Criteria for testing hypotheses about randomness and the absence of a trend. Application Guide

2021 ◽  
Author(s):  
Boris Lemeshko ◽  
Irina Veretel'nikova
Keyword(s):  
Data Analysis ◽  
Statistical Analysis ◽  
Graduate Students ◽  
Statistical Methods ◽  
Random Variables ◽  
Experimental Results ◽  
Testing Hypotheses ◽  
University Teachers ◽  
Statistical Criteria

The monograph discusses the application of statistical criteria aimed at testing hypotheses about the absence of a trend in the analyzed samples. The rejection of such a hypothesis gives grounds to consider the analyzed data as samples of independent equally distributed random variables. We consider a set of special criteria aimed at testing such hypotheses, as well as a set of criteria for the uniformity of laws, the uniformity of averages and the uniformity of variances, which can also be used for these purposes. The disadvantages and advantages of various criteria are emphasized, the application of criteria in conditions of violation of standard assumptions is considered. Estimates of the power of the criteria are given, which allows you to navigate when choosing the most preferred criteria. Following the recommendations will ensure the correctness and increase the validity of statistical conclusions when analyzing data. It is intended for specialists who are interested in the application of statistical methods for the analysis of various aspects and trends of the surrounding reality and who are in contact with the processing of experimental results, the need for data analysis in their activities. It will be useful for engineers, researchers, specialists of various profiles (doctors, biologists, sociologists, economists, etc.) who face the need for statistical analysis of experimental results in their activities. It will also be useful for university teachers, graduate students and students.

Criteria for checking deviations from the exponential law. Application manual

2020 ◽  
Author(s):  
Boris Lemeshko ◽  
Pavel Blinov
Keyword(s):  
Graduate Students ◽  
Statistical Data ◽  
Experimental Results ◽  
Statistical Data Analysis ◽  
Distribution Law ◽  
Distribution Models ◽  
University Teachers ◽  
Exponential Law ◽  
Percentage Points ◽  
Statistical Criteria

The monograph is intended for specialists who are more or less faced with the issues of statistical data analysis, processing of experimental results, and using statistical methods to analyze various aspects and trends of the surrounding reality. The guide discusses the application of statistical criteria aimed at testing the hypothesis that the analyzed sample belongs to the exponential (exponential) distribution law. The disadvantages and advantages of various criteria are indicated. Estimates of the power of the criteria and results of comparative analysis of the criteria are given, as well as tables containing percentage points and statistical distribution models necessary for applying the criteria. Following the recommendations will ensure the correctness and validity of statistical conclusions when analyzing data. It will be useful for engineers, researchers, specialists in various fields (doctors, biologists, sociologists, economists, etc.) who are faced with the need for statistical analysis of experimental results, as well as University teachers, graduate students and students.

Criteria for testing hypotheses about uniformity. Application manual

2020 ◽  
Author(s):  
Boris Levchenko
Keyword(s):  
Graduate Students ◽  
Statistical Data ◽  
Homogeneous Medium ◽  
Statistical Data Analysis ◽  
Distribution Models ◽  
University Teachers ◽  
Percentage Points ◽  
Homogeneity Of Variance ◽  
Correct Application ◽  
Statistical Criteria

The guide discusses the use of statistical criteria focused on the testing of hypotheses about uniformity of laws, which belong to the analyzed sample, of the homogeneous medium (about equality of the mathematical expectations), about the homogeneity of variance (equality of variances of compared samples). The disadvantages and advantages of various criteria are indicated, and the application of criteria in conditions of violation of standard assumptions is considered. Tables containing percentage points and statistical distribution models necessary for the correct application of the criteria are provided. This publication describes a broader set of criteria. Constructed models of marginal distributions of statistics for some sample criteria of law uniformity are proposed. Following the recommendations will ensure the correctness and validity of statistical conclusions when analyzing data. It is intended for specialists who are more or less faced with the issues of statistical data analysis, processing the results of experiments, and using statistical methods to analyze various aspects and trends of the surrounding reality. It will be useful for engineers, researchers, specialists in various fields (doctors, biologists, sociologists, economists, etc.), University teachers, graduate students and students.

scholarly journals Statistical methods for monitoring the operation of cathodic protection stations

2019 ◽  
Vol 121 ◽  
pp. 01004
Author(s):  
Tatiana Gerasina ◽  
Alexey Zarubin ◽  
Oxana Zarubina
Keyword(s):  
Experimental Data ◽  
Data Analysis ◽  
Statistical Analysis ◽  
Statistical Methods ◽  
Cathodic Protection ◽  
Control Charts ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Experimental Data Analysis ◽  
Transportation Company

This article is a result of the research on the methods to monitor the operation of cathodic protection stations. This study presents the experimental data analysis of the work of cathodic protection stations was carried out by the transportation company with measurements for two quarters. Statistical analysis realized on the basis of Shewhart control charts.

Two-stage and sequential sampling for estimation and testing with prescribed precision

2017 ◽  
Vol 01 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Shelemyahu Zacks
Keyword(s):  
Data Analysis ◽  
Random Variables ◽  
Small Error ◽  
Ratio Test ◽  
Type I ◽  
Estimation Of Parameters ◽  
Parametric Inference ◽  
Unknown Parameters ◽  
Testing Hypotheses ◽  
Sampling Procedures

Statistical data analysis includes several phases. First, there is the phase of data collection. Second, there is the phase of analysis and inference. The two phases are interconnected. There are two types of data analysis. One type is called parametric and the other type is nonparametric. In the present paper, we discuss parametric inference. In parametric inference, we model the results of a given experiment as realization of random variables having a particular distribution, which is specified by its parameters. A random sample is a sequence of independent and identically distributed (i.i.d.) random variables. Statistics are functions of the data in the sample, which do not involve unknown parameters. A statistical inference is based on statistics of a given sample. We discuss two kinds of parametric inference. Estimating the values of parameters, or testing hypotheses concerning the parameters in either kind of inference, we are concerned with the accuracy and precision of the results. In estimation of parameters, the results are precise if, with high probability, they belong to a specified neighborhoods of the parameters. In testing hypotheses, one has to decide which one of two or several hypotheses should be accepted. Hypotheses which are not accepted are rejected. We distinguish between two types of errors. Type I error is the one committed by rejecting a correct hypothesis. Type II is that of accepting a wrong hypothesis. It is desired that both types of errors will occur simultaneously with small probabilities. Both precision in estimation or small error probabilities in testing depend on the statistics used (estimators or test functions) and on the sample size. In this paper, we present sampling procedures that attain the desired objectives. In Sec. 2, we discuss estimation of the parameters of a binomial distribution. In Sec. 3, more general results about estimation of expected values are presented. In Sec. 4, we discuss the Wald Sequential Probability Ratio Test (SPRT), which has optimal properties for testing two simple hypotheses.

scholarly journals Meningkatkan Kemampuan Motorik Halus Anak melalui Kegiatan Menulis di Atas Pasir

2019 ◽  
Vol 2 (2) ◽  
pp. 74-85
Author(s):  
Tiara Erlianda ◽  
Ahmad Fauzi ◽  
Khairul Amri
Keyword(s):  
Data Analysis ◽  
Action Research ◽  
Data Collection ◽  
Statistical Methods ◽  
Motor Skills ◽  
T Test ◽  
Fine Motor ◽  
Fine Motor Skills ◽  
Testing Hypotheses ◽  
Analysis Techniques

The fine motor skills of children in the group B2 of TK Islam Terpadu Darul Mukhlishin are still lack. It can be seen from the results of the letters written by the child that is not in accordance with the example given by the teacher. The study aims to an increase in children’s fine motor skills through writing activities on the sand in TK Islam Terpadu Darul Mukhlishin. This type of research is a classroom action research conducted in 2 cycles. This research uses a quantitative approach with descriptive statistical methods. Data collection techniques used were observation, interview and tests. The research instrument used observation sheets, interview sheets and tests. Data analysis techniques used descriptive and inferential statistics using t-test. The results showed that fine motor skills achieved by children in group B2 before the action reached 30.25%.  In the first cycle of action reached 61.125% while in the second cycle of action reached 91.5%. In testing hypotheses through t-test with a significant level of 5%, it show that the value of t-count ≥ t-table is 22.23 ≥ 2.093, it can be concluded that H0 is rejected and Ha is accepted, namely writing on sand can improve children’s fine motor skills in group B2 of TK Islam Terpadu Darul Mukhlishin.

scholarly journals Statistics for linguists revisited: the review of some basic statistical tools in linguistic research and data analysis

2021 ◽  
Vol 17 ◽  
pp. 31-46
Author(s):  
Ewa Kusz ◽  
Keyword(s):  
Data Analysis ◽  
Statistical Analysis ◽  
Statistical Methods ◽  
Applied Linguistics ◽  
Nonparametric Tests ◽  
Visual Methods ◽  
Statistical Tools ◽  
Major Purpose ◽  
Musical Intelligence ◽  
Linguistic Research

The major aim of this paper is to emphasise the importance of implementing statistical tools in the field of linguistic research, as well as to acquaint the reader with the basic statistical methods that can be used while conducting linguistic studies. The article introduces the idea of five steps in data analysis that any researcher of applied linguistics can take in order to carry out relevant studies. The steps include choosing statistical programmes, eliciting data, selecting some visual methods and applying normality tests, as well as choosing applicable parametric or nonparametric tests, all of which requires appropriate planning, designing, analysing and interpreting data. The theoretical part is an interlude to the practical realisation of the above-mentioned five steps, which is based on the part of linguistic research conducted on the students of English Philology. The major purpose of it was to prove (or refute) that there is a positive correlation between participants’ level of musical intelligence and their L2 pronunciation skills. The practical use of statistical methods enables the readers to familiarise themselves with one of the patterns of statistical analysis in the field of applied linguistics.

scholarly journals Numerical Computation of the Small Balls Probability for RandomFunctions with Normal Components

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Data Analysis ◽  
Characteristic Function ◽  
Numerical Computation ◽  
Statistical Methods ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Random Variables ◽  
Random Variable ◽  
Random Functions

Statistical methods are often based on the properties of the distribution of random variables or randomvectors. In functional data analysis (FDA) we do not work with random observation containing a finite randomvector, but the whole function is one observation. We call it the functional random variable or the randomfunction, in short. This paper offers the possibility to generate random functions with normal components. In thiscase, the probability of small balls can be calculated numerically using the characteristic function. This tool canbe very useful in simulations and testing various kinds of estimates.

Expert survey and analysis of the results

2019 ◽  
Vol 85 (7) ◽  
pp. 73-82
Author(s):  
Vladimir O. Tolcheev
Keyword(s):  
Data Analysis ◽  
Research University ◽  
Statistical Processing ◽  
Educational Process ◽  
Expert Survey ◽  
Educational Modules ◽  
Training Modules ◽  
Engineering Institute ◽  
Good Agreement ◽  
Statistical Criteria

The issues of organizing an expert survey and carrying out statistical processing and analysis of the results are considered. The experts are the fifth-year students undergoing training at the Department of Management and Informatics «Moscow Power Engineering Institute» of the National Research University. The goal of the survey is revealing the disciplines that are most useful for employment in their specialty. We discuss the special features of the survey and a concept of «work in the specialty», with due regard for statistical reliability of the results. Data of written questionnaire gained in 2018 were processed and analyzed using cluster analysis (construction of dendrograms and application of the K-means method) and non-parametric statistical criteria (Friedman and Mann – Whitney – Wilcoxon). Data processing is implemented in the program STATISTICA. The analysis is carried out to reveal significant differences between the educational courses and assess the degree of consistency of the respondents to divide them into clusters that unite the students with similar judgments. Data analysis revealed that experts’ estimates in 2018 are in fairly good agreement with the estimates of previous studies; among the respondents there are three coalitions corresponding to the training modules «Software», «Management Theory», «Data Analysis»; the overall consistency of students in the two groups is very low (and, on the contrary, high in the identified clusters); grades are homogeneous and do not depend on training groups (and employment – unemployment of the respondents). The obtained results allow us to address a number of important questions regarding the ways of improving the educational process, e.g., to optimize yearly course hours for different educational modules.

Real options in business valuation and investment

2018 ◽  
Author(s):  
Андрей Гусев ◽  
Andrey Gusev
Keyword(s):  
Graduate Students ◽  
Real Options ◽  
Scientific Publication ◽  
Investment Analysis ◽  
Investment Activity ◽  
Business Valuation ◽  
Investment Projects ◽  
University Teachers ◽  
Specific Calculations

In the presented monograph discusses the major problems associated with the development of methods of investment analysis and application of real options method in the assessment of efficiency of investment projects and valuation of enterprise (business). Disclosed the content of the basic models of evaluation of real options, a classification of real options, the theoretical principles supported by specific calculations. Scientific publication intended for graduate students, University teachers, scientific employees, specializing in the field of management of investment activity of enterprises and business valuation.

PENENTUAN KRITERIA PENILAIAN KESAN JUMLAH LEUKOSIT PADA PEMERIKSAAN APUSAN DARAH TEPI

2018 ◽  
Vol 3 (2) ◽  
pp. 52-61
Author(s):  
Dzikra Arwie ◽  
Islawati
Keyword(s):  
Data Analysis ◽  
Statistical Analysis ◽  
Blood Cells ◽  
Blood Smear ◽  
White Blood Cells ◽  
Peripheral Blood Smear ◽  
Field Of View ◽  
Laboratory Observation ◽  
Number Of Cells

Leukocytes or white blood cells have a characteristic characteristic of different cells. Determination of the impression of the number of leukocytes is determined in the number of cells in the field of view. While the number of viewable field cells expressed is still quite varied. The purpose of this study was to determine the number of leukocytes in the field of view and expressed the impression of a sufficient amount. This research was conducted at the Laboratory of Health Analyst Department Panrita Husada Bulukumba on 9 April 2017 to 14 July 2017. This type of research is a laboratory observation that aims to determine the criteria for assessing the impression of the number of leukocytes on a peripheral blood smear. Data analysis using statistical analysis is the average and standard deviations to determine the impression of the number of leukocytes and use 3 inspection zones. The results of this study obtained results in zone IV the number of leukocyte impressions said to be sufficient was 7-10, in zone V the number of leukocyte impressions said to be sufficient was 4-9, and in zone VI the number of leukocyte impressions said to be sufficient was 3-8.  

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