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The correlation ratio is an analytical method used to understand the correlation between categorical and quantitative data. Let us explain this using a concrete example.
We conducted a survey on 15 people to determine the relationship between their favorite health supplements and their age. Their favorite supplements represent “category data,” while their age constitutes “quantity data.” The basic analysis method for categorical and quantitative data was used to calculate the averages by category. Therefore, we determined the average age for each supplement.
Table 1 shows the response data from 15 people categorized by supplement and the calculated average age.
[Table 1]
The table shows that the average age varied for each supplement. “There is a difference” means that “a certain age group has an increasing preference for a particular supplement,” and it can be determined that “there is a relationship between age and preferred supplements.”
However, the strength of this relationship cannot be determined from the category-wise average.
Measure the strength of the relationship using the correlation ratio
The correlation ratio is an analytical method that reveals the strength of the relationship between categorical and quantitative data. The correlation ratio takes a value between 0 and 1; the higher the value, the stronger the relationship.
In this example, the correlation ratio is 0.604 (the calculation of the correlation ratio is explained next). No statistical standard exists for determining the number of correlation ratio values that must be relevant.
Generally, the standards are set as listed in Table 2. In this example, we can determine the existence of a strong relationship, based on the correlation ratio.
[Table 2] Criteria for determining the correlation ratio
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