Measures of Central Tendency
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Education Quarterly Reviews
Education Quarterly Reviews Allanson, Patricia E., and Notar, Charles E. (2020), Statistics as Measurement: 4 Scales/Levels of Measurement. In: Education Quarterly Reviews, Vol.3, No.3, 375-385. ISSN 2621-5799 DOI: 10.31014/aior.1993.03.03.146 The online version of this article can be found at: https://www.asianinstituteofresearch.org/ Published by: The Asian Institute of Research The Education Quarterly Reviews is an Open Access publication. It May be read, copied, and distributed free of charge according to the conditions of the Creative ComMons Attribution 4.0 International license. The Asian Institute of Research Education Quarterly Reviews is a peer-reviewed International Journal. The journal covers scholarly articles in the fields of education, linguistics, literature, educational theory, research, and methodologies, curriculum, elementary and secondary education, higher education, foreign language education, teaching and learning, teacher education, education of special groups, and other fields of study related to education. As the journal is Open Access, it ensures high visibility and the increase of citations for all research articles published. The Education Quarterly Reviews aiMs to facilitate scholarly work on recent theoretical and practical aspects of education. The Asian Institute of Research Education Quarterly Reviews Vol.3, No.3, 2020: 375-385 ISSN 2621-5799 Copyright © The Author(s). All Rights Reserved DOI: 10.31014/aior.1993.03.03.146 Statistics as Measurement: 4 Scales/Levels of Measurement 1 2 Patricia E. Allanson , Charles E. Notar 1 Liberty University 2 Jacksonville State University. EMail: [email protected] (EMeritus) Abstract This article discusses the basics of the “4 scales of MeasureMent” and how they are applicable to research or everyday tools of life. -
Chapter 4: Central Tendency and Dispersion
Central Tendency and Dispersion 4 In this chapter, you can learn • how the values of the cases on a single variable can be summarized using measures of central tendency and measures of dispersion; • how the central tendency can be described using statistics such as the mode, median, and mean; • how the dispersion of scores on a variable can be described using statistics such as a percent distribution, minimum, maximum, range, and standard deviation along with a few others; and • how a variable’s level of measurement determines what measures of central tendency and dispersion to use. Schooling, Politics, and Life After Death Once again, we will use some questions about 1980 GSS young adults as opportunities to explain and demonstrate the statistics introduced in the chapter: • Among the 1980 GSS young adults, are there both believers and nonbelievers in a life after death? Which is the more common view? • On a seven-attribute political party allegiance variable anchored at one end by “strong Democrat” and at the other by “strong Republican,” what was the most Democratic attribute used by any of the 1980 GSS young adults? The most Republican attribute? If we put all 1980 95 96 PART II :: DESCRIPTIVE STATISTICS GSS young adults in order from the strongest Democrat to the strongest Republican, what is the political party affiliation of the person in the middle? • What was the average number of years of schooling completed at the time of the survey by 1980 GSS young adults? Were most of these twentysomethings pretty close to the average on -
Levels of Measurement and Types of Variables
01-Warner-45165.qxd 8/13/2007 4:52 PM Page 6 6—— CHAPTER 1 evaluate the potential generalizability of research results based on convenience samples. It is possible to imagine a hypothetical population—that is, a larger group of people that is similar in many ways to the participants who were included in the convenience sample—and to make cautious inferences about this hypothetical population based on the responses of the sample. Campbell suggested that researchers evaluate the degree of similarity between a sample and hypothetical populations of interest and limit general- izations to hypothetical populations that are similar to the sample of participants actually included in the study. If the convenience sample consists of 50 Corinth College students who are between the ages of 18 and 22 and mostly of Northern European family back- ground, it might be reasonable to argue (cautiously, of course) that the results of this study potentially apply to a hypothetical broader population of 18- to 22-year-old U.S.col- lege students who come from similar ethnic or cultural backgrounds. This hypothetical population—all U.S.college students between 18 and 22 years from a Northern European family background—has a composition fairly similar to the composition of the conve- nience sample. It would be questionable to generalize about response to caffeine for pop- ulations that have drastically different characteristics from the members of the sample (such as persons who are older than age 50 or who have health problems that members of the convenience sample do not have). Generalization of results beyond a sample to make inferences about a broader popula- tion is always risky, so researchers should be cautious in making generalizations. -
Central Tendency, Dispersion, Correlation and Regression Analysis Case Study for MBA Program
Business Statistic Central Tendency, Dispersion, Correlation and Regression Analysis Case study for MBA program CHUOP Theot Therith 12/29/2010 Business Statistic SOLUTION 1. CENTRAL TENDENCY - The different measures of Central Tendency are: (1). Arithmetic Mean (AM) (2). Median (3). Mode (4). Geometric Mean (GM) (5). Harmonic Mean (HM) - The uses of different measures of Central Tendency are as following: Depends upon three considerations: 1. The concept of a typical value required by the problem. 2. The type of data available. 3. The special characteristics of the averages under consideration. • If it is required to get an average based on all values, the arithmetic mean or geometric mean or harmonic mean should be preferable over median or mode. • In case middle value is wanted, the median is the only choice. • To determine the most common value, mode is the appropriate one. • If the data contain extreme values, the use of arithmetic mean should be avoided. • In case of averaging ratios and percentages, the geometric mean and in case of averaging the rates, the harmonic mean should be preferred. • The frequency distributions in open with open-end classes prohibit the use of arithmetic mean or geometric mean or harmonic mean. Prepared by: CHUOP Theot Therith 1 Business Statistic • If the distribution is bell-shaped and symmetrical or flat-topped one with few extreme values, the arithmetic mean is the best choice, because it is less affected by sampling fluctuations. • If the distribution is sharply peaked, i.e., the data cluster markedly at the middle or if there are abnormally small or large values, the median has smaller sampling fluctuations than the arithmetic mean. -
Chapter 1 Getting Started Section 1.1
Chapter 1 Getting Started Section 1.1 1. (a) The variable is the response regarding frequency of eating at fast-food restaurants. (b) The variable is qualitative. The categories are the number of times one eats in fast-food restaurants. (c) The implied population is responses for all adults in the U.S. 3. (a) The variable is student fees. (b) The variable is quantitative because arithmetic operations can be applied to the fee values. (c) The implied population is student fees at all colleges and universities in the U.S. 5. (a) The variable is the time interval between check arrival and clearance. (b) The variable is quantitative because arithmetic operations can be applied to the time intervals. (c) The implied population is the time interval between check arrival and clearance for all companies in the five-state region. 7. (a) Length of time to complete an exam is a ratio level of measurement. The data may be arranged in order, differences and ratios are meaningful, and a time of 0 is the starting point for all measurements. (b) Time of first class is an interval level of measurement. The data may be arranged in order and differences are meaningful. (c) Class categories is a nominal level of measurement. The data consists of names only. (d) Course evaluation scale is an ordinal level of measurement. The data may be arranged in order. (e) Score on last exam is a ratio level of measurement. The data may be arranged in order, differences and ratios are meaningful, and a score of 0 is the starting point for all measurements. -
Measures of Central Tendency for Censored Wage Data
MEASURES OF CENTRAL TENDENCY FOR CENSORED WAGE DATA Sandra West, Diem-Tran Kratzke, and Shail Butani, Bureau of Labor Statistics Sandra West, 2 Massachusetts Ave. N.E. Washington, D.C. 20212 Key Words: Mean, Median, Pareto Distribution medians can lead to misleading results. This paper tested the linear interpolation method to estimate the median. I. INTRODUCTION First, the interval that contains the median was determined, The research for this paper began in connection with the and then linear interpolation is applied. The occupational need to measure the central tendency of hourly wage data minimum wage is used as the lower limit of the lower open from the Occupational Employment Statistics (OES) survey interval. If the median falls in the uppermost open interval, at the Bureau of Labor Statistics (BLS). The OES survey is all that can be said is that the median is equal to or above a Federal-State establishment survey of wage and salary the upper limit of hourly wage. workers designed to produce data on occupational B. MEANS employment for approximately 700 detailed occupations by A measure of central tendency with desirable properties is industry for the Nation, each State, and selected areas within the mean. In addition to the usual desirable properties of States. It provided employment data without any wage means, there is another nice feature that is proven by West information until recently. Wage data that are produced by (1985). It is that the percent difference between two means other Federal programs are limited in the level of is bounded relative to the percent difference between occupational, industrial, and geographic coverage. -
Redalyc.Robust Analysis of the Central Tendency, Simple and Multiple
International Journal of Psychological Research ISSN: 2011-2084 [email protected] Universidad de San Buenaventura Colombia Courvoisier, Delphine S.; Renaud, Olivier Robust analysis of the central tendency, simple and multiple regression and ANOVA: A step by step tutorial. International Journal of Psychological Research, vol. 3, núm. 1, 2010, pp. 78-87 Universidad de San Buenaventura Medellín, Colombia Available in: http://www.redalyc.org/articulo.oa?id=299023509005 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative International Journal of Psychological Research, 2010. Vol. 3. No. 1. Courvoisier, D.S., Renaud, O., (2010). Robust analysis of the central tendency, ISSN impresa (printed) 2011-2084 simple and multiple regression and ANOVA: A step by step tutorial. International ISSN electrónica (electronic) 2011-2079 Journal of Psychological Research, 3 (1), 78-87. Robust analysis of the central tendency, simple and multiple regression and ANOVA: A step by step tutorial. Análisis robusto de la tendencia central, regresión simple y múltiple, y ANOVA: un tutorial paso a paso. Delphine S. Courvoisier and Olivier Renaud University of Geneva ABSTRACT After much exertion and care to run an experiment in social science, the analysis of data should not be ruined by an improper analysis. Often, classical methods, like the mean, the usual simple and multiple linear regressions, and the ANOVA require normality and absence of outliers, which rarely occurs in data coming from experiments. To palliate to this problem, researchers often use some ad-hoc methods like the detection and deletion of outliers. -
Appropriate Statistical Analysis for Two Independent Groups of Likert
APPROPRIATE STATISTICAL ANALYSIS FOR TWO INDEPENDENT GROUPS OF LIKERT-TYPE DATA By Boonyasit Warachan Submitted to the Faculty of the College of Arts and Sciences of American University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy In Mathematics Education Chair: Mary Gray, Ph.D. Monica Jackson, Ph.D. Jun Lu, Ph.D. Dean of the College of Arts and Sciences Date 2011 American University Washington, D.C. 20016 © COPYRIGHT by Boonyasit Warachan 2011 ALL RIGHTS RESERVED DEDICATION This dissertation is dedicated to my beloved grandfather, Sighto Chankomkhai. APPROPRIATE STATISTICAL ANALYSIS FOR TWO INDEPENDENT GROUPS OF LIKERT-TYPE DATA BY Boonyasit Warachan ABSTRACT The objective of this research was to determine the robustness and statistical power of three different methods for testing the hypothesis that ordinal samples of five and seven Likert categories come from equal populations. The three methods are the two sample t-test with equal variances, the Mann-Whitney test, and the Kolmogorov-Smirnov test. In additional, these methods were employed over a wide range of scenarios with respect to sample size, significance level, effect size, population distribution, and the number of categories of response scale. The data simulations and statistical analyses were performed by using R programming language version 2.13.2. To assess the robustness and power, samples were generated from known distributions and compared. According to returned p-values at different nominal significance levels, empirical error rates and power were computed from the rejection of null hypotheses. Results indicate that the two sample t-test and the Mann-Whitney test were robust for Likert-type data. -
Robust Statistical Procedures for Testing the Equality of Central Tendency Parameters Under Skewed Distributions
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Repository@USM ROBUST STATISTICAL PROCEDURES FOR TESTING THE EQUALITY OF CENTRAL TENDENCY PARAMETERS UNDER SKEWED DISTRIBUTIONS SHARIPAH SOAAD SYED YAHAYA UNIVERSITI SAINS MALAYSIA 2005 ii ROBUST STATISTICAL PROCEDURES FOR TESTING THE EQUALITY OF CENTRAL TENDENCY PARAMETERS UNDER SKEWED DISTRIBUTIONS by SHARIPAH SOAAD SYED YAHAYA Thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy May 2005 ACKNOWLEDGEMENTS Firstly, my sincere appreciations to my supervisor Associate Professor Dr. Abdul Rahman Othman without whose guidance, support, patience, and encouragement, this study could not have materialized. I am indeed deeply indebted to him. My sincere thanks also to my co-supervisor, Associate Professor Dr. Sulaiman for his encouragement and support throughout this study. I would also like to thank Universiti Utara Malaysia (UUM) for sponsoring my study at Universiti Sains Malaysia. Thanks are due to Professor H.J. Keselman for according me access to his UNIX server to run the relevant programs; Professor R.R. Wilcox and Professor R.G. Staudte for promptly responding to my queries via emails; Pn. Azizah Ahmad and Pn. Ramlah Din for patiently helping me with some of the computer programs and En. Sofwan for proof reading the chapters of this thesis. I am deeply grateful to my parents and my wonderful daughter, Nur Azzalia Kamaruzaman for their inspiration, patience, enthusiasm and effort. I would also like to thank my brothers for their constant support. Finally, my grateful recognition are due to (in alphabetical order) Azilah and Nung, Bidin and Kak Syera, Izan, Linda, Min, Shikin, Yen, Zurni and to those who had directly or indirectly lend me their friendship, moral support and endless encouragement during my study. -
To Get SPSS to Conduct a One-Way Chi-Square Test on Your Data
Biomeasurement 4e Dawn Hawkins SPSS24 HELP SHEET: Mann-Whitney U test (using legacy dialogs) CONTENTS 1. How to enter data to do a Mann-Whitney U test test. 2. How to do a Mann-Whitney U test test. 1. How to enter data to do a Mann-Whitney U test test. For general advice on data entry see the “How to enter data into SPSS” help sheet. Mann-Whitney U test tests are used on unrelated data: Data for the dependent variable go in one column and data for the independent variable goes in another. In this example, the dependent variable is BMD and the independent variable is SEX. BMD is bone-density measurement measured in grams per square centimetre of the neck of the femur which is a scale level of measurement). SEX is measured at the nominal level: either 1 (value label = female) or 2 (value label = male). Variable View Data View Data View (View – Value Labels off) (View – Value Labels on) Page 1 of 2 Dawn Hawkins: Anglia Ruskin University, January 2019 Biomeasurement 4e Dawn Hawkins 2. How to do a Mann-Whitney U test test… To get SPSS to conduct a Mann-Whitney U test test : Open your data file. Select: Analyze – Nonparametric Tests – Legacy Dialogs - 2 Independent Samples... This will bring up the Two-Independent-Samples Tests window. Select the variable that you want to analyse, and send it to the Test Variable List box (in the example above this is Bone Density Measurement). Select the independent variable, and send it to the Grouping Variable box (in the example above this is Sex). -
UNIT 1 INTRODUCTION to STATISTICS Introduction to Statistics
UNIT 1 INTRODUCTION TO STATISTICS Introduction to Statistics Structure 1.0 Introduction 1.1 Objectives 1.2 Meaning of Statistics 1.2.1 Statistics in Singular Sense 1.2.2 Statistics in Plural Sense 1.2.3 Definition of Statistics 1.3 Types of Statistics 1.3.1 On the Basis of Function 1.3.2 On the Basis of Distribution of Data 1.4 Scope and Use of Statistics 1.5 Limitations of Statistics 1.6 Distrust and Misuse of Statistics 1.7 Let Us Sum Up 1.8 Unit End Questions 1.9 Glossary 1.10 Suggested Readings 1.0 INTRODUCTION The word statistics has different meaning to different persons. Knowledge of statistics is applicable in day to day life in different ways. In daily life it means general calculation of items, in railway statistics means the number of trains operating, number of passenger’s freight etc. and so on. Thus statistics is used by people to take decision about the problems on the basis of different type of quantitative and qualitative information available to them. However, in behavioural sciences, the word ‘statistics’ means something different from the common concern of it. Prime function of statistic is to draw statistical inference about population on the basis of available quantitative information. Overall, statistical methods deal with reduction of data to convenient descriptive terms and drawing some inferences from them. This unit focuses on the above aspects of statistics. 1.1 OBJECTIVES After going through this unit, you will be able to: Define the term statistics; Explain the status of statistics; Describe the nature of statistics; State basic concepts used in statistics; and Analyse the uses and misuses of statistics. -
Fitting Models (Central Tendency)
FITTING MODELS (CENTRAL TENDENCY) This handout is one of a series that accompanies An Adventure in Statistics: The Reality Enigma by me, Andy Field. These handouts are offered for free (although I hope you will buy the book).1 Overview In this handout we will look at how to do the procedures explained in Chapter 4 using R an open-source free statistics software. If you are not familiar with R there are many good websites and books that will get you started; for example, if you like An Adventure In Statistics you might consider looking at my book Discovering Statistics Using R. Some basic things to remember • RStudio: I assume that you're working with RStudio because most sane people use this software instead of the native R interface. You should download and install both R and RStudio. A few minutes on google will find you introductions to RStudio in the event that I don't write one, but these handouts don't particularly rely on RStudio except in settingthe working directory (see below). • Dataframe: A dataframe is a collection of columns and rows of data, a bit like a spreadsheet (but less pretty) • Variables: variables in dataframes are referenced using the $ symbol, so catData$fishesEaten would refer to the variable called fishesEaten in the dataframe called catData • Case sensitivity: R is case sensitive so it will think that the variable fishesEaten is completely different to the variable fisheseaten. If you get errors make sure you check for capitals or lower case letters where they shouldn't be. • Working directory: you should place the data files that you need to use for this handout in a folder, then set it as the working directory by navigating to that folder when you execute the command accessed through the Session>Set Working Directory>Choose Directory ..