What do (most of) our dispersion measures measure (most)? Dispersion?

This paper discusses the degree to which most of the most widely-used measures of dispersion in corpus linguistics are not particularly valid in the sense of actually measuring dispersion rather than some amalgam of a lot of frequency and a little dispersion. The paper demonstrates these issues on the basis of data from a variety of corpora. I then outline how to design a dispersion measure that only measures dispersion and show that (i) it indeed measures information that is different from frequency in an intuitive way and (ii) has a higher degree of predictive power of lexical decision times from the MALD database than nearly all other measures in nearly all corpora tested.

Estimating spatiotemporal patterns of deaths by COVID-19 outbreak on a global scale

ObjectiveOur main objective is to estimate the trend of deaths by COVID-19 on a global scale, considering the six continents.Study designThe study design was a retrospective observational study conducted using the secondary data provided by the Our World in Data project on a public domain.SettingThis study was conducted based on worldwide deaths by COVID-19 recorded for the Our World in Data project from 29 February 2020 to 17 February 2021.MethodsEstimating the trend in COVID-19 deaths is not a trivial task due to the problems associated with the COVID-19 data, such as the spatial and temporal heterogeneity, observed seasonality and the delay between the onset of symptoms and diagnosis, indicating a relevant measurement error problem and changing the series’ dependency structure. To bypass the aforementioned problems, we propose a method to estimate the components of trend, seasonality and cycle in COVID-19 data, controlling for the presence of measurement error and considering the spatial heterogeneity. We used the proposed model to estimate the trend component of deaths by COVID-19 on a global scale.ResultsThe model was able to capture the patterns in the occurrence of deaths related to COVID-19, overcoming the problems observed in COVID-19 data. We found compelling evidence that spatiotemporal models are more accurate than univariate models to estimate the patterns of the occurrence of deaths. Based on the measures of dispersion of the models’ prediction in relation to observed deaths, it is possible to note that the models with spatial component are significantly superior to the univariate model.ConclusionThe findings suggested that the spatial dynamics have an important role in the COVID-19 epidemic process since the results provided evidence that spatiotemporal models are more accurate to estimate the general patterns of the occurrence of deaths related to COVID-19.

Enhanced Estimators of Population Variance with the Use of Supplementary Information in Survey Sampling

In the present study, we propose the proficient class of estimators of the finite population mean, while incorporating the nonconventional location and nonconventional measures of dispersion with coefficient of variation of the auxiliary variable. Properties associated with the suggested class of improved estimators are derived, and an efficiency comparison with the usual unbiased ratio estimator and other existing estimators under consideration in the present study is established. An empirical study has also been provided to validate the theoretical results. Finally, it is established that the proposed class of estimators of the finite population variance proves to be more efficient than the existing estimators mentioned in this study.

Modelling Geometric Measure of Variation About the Population Mean

Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measureshave allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean.Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance give average of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standarddeviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of this paper was to model a geometric measure of variation about the population mean which could overcome the weaknesses of the existing measures of variation about the population mean. The study was able to formulate the geometric measure of variation about the population mean that obeyedthe algebraic laws behind absolute numbers, which was capable of further algebraic manipulations as it could be used further to estimate the average variation about the mean for weighted datasets, probability mass functions and probability density functions. Lastly, the measure was not affected by outliers and skewed datasets. This shows that the formulated measure was capable of solving the weaknesses of the existing measures of variation about the mean

Estimating Average Variation About the Population Mean Using Geometric Measure of Variation

Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measureshave allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance giveaverage of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and alsointegration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.

EMPIRICAL COMPARISON OF RELATIVE PRECISION OF GEOMETRIC MEASURE OF VARIATION ABOUT THE MEAN AND STANDARD DEVIATION

Measure of dispersion is an important statistical tool used to illustrate the distribution of datasets.The use of this measure has allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers have been able to develop measures of dispersion from the mean such as mean deviation, mean absolute deviation, variance and standard deviation. Studies have shown that standard deviation is currently the most efficient measure of variation about the mean and the most popularly used measure of variation about the mean around the world because of its fewer shortcomings. However, studies have also established that standard deviation is not 100% efficient because the measure is affected by outlier in thedatasets and it also assumes symmetry of datasets when estimating the average deviation about the mean a factor that makes it to be responsive to skewed datasets hence giving results which are biased for such datasets. The aim of this study is to make a comparative analysis of the precision of the geometric measure of variation and standard deviation in estimating the average variationabout the mean for various datasets. The study used paired t-test to test the difference in estimates given by the two measures and four measures of efficiency (coefficient of variation, relative efficiency, mean squared error and bias) to assess the efficiency of the measure. The results determined that the estimates of geometric measure were significantly smaller than those of standard deviation and that the geometric measure was more efficient in estimating the average deviation for geometric, skewed and peaked datasets. In conclusion, the geometric measure was not affected by outliers and skewed datasets, hence it was more precise than standard deviation.

Progression of hospitalizations and hospital costs for Parkinson’s disease in the Brazilian population

Introduction: Parkinson’s disease (PD) is the second most prevalent neurodegenerative disease in the world. Its incidence increases with advancing age. Therefore, in Brazil, a country in transition of age structure, it is relevant to assess the progression of hospitalizations and hospital costs for PD over the years. Objective: Describe the progression of hospitalizations and hospital costs for PD in Brazilian’s public health system, SUS, between 2008-2020. Design and setting: Descriptive ecological observational study made in Brazil, Salvador – BA. Methods: Data from hospitalization and hospital costs were collected from DATASUS in the 5 Brazilian regions. Statistical analysis was based on measures of dispersion and central tendency. Results: Between 2008-2020, 11,565 admissions for PD were notified. The highest numbers of hospitalizations corresponded to the Southeast region (annual average = 370.1), while the smallest to the North region (annual average = 28.4). Regarding the high expenses resulting from hospitalizations, it was observed that the Southeast obtained higher costs with hospital services (annual average = 1,417,716.8), while the North had the lowest (annual average = 18,611.01). Conclusion: Southeast region stood out for having the highest numbers in costs and hospitalizations, the opposite of what happened in North. Brazilian regional disparities, especially regarding to demographic density, HDI, socioeconomic development and access to health care, may explain these demographically uneven.

Excel: Uma ferramenta estatística

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.