Start with a question your observations can answer
A survey can produce a correct percentage and still support a poor conclusion. The sample may miss part of the area, the categories may be unclear, or the conclusion may claim more than was measured. Good fieldwork connects the question, sampling frame, observations and conclusion.
This is a fictional school-ground survey completed entirely from supplied information. Use the sketch and record cards on paper. No travel, entry into restricted areas, contact with students or collection of personal information is required.
Question: “Among eligible centre points in the mapped ground, what proportions have vegetation, constructed hard surface or exposed soil and loose mineral material at the stated observation time?” This asks about classified points. It does not directly measure the percentage of each whole cell covered by vegetation.
Define the frame, unit and categories
The target area contains 24 equal-sized grid cells. Each cell contributes exactly one centre point, so the target population is 24 centre points, not every possible spot in the school. Three points, W8, C8 and E8, are unavailable and excluded before selection. The eligible sampling frame contains 21 points. Conclusions about it must name that restriction.
The sampling unit is one eligible cell-centre point. At each selected point, classify the surface directly beneath the point marker. Use these mutually exclusive rules:
- V, vegetation: living vegetation is the top visible surface at the point.
- H, hard surface: constructed paving or a building surface is visible at the point.
- B, bare/mineral: exposed soil, sand or loose mineral gravel is visible at the point.
If an image is obscured, a boundary cannot be resolved or another surface type occurs, record “unclear” with a note instead of forcing a category. The supplied nine records are all classifiable. Keep the same category definitions and image resolution throughout; changing them midway makes comparisons unreliable.
| Row | West left | West right | Central left | Central right | East left | East right |
|---|---|---|---|---|---|---|
| A | W1 | W2 | C1 | C2 | E1 | E2 |
| B | W3 | W4 | C3 | C4 | E3 | E4 |
| C | W5 | W6 | C5 | C6 | E5 | E6 |
| D | W7 | W8 × | C7 | C8 × | E7 | E8 × |
West, Central and East are geographical zones, not recorded surface categories. Each contains eight target points and seven eligible points. Their equal sizes make an equal allocation proportional in this example.
Worked design 1: convenient-only selection
Draft plan A selects all seven eligible West points plus nearby C1 and C2. This gives nine observations cheaply, but no East point can appear in the sample. The selection reflects convenience rather than coverage of the whole eligible frame.
Adding more West points is impossible here, and repeatedly observing the same ones would not repair the missing East zone. Convenient data may describe those selected locations, but calling them a representative survey of the whole mapped area would be unjustified. No surface counts are supplied for this draft plan, so do not invent its result.
Worked design 2: a systematic route with a problem
Draft plan B reads the original 24-cell sketch row by row, left to right. It selects every third position, starting at position 2: W2, E1, W4, E3, W6, E5, W8 and E7.
The rule is systematic, but it clashes with the repeating six-column layout: it misses the Central zone entirely. W8 is also unavailable, leaving seven usable points rather than eight. This plan was mistakenly made from the unfiltered target list. Audit it before use rather than quietly moving W8 to an easier nearby point.
A redesigned systematic sample could start from the eligible frame and use a randomly selected start. Regular spacing can help coverage, but neither spacing nor a larger count automatically removes bias. A periodic pattern in the frame can still interact badly with the interval.
Worked design 3: a stratified sample
For the completed survey, divide the eligible frame into the three zones and select three points without replacement within each. An imagined random draw supplies W1, W4, W6; C2, C3, C7; E1, E4, E6. These labels and results are invented, not evidence that a real draw or field visit occurred.
All zones are represented, and the sampling fraction is 3/7 in each. Each eligible point has the same inclusion probability under this stated design. That improves the design’s coverage, but a particular small random sample can still differ from the full population. Random selection reduces choice bias; it does not certify the exact result.
The Royal Geographical Society’s sampling guidance compares random, systematic and stratified approaches. Here stratification is justified by the known zones, with random selection inside each zone rather than hand-picking “typical” surfaces.
The completed recording sheet
| Point | Zone | Code | Supplied surface observation |
|---|---|---|---|
| W1 | West | H | Constructed paving |
| W4 | West | H | Constructed paving |
| W6 | West | B | Exposed soil |
| C2 | Central | H | Constructed paving |
| C3 | Central | V | Living grass |
| C7 | Central | H | Constructed paving |
| E1 | East | V | Living grass |
| E4 | East | V | Living groundcover |
| E6 | East | B | Loose mineral gravel |
Count each point once: H = 4, V = 3 and B = 2; total = 9. Compute each sample percentage as category count ÷ 9 × 100.
| Category | Count | Percentage |
|---|---|---|
| H | 4 | 44.4% |
| V | 3 | 33.3% |
| B | 2 | 22.2% |
The displayed percentages sum to 99.9% because of rounding; the exact fractions sum to 100%. This is not a missing observation. The sample includes 9/21, or about 42.9%, of eligible points. That coverage percentage is different from the percentage in any surface category.
Write a limited conclusion
“At fictional snapshot T1, constructed hard surface was the most common category among the nine sampled eligible centre points: 4/9, or 44.4%. Vegetation occurred at 3/9 and bare/mineral surface at 2/9. The proportional stratified design supports a tentative description of the 21 eligible centre points, but the sample may differ from the full frame. The three unavailable points and other locations between cell centres were not observed.”
This conclusion does not say the whole school is exactly 44.4% paved. It does not explain why surfaces differ, prove change through time or establish an effect of student activity. A one-time descriptive sample cannot, by itself, establish cause and effect.
Solved practice
1. Choose the denominator
Find the vegetation percentage in the observed sample. Should the denominator be 9, 21 or 24?
Answer: use the nine completed observations: 3 ÷ 9 × 100 = 33.3%, rounded. Dividing by 21 or 24 would treat unobserved points as if their vegetation status were known.
2. Handle a missing record
Suppose E4 becomes unreadable. Give an honest summary without inventing a replacement value.
Answer: report one missing selected observation and eight classifiable records: H = 4, V = 2, B = 2. Among those eight, percentages are 50%, 25% and 25%. The East zone is now underrepresented in the completed data; the simple pooled percentages are descriptive, not an unchanged proportional-frame estimate.
3. Audit a new allocation
A different eligible frame has zones of 6, 9 and 15 points. Allocate a proportional sample of 10.
Answer: the total is 30. Allocations are 10 × 6/30 = 2, 10 × 9/30 = 3 and 10 × 15/30 = 5. Equal numbers per zone would not be proportional here. Selection within each zone must still be specified.
Frequently asked questions
Is a sample the same as a sampling frame?
No. The frame lists eligible units; the sample contains the units selected from that list.
Does each point represent the average surface of its cell?
No. This protocol records only the surface at the centre. Whole-cell cover needs a different measurement method.
Why keep inaccessible points visible?
They explain the difference between the target population and eligible frame, preventing an unnoticed expansion of the conclusion.
Can a larger sample still be biased?
Yes. Increasing observations within conveniently chosen locations can preserve the same coverage problem.
Does stratified sampling always use equal numbers?
No. Proportional allocation follows stratum size. Equal numbers are proportional here only because all eligible zones are equal.
Can I silently replace a missing point nearby?
No. Document the missing observation and use a specified replacement or redesign rule if appropriate. A convenient substitution changes selection.
How could the investigation be strengthened?
Classify more eligible points, check uncertain categories consistently and repeat the same protocol at another stated time if change is the question.
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