Association analysis is fundamentally about recognizing that events and variables in the world often do not occur in isolation. Instead, they tend to co-occur in meaningful ways. Sometimes those relationships are informal rules of thumb learned through experience, and other times they can be measured rigorously using data. The Chicago taxi dataset provides a concrete example of how we move from intuition to evidence-based conclusions.
1. Associations in Everyday Life: How Humans Naturally Learn Patterns
People have always relied on observed associations to interpret the world and make decisions.
One classic example is the saying: “Red sky at night, sailors’ delight. Red sky in the morning, sailors take warning.” This reflects an association between the color of the sky and upcoming weather conditions. The reddish sky often results from haze or cloud conditions that can be linked to storm systems nearby. Even without modern meteorology, repeated observation across generations created a practical pattern: the sky’s appearance is not random—it is connected to atmospheric conditions that may predict weather changes.
Another everyday association is noticing that falling leaves signal the arrival of autumn. We do not need a calendar to sense seasonal change when we observe consistent environmental signals. Again, the idea is that one phenomenon (leaf drop) tends to co-occur with another phenomenon (seasonal transition), and that repeated co-occurrence becomes meaningful knowledge.
These examples demonstrate an important point: humans are naturally association detectors. Data analysis formalizes this instinct by making associations measurable, testable, and reproducible.
2. Moving From Intuition to Data: The Chicago Taxi Trip Case
To practice discovering associations using real data, consider a dataset of taxi trips in Chicago taken during September 2022.
The dataset has several characteristics that make it suitable for association analysis:
- It is provided by a government source: the City of Chicago’s Department of Business Affairs and Consumer Protection.
- It includes trips made between September 1 and September 30, 2022.
- It contains 217,631 observations and 13 attributes.
- It is large enough to reveal reliable patterns rather than isolated anecdotes.
The key analytical goal is not simply to summarize the data, but to ask association-driven questions that reflect real operational or behavioral mechanisms.
3. What It Means to “See” an Association in Data
In practice, an association becomes visible when we notice that outcomes are not evenly distributed. If two variables are unrelated, we would expect combinations of their values to occur in roughly predictable proportions. When certain combinations occur much more often than expected, we suspect that the variables are associated.
The dataset supports several natural research questions:
- Does the trip destination depend on the pickup area?
- Does trip time depend mainly on distance traveled?
- Do drivers get more tips if passengers pay by credit card?
Each question compares two variables and asks whether one helps explain the other.
4. Example 1: Does Destination Depend on Pickup Area?
Why this question matters
If pickup and dropoff locations are related, then pickup location can be used to anticipate passenger movement patterns. This can be operationally valuable for driver positioning, dispatching, surge strategies, and city planning.
How the data is structured
The dataset groups community areas into a set of focal neighborhoods and two airport regions, plus a large catch-all category called “Other Community.” The focal areas include Lake View, Lincoln Park, Near North Side, Near West Side, Loop, Near South Side, Midway Airport, and O’Hare Airport.
What the counts tell us
Simple frequency tables show that some pickup areas dominate. For instance, Near North Side has the largest pickup count among the highlighted areas, and “Other Community” is also extremely large. The same pattern holds for dropoffs: “Other Community” is the largest dropoff category.
This immediately reveals an important analytical challenge: the “Other Community” category is massive, and its size can visually dominate results. That dominance can hide patterns among the smaller categories unless the analysis is carefully designed.
Why a pickup–dropoff matrix is powerful
A pickup–dropoff table (or a heatmap of that table) shows the number of trips for each pair of pickup and dropoff communities. This is where association becomes “visible” because you can identify which pairs occur frequently and which pairs are rare.
However, raw counts can be misleading because larger pickup areas naturally create larger row totals. That is why row percentages are often more informative.
What row percentages add
When you compute “Percent of trips at each dropoff per pickup community,” you are essentially asking:
Given a specific pickup area, how do passengers distribute across dropoff areas?
This conditional view helps detect whether pickup area changes the destination distribution. If pickup had no relationship with dropoff, then each pickup row would have similar percentages across dropoffs. If the percentages vary substantially by pickup, that is strong evidence of association.
A key observation in this dataset is that the “Other Community” column often absorbs a large share of trips, but not uniformly. Some pickup areas send much larger fractions to “Other Community” than others. This unevenness is exactly what association looks like in categorical data.
5. Example 2: Does Trip Time Depend Mainly on Distance?
Why this is not trivial
In physics, time is proportional to distance if speed is constant. But in real cities, speed is not constant. Traffic, road types, stoplights, route choices, and time-of-day patterns cause trips of similar distance to take different amounts of time.
What the distribution tables suggest
The distance distribution shows most trips fall between 0 and 20 miles, with a steep drop beyond that. A reference point is helpful: downtown to Midway is about 11 miles, and downtown to O’Hare is about 17.5 miles. That contextualizes what “10–20 miles” likely represents operationally.
The time distribution shows that many trips finish within 30 minutes, but a meaningful number extend beyond 60, 90, or more minutes. This again suggests variability in travel conditions.
The key insight: speed variation creates dispersion
Even if distance and time are associated, points on a distance–time scatterplot will not fall on a single straight line because speed varies across trips. Some trips resemble “city driving,” others resemble “freeway driving,” and different speed regimes create different apparent trend lines.
Association here is typically strong and positive, but not perfectly linear due to heterogeneity in driving conditions.
6. Example 3: Do Drivers Get More Tips When Passengers Pay by Credit Card?
Why tip amount alone can be misleading
Drivers care about absolute tips, but analysts often prefer tip percentage because it normalizes tipping behavior relative to fare size. A higher fare naturally permits a larger tip amount even if tipping behavior is unchanged. Tip percentage is a better proxy for willingness to tip.
What the payment distribution tells us
Payment types include Credit Card, Cash, Procurement Card, Mobile, Unknown, and a few rare categories such as Dispute and No Charge.
This breakdown matters because payment type is not just a transaction detail; it often reflects customer type, travel purpose, and behavioral tendencies.
What the tip summary suggests
The descriptive statistics indicate that credit card users have much higher tips on average and in median terms, while cash users often tip near zero. Mobile payments fall between the two, typically higher than most categories but below credit cards.
A behavioral interpretation
A plausible explanation is that people are less psychologically sensitive to spending when paying by credit card because they do not physically experience the transfer of cash. This reduced salience can increase tipping. A similar mechanism may apply to mobile payments, though the behavioral effect may be weaker or depend on app design and default tip prompts.
The important analytical point is that the dataset supports not only a statistical association but also a coherent behavioral story explaining why the association may exist.
7. Why “Other Community” Deserves Special Attention
A recurring theme in this dataset is the “Other Community” category. Because it pools many neighborhoods into one group, it can dominate the analysis and reduce interpretability.
When analysts see a large “Other” bucket, the correct response is not to ignore it, but to treat it as a design issue:
- It may hide meaningful sub-patterns.
- It can distort visual attention in heatmaps.
- It may reflect incomplete mapping or a deliberate aggregation choice.
This becomes an important lesson in association analysis: the way categories are defined can shape what associations you can detect.
8. Interpreting Associations Carefully: Association Is Not Automatically Causation
Even when strong associations are present, interpretation must be disciplined.
For example, pickup community occurs earlier in time than dropoff community, so it is tempting to say pickup “causes” dropoff. However, what we can safely conclude from observational taxi data is:
- Pickup location provides predictive information about destination patterns.
- The association likely reflects underlying mechanisms such as land use patterns, commuting flows, tourism behavior, and airport travel routes.
Causation claims require stronger assumptions or experimental/quasi-experimental designs.
9. The Core Lesson: You Will Know an Association When You See One
This case study illustrates that associations become visible when we:
- Compare distributions across groups (counts and row percentages),
- Examine whether patterns differ systematically rather than randomly,
- Use context (city geography, travel norms, payment behavior) to interpret results,
- And normalize appropriately (tip percentage rather than tip amount).
Ultimately, discovering associations is about turning data into structured understanding: identifying patterns that are stable enough to trust, meaningful enough to interpret, and relevant enough to support decisions.