Examples of Kendall's Tau: 3 Practical, Real-World Uses

Why focus on real examples of Kendall’s tau?

Correlation sounds simple until your data refuses to cooperate. Real datasets are often:

• Ranked instead of measured on a continuous scale
• Full of ties (same rank for multiple items)
• Nonlinear or clearly not normal

That’s where Kendall’s tau comes in. It measures how well two variables move together in terms of order, not distance. If you care about “who ranks higher” more than “how much higher,” Kendall’s tau is usually a better fit than Pearson.

This article centers on examples of Kendall’s tau: 3 practical examples, but we’ll also build several variations around each one so you see how the same logic applies across different fields.

Example of Kendall’s tau in health research: symptom severity vs. quality of life

Health data is rarely neat. Patients report symptoms in ordered categories (none, mild, moderate, severe), and quality of life is often measured with composite scores that don’t behave like clean, continuous variables.

Imagine a study of adults with chronic pain. Researchers record:

• Pain severity rank: 1 = mild, 2 = moderate, 3 = severe
• Quality-of-life rank: 1 = high, 2 = medium, 3 = low

You don’t trust the exact numeric distances, but you do trust the order. That’s a textbook situation for Kendall’s tau.

Let’s say you have data for 10 patients:

Kendall’s tau looks at pairs of patients and asks:

• Are their orders consistent (concordant)?
• Or do they go in opposite directions (discordant)?

If higher pain is usually paired with lower quality of life (worse rank), you’ll see a positive Kendall’s tau close to 1. If the relationship is weak, tau will be near 0. If patients with more pain sometimes report better quality of life, tau may even go negative.

In practice, a health researcher might:

• Use Kendall’s tau to assess the association between depression severity (ranked scale) and sleep quality categories (e.g., good/fair/poor)
• Run the analysis separately by age group to see if the pattern differs in older vs. younger adults
• Report tau alongside confidence intervals and p-values

For instance, a study might report: _“Kendall’s tau between pain severity and quality-of-life rank was 0.62 (p < 0.001), indicating a strong monotonic relationship.”_

This kind of approach is common in epidemiology and clinical research, where variables are often ordinal. For background on how mental health and symptom scales are built, you can browse resources from the National Institute of Mental Health (NIMH) or the NIH.

Here, our example of Kendall’s tau shows why it’s attractive:

• It respects the ordered nature of symptom categories
• It handles ties better than Spearman’s rho in many cases
• It doesn’t assume equal spacing between categories

When you think about real examples of Kendall’s tau in medicine, you’ll see it wherever the outcome is ranked: pain scales, symptom severity, functional status, triage priority, and so on.

Examples of Kendall’s tau: 3 practical examples in business and customer analytics

Let’s move into the world of product and marketing teams. This is where data analysts often reach for Pearson out of habit, even when the data is clearly ordinal. Here we’ll frame examples of Kendall’s tau: 3 practical examples that product managers and analysts are likely to recognize.

1. Comparing product satisfaction rankings across platforms

Suppose you run a SaaS product and track customer satisfaction on two different platforms:

• In-app survey: 1–5 stars
• Email follow-up: 1–5 stars

You collect responses from the same 200 customers on both channels. You don’t fully trust the spacing between 1 and 2 vs. 4 and 5 stars, but you do care whether customers who are happy in-app are also happy via email.

You convert each customer’s scores into ranks and compute Kendall’s tau between:

• Rank of in-app rating
• Rank of email rating

If Kendall’s tau = 0.78, that tells you the ordering of satisfaction is very consistent across channels. Customers who rate you highly in-app also tend to rate you highly by email.

This is one of the best examples of Kendall’s tau in business because:

• Ratings are ordinal, not truly continuous
• The distribution is often skewed (lots of 4s and 5s)
• Ties (many customers with the same rating) are common

2. Ranking marketing channels by lead quality

Another real example: a B2B marketing team ranks leads from different channels by quality (high, medium, low) based on sales outcomes.

You might have:

• Channel rank by marketing (based on engagement metrics)
• Channel rank by sales (based on closed-won deals)

You want to know: _Do the channels that look good to marketing also look good to sales?_

Here you can:

• Assign ranks to each channel from 1 (best) to k (worst)
• Use Kendall’s tau to measure the agreement between the two ranking systems

If tau is close to 1, your marketing scoring system is aligned with actual revenue impact. If it’s near 0 or negative, your “top” channels may not really be top.

3. Prioritizing product features from different stakeholder groups

Product managers often juggle multiple ranked lists of feature priorities:

• Customer success team’s feature priority list
• Engineering team’s feasibility-based priority list
• Executive team’s strategic priority list

You can use Kendall’s tau to compare any pair of these lists:

• Customers vs. executives: Are leaders aligned with user needs?
• Customers vs. engineering: Are the most requested features the hardest to build?

Suppose you rank 15 proposed features. Kendall’s tau between customer and executive rankings is 0.55 (moderate agreement), but between customers and engineering it’s −0.10 (slight disagreement). That tells a political story: engineering may be resisting exactly the features users want most.

Across these business scenarios, the examples of Kendall’s tau: 3 practical examples highlight a pattern: whenever you’re comparing different rankings of the same items—channels, features, customers—Kendall’s tau is usually the right correlation tool.

Education and testing: more real examples of Kendall’s tau in action

Education is full of ordered scores, grade bands, and rankings. That makes it fertile ground for more examples of Kendall’s tau.

Student performance on different types of assessments

Imagine a school district tracking 11th graders’ performance on:

• A multiple-choice standardized test (scaled score, then converted to percentile ranks)
• A project-based assessment scored by rubrics (converted to performance levels: below basic, basic, proficient, advanced)

Researchers don’t want to pretend these scores are perfectly interval-scaled, but they do want to know whether students who rank high on the standardized test also rank high on the project-based assessment.

They can:

• Convert both measures to ranks
• Compute Kendall’s tau between standardized test rank and project rank

If tau = 0.40, that suggests a moderate monotonic relationship: high test scorers tend to do better on projects, but there’s plenty of shuffling in the middle.

This kind of analysis is relevant to debates about standardized testing vs. performance-based measures. For broader context on assessment research, the National Center for Education Statistics (NCES) is a solid starting point.

Teacher rankings vs. algorithmic predictions

Another real example of Kendall’s tau in education: comparing human judgment with algorithmic predictions.

Say a district uses an early-warning system that ranks students by risk of not graduating. Counselors also informally rank students by concern based on their own knowledge.

• Algorithm rank: 1 = highest risk, 200 = lowest risk
• Counselor rank: 1 = most concern, 200 = least concern

You want to know: _How well does the algorithm’s ordering match counselors’ intuition?_ Kendall’s tau answers that by measuring the agreement between the two ranked lists.

A low tau (e.g., 0.15) doesn’t necessarily mean the algorithm is wrong—it may be catching patterns humans miss—but it does tell you there’s low rank agreement, which has implications for training and adoption.

Admissions rankings across different criteria

Colleges and graduate programs often build composite scores to rank applicants, but admissions committees also review qualitative factors: essays, recommendations, interviews.

Consider these two rankings of applicants:

• Score-based rank: built from GPA, test scores, and work experience
• Holistic review rank: after full committee discussion

Kendall’s tau can quantify how much the holistic process reshuffles the purely quantitative ranking.

In this cluster of education examples, Kendall’s tau is doing the same job over and over: measuring how consistently people or systems rank the same set of students.

When are examples of Kendall’s tau better than Pearson or Spearman?

At this point we’ve covered several examples of Kendall’s tau: 3 practical examples and then some. So when should you actually pick Kendall’s tau over the more familiar options?

Think of these conditions:

• Your variables are ordinal (ordered categories) or are continuous but clearly not normal
• You care about rank order more than exact numeric differences
• You expect many ties (e.g., lots of identical ratings, many students with the same grade band)

Kendall’s tau vs. Spearman’s rho:

• Both are rank-based correlations
• Spearman’s rho is based on differences in ranks
• Kendall’s tau is based on concordant vs. discordant pairs

In practice, tau is often preferred when:

• You have smaller samples and want a measure with a clearer probabilistic interpretation (tau can be seen as the difference between the probability of concordance and discordance)
• You have many ties and want a statistic that tends to be more stable in that setting

For more technical details, many university statistics departments host clear notes; for example, you can find rank correlation discussions in online materials from schools like Harvard or other .edu statistics pages.

Extending the 3 core scenarios: more variations and real examples

To hit the 2024–2025 reality, let’s stretch the three main domains—health, business, education—into a few more concrete examples of Kendall’s tau you might actually run into.

Public health dashboards and risk tiers

Public health agencies increasingly categorize regions into risk tiers (low, medium, high) based on different models. Suppose you have:

• Model A: risk tier based on case rates and hospitalizations
• Model B: risk tier including vaccination coverage and testing positivity

Kendall’s tau can measure how consistently counties are ranked by risk under the two models. A high tau means both models tell essentially the same story about relative risk; a low tau signals that changing the model meaningfully reshuffles which counties look most vulnerable.

Given the ongoing focus on infectious disease surveillance after COVID-19, this kind of example of Kendall’s tau is likely to remain relevant for years. For context on surveillance metrics, see resources from the CDC.

Telehealth satisfaction vs. in-person satisfaction

Healthcare systems now routinely compare patient satisfaction with telehealth visits vs. in-person visits. Patients might rate each on a 1–5 scale. For patients who used both, you can:

• Rank telehealth satisfaction
• Rank in-person satisfaction
• Use Kendall’s tau to see whether patients who love telehealth also love in-person care, or whether there’s a split audience

Again, you don’t need to believe that the jump from 2 to 3 stars equals the jump from 4 to 5. You just need to trust that higher stars mean “better.” That’s exactly the territory where Kendall’s tau works well.

EdTech platforms and engagement rankings

In the education technology space, platforms often rank students by engagement based on click data, video completion, and quiz attempts. Teachers may also rank students informally by how engaged they seem in class.

Using Kendall’s tau to compare:

• Platform engagement rank
• Teacher-perceived engagement rank

gives you a quantitative sense of how well the platform’s metrics line up with classroom reality. This is another modern, data-driven example of Kendall’s tau that goes beyond textbook exercises.

FAQ: examples of Kendall’s tau, interpretation, and practice

What is a good example of using Kendall’s tau instead of Pearson?

A clean example of Kendall’s tau beating Pearson is any situation with ordinal survey responses—for instance, 1–5 satisfaction ratings collected from the same people across two different products. The data are ordered but not truly continuous, and there are often many ties. Kendall’s tau respects the ranking and handles ties more gracefully than Pearson’s correlation.

How do I interpret Kendall’s tau in real examples?

Kendall’s tau ranges from −1 to 1:

• 1: perfect agreement in ordering; every pair is concordant
• 0: no systematic monotonic relationship in order
• −1: perfect disagreement; one variable’s order is exactly reversed

In real examples of Kendall’s tau, values around 0.1–0.3 are often described as weak, 0.3–0.5 as moderate, and above 0.5 as strong, though the context and sample size matter more than any rule of thumb.

Are there software tools that make examples of Kendall’s tau easy to run?

Yes. Most major tools support Kendall’s tau directly:

• R: cor(x, y, method = "kendall")
• Python (SciPy): scipy.stats.kendalltau(x, y)
• SPSS / Stata / SAS: all have options for Kendall’s tau in their correlation procedures

This makes it easy to replicate the examples of Kendall’s tau: 3 practical examples described above with your own data.

Can I use Kendall’s tau with small samples in real research examples?

You can, but be cautious. Kendall’s tau works with small samples, yet the uncertainty (wide confidence intervals) can be large. For small n, it’s especially important to report confidence intervals and p-values, and to interpret your real examples of Kendall’s tau as suggestive rather than definitive.

Where can I see published research that uses Kendall’s tau?

You’ll find Kendall’s tau in medical journals, education research, and social science papers whenever the variables are ordinal or heavily tied. Many articles indexed on PubMed report Kendall’s tau for relationships between symptom scales, clinician ratings, or ordinal outcomes.

By anchoring Kendall’s tau in health, business, and education, these examples of Kendall’s tau: 3 practical examples—and their variations—should give you a concrete mental model: whenever your data is about who ranks higher, not how far apart they are, Kendall’s tau deserves a serious look.