Understanding Kendal’s Tau: a handy tool for exploring statistical relationships
Biomedical researchers often find themselves navigating through complex statistical methods to make sense of their data. One such method that can be incredibly useful in analyzing relationships between variables is Kendall's Tau. In this blog post, we'll break down Kendall's Tau in simple terms, making it accessible and applicable.
What is Kendal’s Tau?
Kendall's tau (τ) is a way to measure how strongly two things are connected, like the relationship between two factors in biomedical research. Specifically, it quantifies the similarity in the ordering of data points between two variables, regardless of the actual values of those variables. In other words, it tells us how well the variables move together or in opposite directions.
Kendal’s tau is especially helpful when the data you have doesn't meet the requirements of other tests, like Pearson’s product-moment correlation analysis or Spearman’s rank-order correlation analysis. Instead of assuming a certain shape for the relationship, like some other tests do, Kendall's tau is more flexible.
Calculating Kendall's Tau
To calculate Kendall's Tau, researchers compare the number of concordant and discordant pairs of observations in their data. A concordant pair is when the order of observations is the same for both variables, while a discordant pair is when the order is different.
Interpreting Kendall's Tau
The value of Kendall's Tau ranges from -1 to 1. A positive value indicates a positive association (as one variable increases, the other tends to increase), while a negative value suggests a negative association (as one variable increases, the other tends to decrease). A value close to 0 implies a weak or no association.
Advantages of Kendall's Tau:
One notable advantage of Kendall's Tau is its robustness against outliers, making it a reliable choice when dealing with real-world biomedical data, which often includes variations. Additionally, it does not assume a linear relationship between variables, providing flexibility in capturing different types of associations.
Using Kendal’s Tau in Biomedical Research
Imagine you're investigating the relationship between level of physical activity and patient satisfaction with a mobility device. Using Kendall's tau-b, you could analyze whether there's a connection between the levels of physical activity (e.g., low, moderate, high) and satisfaction with the device (very satisfied, moderately satisfied, not satisfied). This analysis may inform the design of such assistive devices.
In another example, Malmstrøm et al. (2018) used Kendal’s tau to correlate cancer stage as determined by computed tomography and by histopathology, in order to examine the use of computed tomography for preoperative staging of patients with colorectal cancer.
In both examples, Kendall's tau-b serves as a versatile tool for biomedical researchers, allowing them to explore associations between variables without assuming specific patterns, thereby enhancing the depth and accuracy of their analyses.
Conclusion
In biomedical research, understanding the relationships between different ordinal factors is crucial. For example, researchers might want to know if there's a connection between socioeconomic status and cancer stage at diagnosis or between stress levels and critical thinking skills in patients. Kendall's Tau helps researchers quantify and analyze these associations. By understanding this simple yet powerful statistical measure, researchers can gain insights into the connections between variables, ultimately advancing our understanding of diseases, treatments, and patient outcomes.
Looking for expert guidance as you explore relationships among your study variables? Collaborate with a biostatistician, under Editage’s Statistical Analysis & Review Services.
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