The Trail-Counter Data and the Missing Baseline
A regional parks office installed electronic trail counters at two trailheads. The table below summarizes counts for one season.
| Trail | Season total (visitors) | Days counted |
|---|---|---|
| Ridge Trail | 12,400 | 90 |
| Creek Trail | 8,100 | 60 |
A staff memo states: "Ridge Trail is the more popular trail, drawing roughly 138 visitors per day versus 135 per day on Creek Trail. We therefore recommend directing new signage funding to Ridge Trail."
A volunteer notes that the Creek Trail counter was installed three weeks after the Ridge Trail counter, and that a bridge closure diverted hikers from Creek Trail to Ridge Trail for part of the season. The office has no visitor counts from the season before the counters were installed.
1. Check the memo's arithmetic and explain what the per-day figures do and do not establish.
Read the worked answer
The arithmetic is correct: 12,400 ÷ 90 ≈ 137.8, and 8,100 ÷ 60 = 135. So the per-day rates are about 138 and 135.
What the figures establish: over the days each counter ran, the two trails drew nearly identical daily traffic - a difference of about 3 visitors per day, under 2.5%.
What they do not establish: that Ridge Trail is "more popular." Three problems undercut that inference.
- The difference is tiny relative to the counts, so it may be noise rather than a real gap.
- The counting windows differ (90 vs. 60 days), and the memo never says the days are comparable - weekends, holidays, and weather can shift the mix.
- The memo's own conclusion (fund signage on Ridge) rests on a gap of 3 visitors/day, which is a weak basis for a funding decision.
2. The volunteer raises two facts: the later Creek counter start and the bridge closure. Explain how each affects the validity of comparing the two per-day rates.
Read the worked answer
Both facts attack the assumption that the two rates measure the same thing.
Later counter start. If Creek's 60 days fall in a different part of the season than Ridge's 90 days, the comparison mixes different conditions (weather, school calendars, holidays). A per-day average only supports comparison when the days are comparable; here they may not be.
Bridge closure. This is the more serious problem. If hikers were diverted from Creek to Ridge, then Ridge's count is inflated and Creek's is deflated by the same event. The two rates are not independent measurements of each trail's appeal - they partly reflect a temporary detour. The memo treats the counts as if they measured preference, but they measure traffic under a disruption.
Together, these facts mean the per-day comparison is confounded. The honest conclusion is that the data are insufficient to rank the trails.
3. The memo's recommendation is "direct new signage funding to Ridge Trail." Using only the data given, state what additional measurement would most strengthen the recommendation, and explain why.
Read the worked answer
The strongest addition is counts from both trails over the same days, after the bridge reopens - ideally a full matched season.
Why: the current comparison fails on two fronts at once. The counting windows differ, and a known disruption pushed traffic between the trails. Counting both trails on the same days removes the window mismatch, and waiting until the bridge reopens removes the diversion. Only then do the two per-day rates measure the same thing, so a difference between them could be read as a difference in popularity.
A secondary improvement: the office has no pre-installation baseline, so it cannot tell whether current Ridge traffic is typical or elevated. A matched post-repair season would supply that baseline going forward. Note that adding more days of the current (confounded) data would not fix the problem - the issue is comparability, not sample size.