scholarly journals Statistical measures of the central tendency for H+ activity and pH

2017 ◽  
Vol 68 (4) ◽  
pp. 174-181 ◽  
Author(s):  
Izabela Kuna-Broniowska ◽  
Halina Smal
Keyword(s):  
Probability Distributions ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Central Tendency ◽  
Statistical Measures ◽  
Normal Probability ◽  
Explicit Opinion ◽  
Normal Probability Distribution ◽  
Theoretical Considerations

Abstract Despite the numerous papers on the statistical analyses of pH, there is no explicit opinion on the use of arithmetic mean as a measure of the central tendency for pH and H+ activity. The problem arises because the transformation of the arithmetic mean for one does not give the arithmetic mean for the other. The paper presents 1) the theoretical considerations on the distribution of pH and H+ activity and relation between them, properties of these distributions, the choice of distributions which should be consistent with the distribution of pH and the distribution of H+ activity and measures of central tendency for features of such distributions and 2) examples of calculations of measures of central tendency for pH and H+ activity based on the literature data on soil and lake water pH. These data analyses included distributions of pH and H+ activities, properties of distribution, descriptive statistics for pH and for the H+ activity and comparison of arithmetic mean with the geometric mean. From the results, it could be concluded that a uniform approach to the choice of measure for the central tendency of pH and H+ activity requires the determination of the type of measure (mean) for one of them and then consistent transformation of this measure. The choice of measure of the central tendency for the variable should be preceded by determination of its distribution. Normal probability distribution of pH and thus lognormal distribution of H+ activity indicate that the arithmetic mean, and its corresponding geometric mean should be used as proper measures of the central tendency for pH and for H+ activity. Besides, the position statistic that is a median can be used for each of those variables, irrespective of their probability distributions.

Empirical Investigation of Alternative Measures of Central Tendency

2020 ◽  
Author(s):  
William H Black ◽  
Lari B Masten
Keyword(s):  
Geometric Mean ◽  
Predictive Performance ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Central Tendency ◽  
Business Valuation ◽  
Alternative Measures ◽  
Data Points ◽  
Using Data ◽  
Performance Results

There is ongoing controversy in the business valuation literature regarding the preferability of the arithmetic mean or the harmonic mean when estimating ratios for use in business valuation. This research conducts a simulation using data reported from actual market transactions. Successive random samples were taken from data on valuation multiples and alternative measures of central tendency were calculated, accumulating more than 3.7 million data points. The measures (arithmetic mean, median, harmonic mean, geometric mean) were compared using hold-out sampling to identify which measure provided the closest approximation to actual results, evaluated in terms of least squares differences. Results indicated the harmonic mean delivered superior predictions to the other measures of central tendency, with less overstatement. Further, differences in sample size from 5 to 50 observations were evaluated to assess their impact on predictive performance. Results showed substantial improvements up to sample sizes of 20 or 25, with diminished improvements thereafter.

Excel: Uma ferramenta estatística

2021 ◽  
Author(s):  
Eliel Alves Ferreira ◽  
João Vicente Zamperion
Keyword(s):  
Statistical Analysis ◽  
Statistical Study ◽  
Descriptive Statistics ◽  
Central Tendency ◽  
Simple Linear Regression ◽  
The Third ◽  
Statistical Knowledge ◽  
Normal Probability ◽  
Measures Of Dispersion ◽  
Normal Probability Distribution

This study aims to present the concepts and methods of statistical analysis using the Excel software, in a simple way aiming at a greater ease of understanding of students, both undergraduate and graduate, from different areas of knowledge. In Excel, mainly Data Analysis Tools will be used. For a better understanding, there are, in this book, many practical examples applying these tools and their interpretations, which are of paramount importance. In the first chapter, it deals with introductory concepts, such as introduction to Excel, the importance of statistics, concepts and definitions. Being that in this will be addressed the subjects of population and sample, types of data and their levels of measurement. Then it brings a detailed study of Descriptive Statistics, where it will be studied percentage, construction of graphs, frequency distribution, measures of central tendency and measures of dispersion. In the third chapter, notions of probability, binomial and normal probability distribution will be studied. In the last chapter, Inferential Statistics will be approached, starting with the confidence interval, going through the hypothesis tests (F, Z and t tests), ending with the statistical study of the correlation between variables and simple linear regression. It is worth mentioning that the statistical knowledge covered in this book can be useful for, in addition to students, professionals who want to improve their knowledge in statistics using Excel.

COMPARISON OF WEIBULL AND NORMAL PROBABILITY DISTRIBUTION OF FLEXURAL STRENGTH OF DENSE AND POROUS FIRED CLAY

2016 ◽  
Vol 78 (9) ◽  
Author(s):  
Muazu Abubakar ◽  
Muhamad Azizi Mat Yajid ◽  
Norhayati Ahmad
Keyword(s):  
Probability Distribution ◽  
Flexural Strength ◽  
Normal Distribution ◽  
Probability Distributions ◽  
Bending Test ◽  
Strength Data ◽  
Normal Probability ◽  
Distribution Parameters ◽  
Normal Probability Distribution ◽  
Two Parameter

In this research, dense and porous fired clay were produced at a firing temperature of 1300°C. The flexural strength data of the dense and the porous fired clay were determined using three point bending test. Two-parameter Weibull and normal probability distributions were used to estimate the reliability of the flexural strength data of the dense and the porous fired clay. From the result, the Weibull probability distribution scale parameter for the dense (36.31MPa) and Porous (18.85MPa) fired clay are higher than the mean strength value for the dense (33.84MPa) and the porous (17.87MPa) of the normal distribution. Distributions of flaws in the dense and the porous fired clay have a significant effect on the Weibull and normal distribution parameters. The fractured surface of the dense fired clay shows a random distribution of cracks while that of the porous fired clay shows a distribution of pores in the morphology. The normal distribution considers failure at 50% of the flexural strength data while Weibull probability distribution is failure at 62.3% of the strength data. Therefore, two-parameter Weibull is the suitable tool to model failure strength data of the dense and porous fired clay.  

On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

2012 ◽  
Vol E95-B (2) ◽  
pp. 647-650
Author(s):  
Ning WANG ◽  
Julian CHENG ◽  
Chintha TELLAMBURA
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Log Ratio

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals Faecal contamination of drinking water during collection and household storage: the need to extend protection to the point of use

2003 ◽  
Vol 1 (3) ◽  
pp. 109-115 ◽  
Author(s):  
Thomas F. Clasen ◽  
Andrew Bastable
Keyword(s):  
Drinking Water ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Faecal Contamination ◽  
Household Level ◽  
Safe Water ◽  
Female Head ◽  
Point Of Use ◽  
Thermotolerant Coliforms ◽  
And Storage

Paired water samples were collected and analysed for thermotolerant coliforms (TTC) from 20 sources (17 developed or rehabilitated by Oxfam and 3 others) and from the stored household water supplies of 100 households (5 from each source) in 13 towns and villages in the Kailahun District of Sierra Leone. In addition, the female head of the 85 households drawing water from Oxfam improved sources was interviewed and information recorded on demographics, hygiene instruction and practices, sanitation facilities and water collection and storage practices. At the non-improved sources, the arithmetic mean TTC load was 407/100 ml at the point of distribution, rising to a mean count of 882/100 ml at the household level. Water from the improved sources met WHO guidelines, with no faecal contamination. At the household level, however, even this safe water was subject to frequent and extensive faecal contamination; 92.9% of stored household samples contained some level of TTC, 76.5% contained more than the 10 TTC per 100 ml threshold set by the Sphere Project for emergency conditions. The arithmetic mean TTC count for all samples from the sampled households was 244 TTC per 100 ml (geometric mean was 77). These results are consistent with other studies that demonstrate substantial levels of faecal contamination of even safe water during collection, storage and access in the home. They point to the need to extend drinking water quality beyond the point of distribution to the point of consumption. The options for such extended protection, including improved collection and storage methods and household-based water treatment, are discussed.

scholarly journals Objective determination of the sea age of Atlantic salmon from the sizes and dates of capture of individual fish

2010 ◽  
Vol 68 (1) ◽  
pp. 130-143 ◽  
Author(s):  
Philip J. Bacon ◽  
William S. C. Gurney ◽  
Eddie McKenzie ◽  
Bryce Whyte ◽  
Ronald Campbell ◽  
...  
Keyword(s):  
Atlantic Salmon ◽  
Fishery Management ◽  
East Coast ◽  
Probability Distributions ◽  
Age Classes ◽  
Individual Fish ◽  
Bivariate Probability ◽  
Management And Conservation ◽  
Objective Determination

Abstract Bacon, P. J., Gurney, W. S. C., McKenzie, E., Whyte, B., Campbell, R., Laughton, R., Smith, G., and MacLean, J. 2011. Objective determination of the sea age of Atlantic salmon from the sizes and dates of capture of individual fish. – ICES Journal of Marine Science, 68: 130–143. The sea ages of Atlantic salmon indicate crucial differences between oceanic feeding zones that have important implications for conservation and management. Historical fishery-catch records go back more than 100 years, but the reliability with which they discriminate between sea-age classes is uncertain. Research data from some 188 000 scale-aged Scottish salmon that included size (length, weight) and seasonal date of capture on return to the coast were investigated to devise a means of assigning sea age to individual fish objectively. Two simple bivariate probability distributions are described that discriminate between 1SW and 2SW fish with 97% reliability, and between 2SW and 3SW fish with 70% confidence. The same two probability distributions achieve this accuracy across five major east coast Scottish rivers and five decades. They also achieve the same exactitude for a smaller recent dataset from the Scottish west coast, from the River Tweed a century ago (1894/1895), and for salmon caught by rod near the estuary. More surprisingly, they also achieve the same success for rod-caught salmon taken at beats remote from the estuary and including capture dates when some fish could have been in the river for a few months. The implications of these findings for fishery management and conservation are discussed.

scholarly journals On the determination of step energies. Theoretical considerations and application to an anisotropic Kossel model

2006 ◽  
Vol 39 (4) ◽  
pp. 563-570 ◽  
Author(s):  
M. A. Deij ◽  
J. H. Los ◽  
H. Meekes ◽  
E. Vlieg
Keyword(s):  
Lattice Models ◽  
Single Step ◽  
Spiral Growth ◽  
Growth Theory ◽  
Two Dimensional ◽  
Island Growth ◽  
Growth Step ◽  
Step Flow ◽  
Theoretical Considerations

Steps on surfaces are important in crystal growth theory, as the step free energy determines the two-dimensional nucleation rate, island growth, step flow and spiral growth. In this paper, it is illustrated that in general in lattice models the step energy of a single step cannot be determined directly by counting broken bonds. A new method is proposed that uses the geometry of a step together with the bonding topology, allowing for a straightforward determination of single-step energies for any case. The method is applied to an anisotropic Kossel model.

Sign in / Sign up

Export Citation Format

Share Document