreting the Strength of Relationship

The final interpretation method is to determine the strength of the relationship. When reading research articles, we sometimes come across statements like “the relationship is very strong” or “the correlation is considered strong” in another article.

Here is an example of applying the interpretation of the strength of the relationship. The categories for the strength of a relationship can be grouped into very weak, weak, moderate, strong, and very strong. Some references divide the relationship into strong and weak.

When we observe a correlation coefficient value of 0.875, the correlation value approaches 1, which signifies a strong relationship.

It’s time to conclude after discussing the interpretation of the correlation analysis results. When researchers choose correlation analysis, they need to consider the measurement scale of the data and the required assumptions.

In the choice of correlation analysis, the interpretation should include at least three aspects: hypothesis testing, direction of the relationship, and strength.

Well, this is the article I can write for now. I hope it is beneficial and adds value to our knowledge. See you in the educational articles from Kanda Data next week. Thank you.

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