Pebble Size Along a Pocket Beach: Testing a Spearman Result in the IA
For her HL internal assessment, a student tests whether beach sediment becomes finer with distance from a headland on a 1.3 km pocket beach. She measures five sites at 0, 300, 600, 900 and 1,200 m. At each she runs a 30 m tape perpendicular to the shoreline and picks up the first pebble her finger touches at every 1 m interval, measuring its long axis with calipers; where no pebble is exposed she records 'no data'. She also measures beach gradient with a clinometer and ranging poles. Her median long axes are 64, 55, 47, 40 and 38 mm. Thirteen of 150 sampling points had no data. Spearman's rank correlation between distance and median size is −0.80. The critical value at p = 0.05 (one-tailed, n = 5) is 0.900. She surveyed once, 10:40–14:10 on 16 July; low tide was 11:05 and tidal range 3.1 m. She concludes: 'Sediment size decreases significantly along the beach because wave energy decreases away from the headland.' Her teacher asks her to justify the inferential claim and the causal claim separately.
1. Evaluate the statistical claim using the Spearman result and the sampling design.
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The statistical claim fails its own test. The null hypothesis is no monotonic association between distance and median sediment size. With n = 5 sites, a one-tailed test at p = 0.05 has a critical value of 0.900. The observed rs = −0.80 has |rs| = 0.80, which is less than 0.900, so she cannot reject the null. The result is a strong negative effect size, but it is not statistically significant at the stated threshold. Writing 'significant' because −0.80 is close to −1 confuses magnitude with evidence.
The design weakens the test further. The five medians are not five independent random samples from a defined population; they are fixed sites along one beach. Treating n = 5 as the sample size is pseudo-replication. The 20 pebbles per site are subsamples, and the median discards within-site variation. With five points, power is very low: a true correlation would often fail to reach significance.
Missing data may bias the pattern. 13 of 150 points had no exposed pebble. If those points are concentrated at the finer, sandier end, the median at that site is based on a biased subset of isolated lag pebbles. That could flatten or steepen the gradient artificially.
What she can claim. There is a strong negative association in her data, consistent with her hypothesis, but it is not statistically significant at p = 0.05 with n = 5. She should report the rs, the critical value, the sample size and the limitation. She should not claim proof of a process. A better inferential approach would use all 150 points or site-level bootstrapping, while acknowledging the non-random site selection.
2. Distinguish the pattern from the process: what evidence would be needed to support the wave-energy explanation?
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The pattern is the spatial association: median clast size falls from 64 mm at 0 m to 38 mm at 1,200 m. The process is the mechanism that produced it. Her conclusion jumps from one to the other.
A wave-energy explanation requires energy data. She would need offshore wave height and period, fetch, and evidence of refraction or diffraction around the headland. If wave energy declines along the beach, the competence to transport coarse material falls, leaving finer sediment downdrift. She could measure wave height with a simple staff or pressure sensor, or use hindcast data, and map longshore currents with dye or floats.
Alternative explanations must be tested. The coarse sediment at 0 m may come from erosion of the headland itself, not from high energy. If so, the gradient is a source effect. Longshore drift may carry fines downdrift, producing a textural gradient without a wave-energy gradient. Beach gradient, which she measured, is a proxy for energy but also reflects sediment size; it is not independent evidence.
Evidence that would strengthen the causal claim. Repeated surveys after storms and in calm periods would show whether the pattern is stable or reworked. Tracer pebbles would show transport direction. Grain shape and roundness would indicate whether the 0 m material is freshly eroded or long-transported. A sediment budget would identify inputs and outputs.
Judgement. The pattern is well described; the process is inferred. For the IA, she should present the gradient as consistent with, but not proof of, the wave-energy hypothesis, and identify the source and longshore-drift alternatives as limitations.
3. Recommend two modifications to the fieldwork and explain how each would improve the internal assessment.
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Modification 1: stratify sampling across the beach profile and repeat at the same tidal stage. At each site, place three transects 20 m apart, and sample at fixed intervals in the upper, mid and lower beach rather than only along one 30 m tape. Repeat the survey on three days at the same state of tide, within one hour of low water. This improves the IA because the swash zone shifts with tide; a single survey from 10:40 to 14:10 spans a 3.1 m tidal range and mixes different energy environments. Repeating reduces the chance that one day's waves drive the result, and stratification captures the across-beach sorting that her single tape misses.
Modification 2: increase the number of sites and use a random offset. Add five more sites at 150 m intervals, with random offsets along the beach, and measure all clasts above 2 mm at each point rather than selecting the first touched pebble. This raises n for the correlation and reduces selection bias. If she keeps five sites, she should use all 150 point measurements in a grouped analysis rather than five medians.
Additional improvements. Record wave height and wind at each survey; photograph the surface before sampling; note whether the point is sand, gravel or mixed. Use a GPS to relocate sites. Measure the b-axis as well as the a-axis, because shape affects transport.
How this changes the conclusion. More sites and repeats would either strengthen the gradient or reveal that it is a one-day artefact. The IA would then distinguish a robust spatial pattern from a snapshot, which is the geographical thinking the criteria reward.