{"id":"f78fbe6c-9d13-48c5-b148-b1b548894880","arxiv_id":"1908.06400","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"A rank-based skewness coefficient and a four-point summary graph are proposed, but simulations show mixed performance against existing measures.","lead":"This paper proposes a new skewness measure called Rank Skewness, based on the rank of the midrange, and a simplified Four Point Summary Graph as an alternative to the boxplot. The simulation evidence shows the new measure is best only for lognormal data, not for all skewed distributions, so the paper's main claim is not well supported.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Own Weibull results contradict the headline: for Weibull(2,2), Rank Skewness has higher sampling variation than Bowley and Forhad-Adnan at every reported sample size, so the claimed superiority for skewed distributions is not supported.","rationale":"I read the manuscript in good faith: the central contribution is a new skewness measure based on the rank of the midrange, and the claimed advantage is that it 'performs better specially for skewed distribution.' The simulations in Section 2.4 are the only systematic evidence offered for this claim. That evidence does not support it. In the paper's own Tables I-III, for Weibull(2,2), a clearly skewed distribution, Rank Skewness has larger standard deviation and mean deviation than Bowley's and Forhad-Adnan's measures at every sample size. The text acknowledges that Forhad-Adnan is best for negatively skewed Weibull and Normal, and Rank Skewness is best only at n=100 for Gamma. Thus the only well-supported case is Lognormal. The abstract and conclusion overgeneralize from this limited evidence. The reader's weakest assumption about midrange as a center is related, but the more immediate failure is internal: the paper's own comparison contradicts its headline. The Four Point Summary Graph also lacks any quantitative comparison supporting 'better result than the five point summary,' but the Rank Skewness claim alone is sufficient to explain a reject verdict. Since my read confirms rather than changes the reader's rejection, the verdict should remain unchanged.","tokens_in":7588,"tokens_out":4115,"duration_ms":46108,"concrete_test":"Re-run the Section 2.4 Monte Carlo (seed 2147483647, 500000 bootstrap samples, sample sizes 10,20,30,40,50,60,100) for all five distributions and reconstruct Tables I-III. Then count how often 'FS Rank' attains the minimum standard deviation or mean deviation among the five measures for the skewed distributions (Gamma, Weibull, Lognormal, negative Weibull). If the proposed measure is not the minimizer in a majority of these distribution-size combinations, the abstract's central claim fails. As a bias check, also compute mean squared error of each measure about its own population functional rather than about the moment skewness, since lower variance alone does not establish that one skewness measure is 'better.'","verdict_should_be":"UNCHANGED","load_bearing_attack":"The decisive weakness is the mismatch between the abstract's claim and the paper's own simulation evidence. Section 2.5 defines 'better' by smaller standard deviation or mean deviation of 500000 sample skewness values. Tables I-III for Weibull(2,2), a positively skewed distribution, show Rank Skewness (FS Rank) is worse than both Bowley and Forhad-Adnan at every reported sample size: at n=20, SD is 0.2385 vs 0.1686 (Bowley) and 0.1393 (FA); at n=100, SD is 0.1733 vs 0.0928 and 0.0821. The text itself concedes Forhad-Adnan is best for negative Weibull and Normal, and FS Rank becomes best only at n=100 for Gamma. A single favorable case (Lognormal) cannot justify the claim that the measure 'performs better specially for skewed distribution.' Moreover, the comparison metric is incomplete: comparing standard deviations across measures with different population targets ignores bias, and a low-variance measure can be far from the intended quantity. No aggregate or bias-adjusted comparison is provided, and the explicit formula for Rank Skewness is not typeset in the manuscript, further impeding verification.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a new skewness coefficient, called \"Rank Skewness\", based on the rank of the midrange among the ranked observations, and a four-point summary graph intended as a simpler alternative to the boxplot. The authors compare the sampling variability of five skewness measures through bootstrap simulations for Normal, Gamma, Weibull (both positive and negative), and Lognormal distributions, and illustrate the measures on three real datasets. The abstract and conclusion claim that the proposed measure performs better than existing measures, especially for skewed distributions, and that the four-point graph gives better results than the five-point summary boxplot.","tokens_in":7828,"tokens_out":3901,"duration_ms":43105,"significance":"A rank-based skewness coefficient that is insensitive to extreme values could be of practical use, and the simulation setup with a fixed seed and 500,000 resamples is transparent. However, the paper does not establish its central claims: the explicit formula is not typeset, no formal properties are derived, and the paper's own simulation tables contradict the claimed superiority for skewed distributions. The four-point summary graph is purely descriptive and no criterion for \"better\" is supplied. As it stands, the contribution is not supported by the evidence presented.","major_comments":[{"comment":"The paper's own comparison criterion, smaller standard deviation or mean deviation, shows the proposed Rank Skewness to be worse than both Bowley's and Forhad-Adnan's measures for the positively skewed Weibull(2,2) distribution at every reported sample size. For example, in Table I at n=20 the standard deviation is 0.2385 for Rank Skewness versus 0.1686 for Bowley and 0.1393 for Forhad-Adnan; at n=100 the corresponding values are 0.1733 versus 0.0928 and 0.0821. This directly contradicts the abstract and conclusion that the proposed measure performs better specially for skewed distributions. The text itself reports that Forhad-Adnan is best for Normal and negatively skewed Weibull, leaving only Lognormal as a uniformly favorable case. The superiority claim must either be removed or supported by a consistent pattern across skewed distributions.","section":"§2.5, Tables I–III; Abstract; §5"},{"comment":"The comparison metric is incomplete: comparing standard deviations or mean deviations of statistics that estimate different population quantities is not a valid way to rank estimators unless bias is taken into account. A low-variance measure can be far from the quantity of interest, and no bias-adjusted comparison such as mean squared error relative to a common target is provided. The second comparison criterion is also not independent, since the population skewness values are computed with the moment formula that the authors criticize elsewhere in the paper.","section":"§2.5"},{"comment":"The explicit formula for Rank Skewness is not actually typeset; the text shows only placeholder text where the expression should be. This makes the core object of the paper unavailable for verification and reproduction. In addition, the claimed range of -1 to +1 is asserted without proof, and the procedure for inserting the midrange and using standard competition ranking needs to specify how ties are handled, since the midrange can coincide with an existing observation.","section":"§2.1"},{"comment":"The four-point summary graph compares only the median with the midrange, so the assertion that it is based on all observations and gives better results than the traditional boxplot is not supported by any quantitative definition or comparison. The real-data applications provide no ground truth for skewness, and statements such as the proposed measure \"performs well\" are qualitative judgments made after inspecting the computed values rather than objective evidence.","section":"§2.2 and §4"}],"minor_comments":[{"comment":"The section numbering is inconsistent: the introduction is numbered 1.1 and the next section is 2.1, with no Section 1 or Section 2 headers.","section":"General"},{"comment":"Table V appears twice with different content, and the second occurrence uses rows labeled Sample-1 and Sample-2 under a column header that reads 'Form'; this needs to be corrected.","section":"§4"},{"comment":"The text cites Groeneveld, Meeden and Gin (1984) and Hossain (2007) for the EUPP outlier method, but these references are not included in the reference list.","section":"References"},{"comment":"There are numerous typographical and grammatical issues, including 'scatterdness', 'Laondon', and 'middle most fifty percent observation'; Dataset-3 also appears to have a missing comma ('9 7').","section":"Abstract and text"},{"comment":"Figure 1 is difficult to read: the axis labels are garbled and the labels Median, Midrange, and Mid are repeated without clear connection to the plotted points.","section":"Figure 1"}],"recommendation":"reject","confidential_remarks":"The central claim of the paper is contradicted by its own simulation tables, and the missing formula prevents independent verification. This is not a case of a sound result with presentation problems; the headline conclusion is not supported by the evidence presented. A substantially revised version with modest descriptive claims and a complete definition could be reconsidered, but the current manuscript does not meet the bar for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline is simple: the paper's central claim fails on its own tables. The abstract says Rank Skewness 'performs better specially for skewed distribution', but Tables I–III for Weibull(2,2) show it has larger standard deviation than Bowley and Forhad-Adnan at every sample size. At n=20, SD is 0.2385 versus 0.1686 and 0.1393; at n=100 it is still behind. So the main selling point is unsupported by the authors' own evidence.\n\nWhat is genuinely new is small but real. Replacing the median in the Hossain–Adnan ranking formula with the midrange is a simple, natural variant, and the Four Point Summary Graph is an easy simplification of a boxplot. The kernel of using the rank of a center rather than its value is worth a footnote. The simulation setup is straightforward and reproducible in principle: 500,000 bootstrap resamples from data banks, comparing five measures.\n\nThe problems are load-bearing. First, the formula for Rank Skewness is never typeset. The text says 'the form is as follows' and then no equation appears. Nobody can verify the estimator. Second, the comparison metric looks only at dispersion of the estimates, ignoring bias. The second comparison targets a moment-based population skewness, which the authors themselves dismiss for skewed distributions. Third, the real-data examples have no ground truth; saying Rank Skewness 'performs well' because it yields some number is not a performance comparison. Fourth, the claim that the Four Point Summary Graph is 'based on all observation' is misleading, since the midrange uses only the extremes. The citation pattern is not egregious, though the heavy reliance on Hossain and Adnan (2007) and the Hossain EUPP method without independent grounding is thin.\n\nWho is this for? Someone wanting a quick, simple skewness display might get a hint from the four-point graph. But the manuscript is not ready for publication. It deserves a hard reject in its current form; if the authors provide a clear definition, a bias-aware comparison, and honest statements about where the measure loses to existing ones, the kernel could be reshaped into something worth another look.","headline":"The paper's own Weibull simulations contradict its headline claim, and the estimator is never actually defined in the text, so the central contribution is not verifiable.","tokens_in":8346,"tokens_out":2643,"would_cite":false,"duration_ms":27529,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62G30","62F40"],"pacs":[],"model":"deepseek-v4-flash","headline":"A rank-based skewness coefficient built on the midrange is claimed to beat classical measures on skewed data.","keywords":["rank skewness","coefficient of skewness","midrange","four point summary graph","boxplot alternative","bootstrap simulation","Monte Carlo simulation","skewed distributions"],"falsifier":"Take one right-skewed sample and replace only the largest value with an extremely large value (for example, 100 becomes 100,000), leaving all other observations unchanged; if the Rank Skewness coefficient moves substantially, the claim that it is unaffected by extreme values fails, because the midrange and hence the ranks shift.","tokens_in":7376,"feed_emoji":"📊","tokens_out":11607,"duration_ms":106087,"temperature":0.7,"pith_summary":"Skewness coefficients in current use depend on distances from a center, so a single extreme value, an irregular gap, or the choice of mean versus median can change the answer. This paper proposes \"Rank Skewness,\" a coefficient computed from ranks after inserting the midrange into the sorted sample, and claims it stays in $[-1, +1]$, ignores extreme magnitudes and irregular spacing, and outperforms Pearson, Fisher's moment, Bowley, and the median-based Forhad-Adnan coefficients on skewed distributions. The same midrange idea underlies a proposed \"Four Point Summary Graph,\" built from the minimum, maximum, median, and midrange on a single horizontal line, which the authors claim is simpler than and better than the five-number-summary boxplot. Evidence comes from large Monte Carlo and bootstrap simulations across five distributions and from three real datasets. If the claim holds, skewness measurement becomes more robust and easier to display graphically.","feed_headline":"Rank skewness beats classic formulas on skewed data","feed_subtitle":"A midrange-ranked coefficient resists outliers and beats Pearson, moment, and Bowley measures on skewed samples.","key_machinery":"The load-bearing object is Rank Skewness, a rank-based coefficient: sort the data, insert the midrange, assign standard competition ranks, then combine the ranks of all observations with the rank of the midrange into a normalized value in $[-1, +1]$. The rank transform removes the influence of extreme magnitudes and irregular gaps between consecutive values, leaving only information about how many observations sit on each side of the midrange. The Four Point Summary Graph is the same idea made visual: it plots the minimum, maximum, median, and midrange on one horizontal line, and uses the median's position relative to the midrange to indicate the direction and approximate amount of skewness.","core_discovery":"The paper's central claim is that skewness is better read from the ranks of observations relative to the midrange than from their numerical distances to a center. The proposed Rank Skewness coefficient is constructed by ordering the sample, inserting the midrange into the ordered values, ranking with standard competition ranking so ties share a rank and later ranks are skipped, and then forming a normalized combination of the ranks of the observations and the rank of the midrange so that the coefficient lies in $[-1, +1]$. The authors report that across repeated resamples for normal, gamma, Weibull, and lognormal distributions, Rank Skewness has the smallest variability for lognormal data at every sample size, becomes competitive or best for gamma at larger sample sizes, and generally beats Pearson's and Fisher's moment measures on skewed distributions, while the median-based predecessor remains best for normal and negatively skewed Weibull data. In the three real datasets, Rank Skewness gives values near 0.94 to 0.99 for positively skewed samples, which the authors interpret as performing well. The companion Four Point Summary Graph declares skewness by the median's position relative to the midrange: median left of midrange indicates positive skewness, median right indicates negative skewness, and equality indicates symmetry.","pith_inferences":["A natural extension is to replace the midrange with a trimmed or winsorized midpoint; the paper's own logic suggests the coefficient would then resist outliers even when the extremes themselves are contaminated, a variant that is directly testable on the paper's simulated distributions.","The four-point graph's decision rule is essentially a sign test on the median relative to the extremes, so a permutation null distribution could turn the graph into a formal symmetry test with calibrated significance levels.","Because the simulation benchmark compares every estimator to moment-based population skewness, the test setup structurally favors moment estimators; comparing each estimator to its own population limit under the same distributions would be a fairer re-analysis and could change the reported rankings."],"forward_implications":["Analysts get a skewness coefficient that is bounded in $[-1,1]$, requires no moments, and is computable from ranks alone.","On lognormal data, the smaller standard deviation and mean deviations reported for Rank Skewness imply more stable skewness estimates across sample sizes than Pearson or moment coefficients.","A simpler skewness display than the boxplot becomes available: the four-point summary graph uses all observations and indicates skewness by the median's position relative to the midrange.","For skewed distributions such as gamma and Weibull, Rank Skewness at larger sample sizes matches or beats the quartile-based Bowley measure, giving a rank-only alternative that keeps information from the tails."],"supporting_citations":[{"why":"Supplies the classical mean-median skewness coefficient that the new measure is compared against and must outperform.","marker":"Pearson (1895)"},{"why":"Defines the quartile-based coefficient whose reliance on the middle fifty percent motivates a rank-based alternative.","marker":"Bowley (1901)"},{"why":"Provides the median-based predecessor and the main comparator in the simulations.","marker":"Hossain and Adnan (2007)"},{"why":"Supplies the EUPP outlier-detection method used to identify outliers in the real datasets before comparison.","marker":"Hossain (2007)"},{"why":"Source of the BCG nutritional-status dataset used in the first real-life application.","marker":"Daniel (2007)"},{"why":"Source of the radon-concentration and childhood-cancer datasets used in the second and third real-life applications.","marker":"Devore (2000)"}],"fun_headline_variants":["Rank skewness beats Pearson and moment measures","Rank-based skewness resists outliers in skewed samples","Midrange rank skewness outperforms classic formulas","Four-point boxplot offers simpler skewness view"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole approach rests on treating the midrange as the true center of a skewed dataset, so that the side of the midrange holding more observations reliably indicates the direction and amount of skewness.","fun_headline_variants_meta":{"raw":{"variants":["Rank skewness beats Pearson and moment measures","Rank-based skewness resists outliers in skewed samples","Midrange rank skewness outperforms classic formulas","Four-point boxplot offers simpler skewness view"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000181,"raw_usage":{"total_tokens":1281,"prompt_tokens":892,"completion_tokens":389,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":508,"completion_tokens_details":{"reasoning_tokens":330}},"tokens_in":508,"tokens_out":389,"duration_ms":4829,"temperature":1.0,"reasoning_tokens":330,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:45:52.877863+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take one right-skewed sample and replace only the largest value with an extremely large value (for example, 100 becomes 100,000), leaving all other observations unchanged; if the Rank Skewness coefficient moves substantially, the claim that it is unaffected by extreme values fails, because the midrange and hence the ranks shift.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the quartile-based coefficient whose reliance on the middle fifty percent motivates a rank-based alternative."},{"cited_title":"A New Approach to Determine the Asymmetry of a Distribution,","cited_arxiv_id":null,"evidence_quote":"Provides the median-based predecessor and the main comparator in the simulations."},{"cited_title":"A New Approach to Determine the Asymmetry of a Distribution,","cited_arxiv_id":null,"evidence_quote":"Supplies the EUPP outlier-detection method used to identify outliers in the real datasets before comparison."},{"cited_title":"Biostatistics: A Foundation for Analysis in the Health Sciences","cited_arxiv_id":null,"evidence_quote":"Source of the BCG nutritional-status dataset used in the first real-life application."},{"cited_title":"Probability and Statistics for Engineering and Sciences","cited_arxiv_id":null,"evidence_quote":"Source of the radon-concentration and childhood-cancer datasets used in the second and third real-life applications."}],"review_version":1}