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Concept: Median absolute deviation


BACKGROUND: To evaluate institutional nursing care performance in the context of national comparative statistics (benchmarks), approximately one in every three major healthcare institutions (over 1,800 hospitals) across the United States, have joined the National Database for Nursing Quality Indicators[REGISTERED SIGN] (NDNQI[REGISTERED SIGN]). With over 18,000 hospital units contributing data for nearly 200 quantitative measures at present, a reliable and efficient input data screening for all quantitative measures for data quality control is critical to the integrity, validity, and on-time delivery of NDNQI reports. METHODS: With Monte Carlo simulation and quantitative NDNQI indicator examples, we compared two ad-hoc methods using robust scale estimators, Inter Quartile Range (IQR) and Median Absolute Deviation from the Median (MAD), to the classic, theoretically-based Minimum Covariance Determinant (FAST-MCD) approach, for initial univariate outlier detection. RESULTS: While the theoretically based FAST-MCD used in one dimension can be sensitive and is better suited for identifying groups of outliers because of its high breakdown point, the ad-hoc IQR and MAD approaches are fast, easy to implement, and could be more robust and efficient, depending on the distributional property of the underlying measure of interest. CONCLUSION: With highly skewed distributions for most NDNQI indicators within a short data screen window, the FAST-MCD approach, when used in one dimensional raw data setting, could overestimate the false alarm rates for potential outliers than the IQR and MAD with the same pre-set of critical value, thus, overburden data quality control at both the data entry and administrative ends in our setting.

Concepts: Median, Dimension, Absolute deviation, Normal distribution, Standard deviation, Robust statistics, Outlier, Median absolute deviation


Recently, there has been significant interest in robust fractal image coding for the purpose of robustness against outliers. However, the known robust fractal coding methods (HFIC and LAD-FIC, etc.) are not optimal, since, besides the high computational cost, they use the corrupted domain block as the independent variable in the robust regression model, which may adversely affect the robust estimator to calculate the fractal parameters (depending on the noise level). This paper presents a Huber fitting plane-based fractal image coding (HFPFIC) method. This method builds Huber fitting planes (HFPs) for the domain and range blocks, respectively, ensuring the use of an uncorrupted independent variable in the robust model. On this basis, a new matching error function is introduced to robustly evaluate the best scaling factor. Meanwhile, a median absolute deviation (MAD) about the median decomposition criterion is proposed to achieve fast adaptive quadtree partitioning for the image corrupted by salt & pepper noise. In order to reduce computational cost, the no-search method is applied to speedup the encoding process. Experimental results show that the proposed HFPFIC can yield superior performance over conventional robust fractal image coding methods in encoding speed and the quality of the restored image. Furthermore, the no-search method can significantly reduce encoding time and achieve less than 2.0 s for the HFPFIC with acceptable image quality degradation. In addition, we show that, combined with the MAD decomposition scheme, the HFP technique used as a robust method can further reduce the encoding time while maintaining image quality.

Concepts: Regression analysis, Function, Median, Absolute deviation, Standard deviation, Errors and residuals in statistics, Robust statistics, Median absolute deviation


Oxygen isotope analysis of archaeological skeletal remains is an increasingly popular tool to study past human migrations. It is based on the assumption that human body chemistry preserves the δ18O of precipitation in such a way as to be a useful technique for identifying migrants and, potentially, their homelands. In this study, the first such global survey, we draw on published human tooth enamel and bone bioapatite data to explore the validity of using oxygen isotope analyses to identify migrants in the archaeological record. We use human δ18O results to show that there are large variations in human oxygen isotope values within a population sample. This may relate to physiological factors influencing the preservation of the primary isotope signal, or due to human activities (such as brewing, boiling, stewing, differential access to water sources and so on) causing variation in ingested water and food isotope values. We compare the number of outliers identified using various statistical methods. We determine that the most appropriate method for identifying migrants is dependent on the data but is likely to be the IQR or median absolute deviation from the median under most archaeological circumstances. Finally, through a spatial assessment of the dataset, we show that the degree of overlap in human isotope values from different locations across Europe is such that identifying individuals' homelands on the basis of oxygen isotope analysis alone is not possible for the regions analysed to date. Oxygen isotope analysis is a valid method for identifying first-generation migrants from an archaeological site when used appropriately, however it is difficult to identify migrants using statistical methods for a sample size of less than c. 25 individuals. In the absence of local previous analyses, each sample should be treated as an individual dataset and statistical techniques can be used to identify migrants, but in most cases pinpointing a specific homeland should not be attempted.

Concepts: Statistics, Median, Data, Absolute deviation, Standard deviation, Archaeology, Median absolute deviation, Oxygen isotope ratio cycle


We analysed the peer review of grant proposals under Marie Curie Actions, a major EU research funding instrument, which involves two steps: an independent assessment (Individual Evaluation Report, IER) performed remotely by 3 raters, and a consensus opinion reached during a meeting by the same raters (Consensus Report, CR). For 24,897 proposals evaluated from 2007 to 2013, the association between average IER and CR scores was very high across different panels, grant calls and years. Median average deviation (AD) index, used as a measure of inter-rater agreement, was 5.4 points on a 0-100 scale (interquartile range 3.4-8.3), overall, demonstrating a good general agreement among raters. For proposals where one rater disagreed with the other two raters (n=1424; 5.7%), or where all 3 raters disagreed (n=2075; 8.3%), the average IER and CR scores were still highly associated. Disagreement was more frequent for proposals from Economics/Social Sciences and Humanities panels. Greater disagreement was observed for proposals with lower average IER scores. CR scores for proposals with initial disagreement were also significantly lower. Proposals with a large absolute difference between the average IER and CR scores (≥10 points; n=368, 1.5%) generally had lower CR scores. An inter-correlation matrix of individual raters' scores of evaluation criteria of proposals indicated that these scores were, in general, a reflection of raters' overall scores. Our analysis demonstrated a good internal consistency and general high agreement among raters. Consensus meetings appear to be relevant for particular panels and subsets of proposals with large differences among raters' scores.

Concepts: Median, Interquartile range, Absolute deviation, Mean, Seventh Framework Programme, Consensus, Marie Curie, Median absolute deviation


Fallout from the Fukushima Dai-ichi nuclear power plant accident resulted in a 3000-km(2) radioactive contamination plume. Here, we model the progressive dilution of the radiocesium contamination in 327 sediment samples from two neighboring catchments with different timing of soil decontamination. Overall, we demonstrate that there has been a ~90% decrease of the contribution of upstream contaminated soils to sediment transiting the coastal plains between 2012 (median - M - contribution of 73%, mean absolute deviation - MAD - of 27%) and 2015 (M 9%, MAD 6%). The occurrence of typhoons and the progress of decontamination in different tributaries of the Niida River resulted in temporary increases in local contamination. However, the much lower contribution of upstream contaminated soils to coastal plain sediment in November 2015 demonstrates that the source of the easily erodible, contaminated material has potentially been removed by decontamination, diluted by subsoils, or eroded and transported to the Pacific Ocean.

Concepts: Sediment, Median, Soil, Absolute deviation, Mean, Pacific Ocean, Median absolute deviation, Plain


The aim of this study was to analyse gait variability and symmetry in race walkers. Eighteen senior and 17 junior athletes race walked on an instrumented treadmill (for 10 km and 5 km, respectively) at speeds equivalent to 103% of season’s best time for 20 km and 10 km, respectively. Spatio-temporal and ground reaction force (GRF) data were recorded at 2.5 km, and at 4.5, 6.5 and 8.5 km for a subsection of athletes. Gait variability was measured using median absolute deviation (MAD) whereas inter-leg symmetry was measured using the symmetry angle. Both groups showed low variability for step length (<0.9%), step frequency (<1.1%), contact time (≤1.2%) and vertical peak force values (<5%), and neither variability nor symmetry changed with distance walked. Junior athletes were more variable for both step length (P = 0.004) and loading force (P = 0.003); no differences for gait symmetry were found. Whereas there was little mean asymmetry overall, individual analyses identified asymmetry in several athletes (symmetry angle ≥ 1.2%). Importantly, asymmetrical step lengths were found in 12 athletes and could result from underlying imbalances. Coaches are advised to observe athletes on an individual basis to monitor for both variability and asymmetry.

Concepts: Median, Symmetry, Absolute deviation, Mean, Reaction, Ground reaction force, Asymmetry, Median absolute deviation


Methods are needed for rapid screening of environmental compounds for neurotoxicity, particularly ones that assess function. To demonstrate the utility of microelectrode array (MEA)-based approaches as a rapid neurotoxicity screening tool, 1055 chemicals from EPA’s phase II ToxCast library were evaluated for effects on neural function and cell health. Primary cortical networks were grown on multi-well microelectrode array (mwMEA) plates. On day in vitro 13, baseline activity (40 min) was recorded prior to exposure to each compound (40 µM). Changes in spontaneous network activity [mean firing rate (MFR)] and cell viability (lactate dehydrogenase and CellTiter Blue) were assessed within the same well following compound exposure. Following exposure, 326 compounds altered (increased or decreased) normalized MFR beyond hit thresholds based on 2× the median absolute deviation of DMSO-treated wells. Pharmaceuticals, pesticides, fungicides, chemical intermediates, and herbicides accounted for 86% of the hits. Further, changes in MFR occurred in the absence of cytotoxicity, as only eight compounds decreased cell viability. ToxPrint chemotype analysis identified several structural domains (e.g., biphenyls and alkyl phenols) significantly enriched with MEA actives relative to the total test set. The top 5 enriched ToxPrint chemotypes were represented in 26% of the MEA hits, whereas the top 11 ToxPrints were represented in 34% of MEA hits. These results demonstrate that large-scale functional screening using neural networks on MEAs can fill a critical gap in assessment of neurotoxicity potential in ToxCast assay results. Further, a data-mining approach identified ToxPrint chemotypes enriched in the MEA-hit subset, which define initial structure-activity relationship inferences, establish potential mechanistic associations to other ToxCast assay endpoints, and provide working hypotheses for future studies.

Concepts: Median, Cerebral cortex, Assessment, Absolute deviation, Mean, Chemical compound, Deviation, Median absolute deviation


Cognitive tasks impact postural control when performed concurrently as dual-tasks. This is presumed to result from capacity limitations in relevant brain regions. We used functional near-infrared spectroscopy (fNIRS) to measure brain activation of the left motor, temporal, and dorsal-lateral prefrontal brain regions of younger (n=6) and older (n=10) adults. Brain activation was measured during an auditory choice reaction task (CRT) and standing on a dynamic posturography platform, both as single-tasks and concurrently as dual-task. Body sway was assessed by median absolute deviation (MAD) of anterior-posterior translation of the center of mass (COM). Brain activation was measured as changes in oxy-hemoglobin by fNIRS. During both single- and dual-task conditions, we found that older adults had greater brain activation relative to younger adults. During dual task performance, the total activation was less than expected from the sum of individual conditions for both age groups, indicating a dual-task interference (reduction in younger adults=53% [p=0.02]; in older adults=53%; [p=0.008]). This reduction was greater for the activation attributable to the postural task (reduction younger adults=75% [p=0.03]; older adults=59% [p=0.005]) compared to the CRT task (reduction younger adults=10%, [p=0.6]; older adults=7.3%, [p=0.5]) in both age groups. Activation reduction was not accompanied by any significant changes in body sway in either group (older adults: single-task MAD=0.94cm, dual-task MAD=1.10cm, p=0.20; younger adults: single-task RMS=0.95cm, dual-task MAD=1.08cm, p=0.14). Our results indicate that neural resources devoted to postural control are reduced under dual-task conditions that engage attention.

Concepts: Psychology, Brain, Median, Cerebrum, Absolute deviation, Deviation, Prefrontal cortex, Median absolute deviation


Geospatial analysis software provides a range of tools that can be used to measure landform morphometry. Often, a metric can be computed with different techniques that may give different results. This study is an assessment of 5 different methods for measuring longitudinal, or streamlined, subglacial bedform morphometry: orientation, length and longitudinal asymmetry, all of which require defining a longitudinal axis. The methods use the standard deviational ellipse (not previously applied in this context), the longest straight line fitting inside the bedform footprint (2 approaches), the minimum-size footprint-bounding rectangle, and Euler’s approximation. We assess how well these methods replicate morphometric data derived from a manually mapped (visually interpreted) longitudinal axis, which, though subjective, is the most typically used reference. A dataset of 100 subglacial bedforms covering the size and shape range of those in the Puget Lowland, Washington, USA is used. For bedforms with elongation > 5, deviations from the reference values are negligible for all methods but Euler’s approximation (length). For bedforms with elongation < 5, most methods had small mean absolute error (MAE) and median absolute deviation (MAD) for all morphometrics and thus can be confidently used to characterize the central tendencies of their distributions. However, some methods are better than others. The least precise methods are the ones based on the longest straight line and Euler's approximation; using these for statistical dispersion analysis is discouraged. Because the standard deviational ellipse method is relatively shape invariant and closely replicates the reference values, it is the recommended method. Speculatively, this study may also apply to negative-relief, and fluvial and aeolian bedforms.

Concepts: Median, Absolute deviation, Mean, Standard deviation, Deviation, Morphometrics, Median absolute deviation, Statistical deviation and dispersion


This study investigated the kinematic variability and the local stability of walking and pole walking using two tri-axial accelerometers placed on the seventh cervical (C7) and the second sacral (S2) vertebrae of twenty-one adults. Each participant performed three 1-min trials of walking and pole walking on a motorized treadmill (60, 80, 100% of the preferred walk-to-run transition speed). Forty strides per trial were used to calculate, in all directions of C7 and S2, the median of the stride-to-stride median absolute deviation (medMAD) and the local divergence exponent (λ). Generalised estimating equations and pairwise contrasts revealed, during pole walking, a higher medMAD (all directions, most speeds, C7 level only), and a lower λ (all directions, all speeds, both C7 and S2 level). As speed increased, so did medMAD (all directions, both walking with or without poles), with higher values at C7 compared to S2 level. A similar effect was observed for λ in the vertical direction (walking and pole walking), and in the anterior-posterior direction (only pole walking). An increase in speed brought about a λ reduction in the medial-lateral direction (C7 level only), especially during walking. Finally, both medMAD and λ were higher at C7 than S2 level (all directions, both walking and pole walking) except for λ in the anterior-posterior direction, which resulted higher in walking (C7 level only). In conclusion, despite a higher kinematic variability, pole walking appears to be more locally stable than walking at any speed, especially at C7 level.

Concepts: Median, Absolute deviation, Velocity, Kinematics, Deviation, Walking, Speed, Median absolute deviation