Deviation Of Data Points Research Articles

Study on Analysis of Variance in Statistics

Variance is a key statistical measure that quantifies the spread of values within a dataset, offering insights into data variability. It evaluates the average squared deviation of data points from the mean and serves as the foundation for statistical methods such as ANOVA and regression analysis. Introduced by Ronald Fisher in 1918, variance builds upon earlier concepts by Gauss and is calculated differently for populations and samples, using Bessel’s correction for unbiased estimation in samples. Unlike range, variance incorporates all data points, ensuring comparability across datasets of varying sizes. Its properties, including invariance to additive constants and scalability by squared factors, make it a robust metric for analyzing data spread. Variance is especially critical in experimental designs to distinguish between systematic (between-groups) and unsystematic (within-groups) variance, enabling researchers to assess and interpret variability in diverse contexts

Identifying sources of groundwater and recharge zone using stable environmental isotopes in the Erbil basin-northern Iraq

The Dashty-Hewler basin is a groundwater basin located in Erbil in northern Iraq. It comprises three distinct sub-basins (Kapran, Central, and Bashtapa) covering a total basin area of 2,660 ​km2. It is bounded by the greater Zab river to the north and the little Zab to the south. The groundwater in this catchment has never been investigated using modern environmental isotope evidence. Since the groundwater in this basin serves as both drinking water and a source of irrigation, its management is crucial. Recently, due to the increase in population, excessive pumping has taken place, which has led to a decline in the water table. Accordingly, it is necessary to address the issues of where the groundwater will recharge and what the source of the recharge will be. For this purpose, 27 groundwater samples from different wells and two river water samples were analyzed for stable isotopes (δ18O and δ2H). The distribution of δ18O and δ2H over the study area was utilized by inverse distance weighted (IDW) interpolation within ESRI ArcGIS (10.8). The results indicated that the relationship between δ18O and δ2H in the groundwater samples (δ2H ​= ​6.59 δ18O +7.48‰) showed relative shifts of both the slope and the deuterium excess when compared to the Iraq meteoric water line (δ2H ​= ​7.66 δ18O ​+ ​14.19‰). The deviation of data points from the meteoric line can be attributed to high evaporation both during the rainy season and through run-off on the ground surface before infiltration. Most of the groundwater samples had a deuterium excess above 10‰ between 12.14 and 22.72‰, suggesting the precipitation present in the groundwater comes from the Mediterranean sector. Based on local isotopic gradients (δ18O, −0.22/100 ​m), in combination with topographic and geologic criteria, the recharge areas were identified as being between 400 ​m and 1,100 ​m above sea level.

Multi-objective Semi-supervised clustering for finding predictive clusters

This study concentrates on clustering problems and aims to find compact clusters that are informative regarding the outcome variable. The main goal is partitioning data points so that observations in each cluster are similar and the outcome variable can be predicted using these clusters simultaneously. We model this semi-supervised clustering problem as a multi-objective optimization problem with considering deviation of data points in clusters and prediction error of the outcome variable as two objective functions to be minimized. For finding optimal clustering solutions, we employ a non-dominated sorting genetic algorithm II approach and local regression is applied as the prediction method for the output variable. For comparing the performance of the proposed model, we compute seven models using five real-world data sets. Furthermore, we investigate the impact of using local regression for predicting the outcome variable in all models and examine the performance of the multi-objective models compared to single-objective models.

Hydrogeological Conceptual Model of Groundwater from Carbonate Aquifers Using Environmental Isotopes (<sup>18</sup>O, <sup>2</sup>H) and Chemical Tracers: A Case Study in Southern Latium Region, Central Italy

The present work provides hydrochemical and stable isotope data and their interpretations for 54 springs and 20 wells, monitored from 2002 to 2006, in the Southern Latium region of Central Italy to identify flow paths, recharge areas and hydrochemical processes governing the evolution of groundwater in this region. The hydrogeological conceptual model of the carbonate aquifers of southern Latium was based on environmental isotopic and hydrochemical investigation techniques to characterize and model these aquifer systems with the aim of achieving proper management and protection of these important resources. Most of the spring samples, issuing from Lepini, Ausoni and Aurunci Mts., are characterized as Ca-Mg-HCO3 water type, however, some samples show a composition of Na-Cl and mixed Ca-Na-HCO3-Cl waters. Groundwater samples from Pontina Plain are mostly characterized by Na-Cl and Ca-Cl type waters. Geochemical modeling and saturation index computation of the Lepini, Ausoni Aurunci springs and Pontina Plain wells shows an interaction with carbonate rocks. Most of the spring and well water samples were saturated with respect to calcite and dolomite, however all sampled waters were undersaturated with respect to gypsum and halite. The relationship between δ18O and δ2H, for spring and well water samples, shows shifts of both the slope and the deuterium excess when compared to the world meteoric (WMWL) and central Italy meteoric (CIMWL) water lines. The deviation of data points from the meteoric lines can be attributed to evaporation both during the falling of the rain and by run-off on the ground surface before infiltration. Most springs and wells have a deuterium excess above 10 ‰ suggesting the precipitation in the groundwater comes from the Mediterranean sector. On the basis of local isotopic gradients, in combination with topographic and geologic criteria, four recharge areas were identified in the Aurunci Mountains. In Pontina Plain, the elevations of the recharging areas suggest that the Lepini carbonate aquifers are feeding them.

A Note Concerning Professor Jolicoeur’s Comments

The ordinary major axis of a bivariate normal distribution is unsuitable for describing the functional relationship (in Lindley’s general sense) between two naturally variable quantities, because it is not invariant with scale and because qualitatively unlike quantities are subtracted in computing it. The bivariate structural relationship is unsuitable because one of the parameters required, λ, cannot be estimated from naturally variable data; in fact λ has no objective meaning for such data. The standard major axis (or GM regression line) has neither of these defects, and it is the line that minimizes the sum of products of the absolute vertical and horizontal deviations of data points from itself.

THE USE OF LINEAR PROGRAMMING TO FILTER DIGITIZED MAP DATA

The procedure used to discover subsurface formations where mineral resources may exist normally requires the accumulation and processing of large amounts of data concerning the earth’s fields. Data errors may strongly affect the conclusions drawn from the analysis. Thus, a method of checking for errors is essential. Since the field should be relatively smooth locally, a typical approach is to fit the data to a surface described by a low‐order polynomial. Deviations of data points from this surface can then be used to detect errors. Frequently a least‐squares approximation is used to determine the surface, but results could be misleading. Linear programming can be applied to give more satisfactory results. In this approach, the sum of the absolute values of the deviations is minimized rather than the squares of the deviations as in least squares. This paper describes in detail the formulation of the linear programming problem and cites an example of its application to error detection. Through this formulation, once errors are removed, the results are meaningful physically and, hence, can be used for detecting subsurface phenomena directly.