This article has been completely rewritten in response to constructive criticism of my original post (“The statistical improbability of a Ramson Cliff glacial erratic”, 22 October 2025). I fully acknowledge that the earlier version contained unintended ambiguity in the description of the dataset, particularly the phrasing around “Croyde–Saunton Foreshore Erratics” and “approximately 30 additional” boulders from Madgett & Inglis (1987). This could reasonably have been read as double-counting or artificial weighting of low-elevation data points, even though there was no actual double counting or artificial weighting. I apologise for any confusion this caused. The conclusion of the exercise is unchanged.
In this revised version every data source is stated explicitly, the construction of the dataset is described step-by-step, and no boulders are counted twice. The statistical tests themselves remain unchanged in method, but the dataset is now fully transparent and reproducible. The purpose of the analysis is solely to explore the relative distribution of recorded elevations within the published North Devon erratic record.
Abstract
Glacial erratics in North Devon provide valuable insights into Pleistocene ice dynamics, with their elevations above Ordnance Datum (OD) serving as proxies for depositional processes. This study analyses a dataset of 49 erratic site elevations (ranging from 5 to 80 m OD), drawn from two source categories: 37 boulders catalogued by Madgett & Inglis (1987) and 12 individually documented sites or exposures from other geological records, these are all the claimed glacial erratics in the area discovered from a deep literature search. Of the Madgett & Inglis catalogue, 36 are foreshore or raised-platform boulders, here assigned a nominal elevation of 5 m OD; the 37th is the Ramson Cliff epidiorite (No. 8) at ~80–85 m OD. The Ramson Cliff value is flagged as anomalous by Z-score, Grubbs’ test, and Dixon’s Q test (all at α = 0.05). The IQR method, though it also flags 80 m OD, is uninformative for this dataset: the dominance of the 5 m OD cluster compresses the IQR to zero, causing it to flag every value above 5 m OD indiscriminately. Only boulders with high or medium context security — those in demonstrably undisturbed depositional settings — are included; two further high-altitude Baggy Point boulders (at ~45 m and ~60 m OD) are excluded on this basis. The results underscore the need for further verification of the Ramson Cliff erratic’s depositional context, while the bulk of values align with coastal and estuarine deposition.
Keywords: Outlier detection, glacial erratics, Grubbs’ test, Dixon’s Q test, North Devon, Saunton–Croyde suite, context security
Introduction
Glacial erratics — boulders transported and deposited by ice — offer palaeoenvironmental evidence, particularly in regions like North Devon, UK, where Devensian ice limits are debated. Elevations above sea level (m OD) can indicate transport modes, with low-level coastal erratics (e.g., Saunton Sands) suggesting marine reworking, and higher inland examples implying direct glacial deposition.
Data sources
The most complete published record of North Devon glacial erratics is the catalogue of Madgett & Inglis (1987), who documented 37 boulders (long axis ≥25 cm) in the Saunton and Croyde areas with grid references, dimensions, and lithologies. Of these, 36 (Nos. 1–7, 9–37) were found on the foreshore, raised shore platforms, or in beach and raised-beach contexts, and are described as lying below 30 m OD; individual altitudes are not given except for No. 8, the Ramson Cliff epidiorite on Baggy Point at ~80–85 m OD (Daw, 2026). A further 12 site or exposure elevations are drawn from other geological records (see Table 1).
Two further high-altitude boulders on Baggy Point — a tuff/agglomerate at ~60 m OD and another at ~45–46 m OD, documented by Berry (2021) and Madgett — are excluded from this analysis. Both were ploughed from fields and placed on stone walls in the late 1980s–1990s; their context security is low, meaning their recorded positions cannot reliably be taken to reflect original glacial emplacement. Their existence is noted here for completeness.
Inclusion criterion: context security
This analysis includes only boulders assessed as having high or medium context security, meaning they are in situ or in demonstrably undisturbed (or minimally disturbed) depositional settings. Boulders known to have been relocated by agricultural activity are excluded, as their present elevation cannot serve as a proxy for glacial deposition height. The Ramson Cliff erratic (No. 8), though flagged by Madgett & Inglis (1987) as having been ploughed and possibly moved, is retained as the subject of the outlier analysis; its low context security is itself part of the reason its elevation warrants scrutiny.
Dataset construction
For the 36 Madgett & Inglis foreshore boulders, individual altitudes are not published. For the purposes of this statistical exercise, each is assigned a nominal elevation of 5 m OD to approximate sea-level deposition. This is a deliberate simplification: assigning a single value to all 36 creates a large artificial cluster at the low end of the distribution. This has significant consequences for the summary statistics and for the IQR-based test in particular, as discussed below.
| Site/Exposure | Elevation (m OD) | n | Source | Notes |
|---|---|---|---|---|
| Madgett & Inglis foreshore erratics (Nos. 1–7, 9–37) | 5 (nominal) | 36 | Madgett & Inglis (1987) | Foreshore and raised-platform boulders; all <30 m OD; individual altitudes not published; 5 m OD assigned as sea-level approximation |
| Ramson Cliff Erratic (No. 8, Baggy Point) | 80 | 1 | Madgett & Inglis (1987) | ~80–85 m OD; context security low (ploughed/moved; possible manuport). Retained as subject of outlier analysis |
| Saunton Sands (micro-granite erratic) | 5 | 1 | Other geological records | |
| Freshwater Gut (coastal erratic) | 7.5 | 1 | Other geological records | |
| Bickington Pits (Tews Lane Pits) | 15 | 1 | Other geological records | |
| Combrew Farm Pit | 15 | 1 | Other geological records | |
| Chilcotts Farm Pit | 15 | 1 | Other geological records | |
| Roundswell Well-Boring | 15 | 1 | Other geological records | |
| Fremington Railway Cutting | 15 | 1 | Other geological records | |
| Brannam’s Clay Pit (Higher Gorse) | 25 | 1 | Other geological records | |
| Barnstaple Bypass Cutting (Lake Cutting) | 25 | 1 | Other geological records | |
| Clampitt Workings | 25 | 1 | Other geological records | |
| Head Deposits near Brannam’s | 25 | 1 | Other geological records | |
| Westonzoyland (Somerset Levels) | 5 | 1 | Other geological records |
The resulting dataset of 49 values has the following frequency distribution: 5 m OD × 38, 7.5 m OD × 1, 15 m OD × 5, 25 m OD × 4, 80 m OD × 1. All 48 values excluding Ramson Cliff fall within the 5–25 m OD range (98.0% of the dataset). The single value at 80 m OD stands as a potential outlier.
A Shapiro–Wilk test yields W = 0.40, p < 0.001, indicating severe non-normality. This is not driven solely by the 80 m OD value: 78% of the dataset consists of a single repeated value (5 m OD), a direct consequence of the nominal-elevation assignment. The distribution is fundamentally unlike a normal one. This has implications for the Z-score and Grubbs’ tests, which assume normality, as discussed below.
The objective is to apply four standard outlier detection methods — the IQR rule, Z-score, Grubbs’ test, and Dixon’s Q test — to assess whether the Ramson Cliff value warrants further field investigation.
Methods — Application of Standard Outlier Tests
Data Preparation
Elevations were treated as a univariate sample (n = 49). Descriptive statistics were computed: mean (μ), sample standard deviation (s), first quartile (Q1), third quartile (Q3), and IQR = Q3 − Q1.
Outlier Tests
- IQR Method: Flag values > Q3 + 1.5 × IQR or < Q1 − 1.5 × IQR. This non-parametric approach is robust to non-normality but is sensitive to data compression: when a large majority of values are identical, Q1 and Q3 converge, producing a zero IQR and fences that flag any deviation from the dominant value. In this dataset, that limitation is fully realised.
- Z-Score: Compute z = (x − μ) / s for each value. Flag if |z| > 3 (common threshold for n ≈ 30–50). Assumes approximate normality.
- Grubbs’ Test (One-Sided, Upper): For the suspected maximum outlier, test statistic G = (max − μ) / s. Reject H₀ (no outlier) if G > Gcrit, where
Gcrit = [(n−1)/√n] × √[t² / (n−2 + t²)],
t = t1−α, n−2 (from the t-distribution, one-sided). Here, α = 0.05. Like the Z-score, this test assumes approximate normality. - Dixon’s Q Test: Q = (max − second max) / (max − min). Reject if Q > Qcrit. Caveat: Dixon’s Q test is designed for small samples (typically n ≤ 25; some tables extend to n = 30). Its application to n = 49 is an extrapolation well beyond the test’s intended range, and the critical value used (≈0.38) is an approximation. Results should be treated as indicative rather than formally valid.
All computations used Python 3.12 with NumPy and SciPy libraries.
Results
Descriptive Statistics
| Statistic | Value |
|---|---|
| Mean (μ) | 9.23 m OD |
| Median | 5.00 m OD |
| Sample std. dev. (s) | 11.95 m OD |
| Q1 | 5.00 m OD |
| Q3 | 5.00 m OD |
| IQR | 0.00 m OD |
| Upper IQR fence (Q3 + 1.5 × IQR) | 5.00 m OD |
| Lower IQR fence (Q1 − 1.5 × IQR) | 5.00 m OD |
Because 38 of the 49 observations are at 5 m OD (78%), Q1 and Q3 are both 5.00, producing an IQR of zero. The upper and lower fences collapse to 5.00 m OD, meaning the IQR method flags every value that is not exactly 5 m OD. This is a well-known failure mode of the IQR method when applied to heavily tied data, and the result is uninformative for distinguishing genuine outliers from normal variation.
Outlier Test Results
| Test | Test Statistic | Critical Value (α = 0.05) | Result |
|---|---|---|---|
| IQR (upper fence) | Upper fence = 5.00 m OD | — | All values above 5 m OD flagged (11 observations); method uninformative due to zero IQR |
| Z-Score (max) | z = 5.92 (for 80 m OD) | 3.00 | 80 m OD flagged; no other value exceeds 3 |
| Grubbs’ G (one-sided upper) | G = 5.92 | Gcrit ≈ 1.63 | Reject H₀ (p << 0.001) |
| Dixon’s Q (r10) | Q = 0.73 | ≈0.38 (extrapolated) | Reject H₀ (caveat: n = 49 exceeds test’s valid range) |
IQR Method: With IQR = 0, the fences equal Q3 itself (5.00 m OD), and every observation above 5 m OD is flagged: Freshwater Gut at 7.5 m OD, all five values at 15 m OD, all four at 25 m OD, and Ramson Cliff at 80 m OD — 11 observations in total, including well-documented inland erratic-bearing deposits such as Bickington Pits, Combrew Farm, and Brannam’s Clay Pit. The IQR method is effectively broken for this dataset and cannot distinguish the Ramson Cliff value from routine inland sites.
Z-Score: The maximum |z| = 5.92 (for 80 m OD) far exceeds the threshold of 3. The next highest z-scores are for the 25 m OD values (z ≈ 1.32), well within the normal range. Only Ramson Cliff is flagged.
Grubbs’ Test: G = 5.92, against a critical value of approximately 1.63 (computed from t0.95, 47 ≈ 1.68). H₀ is rejected with p << 0.001. However, the severe non-normality of this dataset (Shapiro–Wilk W = 0.40) means the test’s p-value should not be taken at face value.
Dixon’s Q Test: Q = (80 − 25) / (80 − 5) = 0.73, exceeding the approximate critical value of 0.38. As noted, the test is being applied well beyond its intended sample-size range (n ≤ 25), so this result is indicative only.
Discussion
Three of the four tests flag the Ramson Cliff elevation (80 m OD) specifically and uniquely as a potential outlier. The Z-score and Grubbs’ test both isolate it; Dixon’s Q test, though applied outside its valid range, concurs. The IQR method, by contrast, is uninformative: the dominance of the nominal 5 m OD cluster collapses the IQR to zero, causing it to flag every non-5 m value indiscriminately.
Three methodological limitations warrant emphasis:
1. Nominal elevation assignment. The assignment of a single nominal elevation (5 m OD) to 36 foreshore boulders dominates the distribution and shapes the summary statistics: the mean (9.23 m OD), median (5.00 m OD), and the collapsed IQR are all consequences of this design choice. Madgett & Inglis (1987) describe these boulders as lying on the foreshore, raised shore platforms, or in beach and raised-beach contexts below 30 m OD, but do not publish individual altitudes. A different nominal value — or, better, individually surveyed elevations — would shift these figures and would likely restore the IQR method’s discriminating power.
2. Non-normality. The Shapiro–Wilk test confirms severe non-normality (W = 0.40, p < 0.001). With 78% of the dataset at a single value, this non-normality is structural, not driven by the outlier alone. Removing the 80 m OD value would not produce an approximately normal distribution. The Z-score and Grubbs’ test both assume normality, and their results should be interpreted cautiously.
3. Context security. The Ramson Cliff erratic itself has low context security: Madgett & Inglis (1987) note it was ploughed, and its recorded elevation of ~80–85 m OD may not reflect original glacial emplacement. Two further high-altitude boulders on Baggy Point (~60 m and ~45 m OD) are excluded from this analysis on grounds of low context security (ploughed from fields and placed on stone walls). Their existence, however, hints that the Ramson Cliff value may not be a solitary anomaly but part of a sparse high-altitude population whose apparent rarity partly reflects the difficulty of recovering disturbed boulders. This possibility cannot be tested statistically with the present data.
Excluding the Ramson Cliff value yields a reduced dataset (n = 48) with mean = 7.76 m OD and standard deviation = 6.09 m OD, improving coherence for ice-limit modelling. However, exclusion should follow field verification rather than statistical fiat, as outliers can represent critical signal — for instance, evidence of thicker ice lobes or periglacial sorting at higher elevations.
In summary, the Ramson Cliff Erratic at ~80–85 m OD is consistently identified as a statistical outlier by those tests capable of discriminating it (Z-score, Grubbs’, Dixon’s Q), while the IQR method fails to provide useful discrimination given the dataset’s structure. Notwithstanding the constraints of the dataset, the elevation distribution of recorded erratics is demonstrably non-random and does not approximate any common natural statistical form, being overwhelmingly concentrated within a narrow low-elevation band (~5 m OD) with an abrupt absence of intermediate values. While this structure reflects both geomorphological reality and necessary standardisation of shoreline contexts, it also means that the occurrence of a single example at ~80 m OD is not merely an extreme value but a clear statistical discontinuity. In this sense, the designation of the Ramson Cliff erratic as “statistically improbable” is justified descriptively: it lies far outside the observed distribution and is not part of any continuous elevation trend. While the dataset necessarily reflects recorded rather than exhaustively surveyed occurrences, there is no evidence of a missing intermediate-elevation population that would bridge the observed discontinuity. At the same time, given the discretised and non-normal character of the dataset, formal parametric outlier tests should be treated as illustrative rather than determinative. The key result is therefore the identification of a pronounced empirical anomaly within the known record, one which is unlikely to arise from the same processes that account for the clustered low-elevation population, and which consequently warrants specific geological explanation rather than straightforward inclusion within an assumed continuum.
References
- Berry, P. 2021. Field observations, Baggy Point coastal-walk records (photographs of ~45 m and ~60 m examples).
- Daw, T.D. 2026. North Devon Glacial Erratics: A Master Catalogue. sarsen.org, 10 April 2026. https://www.sarsen.org/2026/04/north-devon-glacial-erratics-master_10.html
- Madgett, P.A. and Inglis, A.E. 1987. A re-appraisal of the erratic suite of the Saunton and Croyde Areas, North Devon. Transactions of the Devon Association 119, 99–110.
- Miller, R.L. and Miller, J.N. 2005. Statistics and Chemometrics for Analytical Chemistry. Pearson Education.
