Free Essay

In: Other Topics

Submitted By annengg

Words 763

Pages 4

Words 763

Pages 4

The word parametric comes from “metric” meaning to measure, and “para” meaning beside or closely related. The combined term refers to the assumptions about the population from which the measurements were obtained.

The two classes of statistical tests are:

Parametric Statistics

Nonparametric Statistics

i. Parametric Statistics:

Parametric statistics are statistical tests for population parameters such as means, variances and proportions that involve assumptions about the populations from which the samples were selected. These assumptions include:

Observations must be independent i.e. when values in one set are different and unrelated from another set

Observations must be drawn from normally distributed populations

The populations must have the same variances

The sample must be random

Use of Parametric Statistics in Data Analysis:

Parametric tests are used when the above parametric assumptions are met.

Parametric tests are also used to analyze interval and ratio data. Interval data are numerical data in which we not only know the order but also the exact differences between the values e.g. the time interval between the starts of years 1981 and 1982 is the same as that between 1983 and 1984 which is 365 days. Ratio data on the other hand describe measurements with attributes that have the qualities of nominal, ordinal and interval data and a true zero point can be defined e.g. height and weight.

Examples of parametric tests include t-test, f test and z test. ii. Nonparametric Statistics:

Nonparametric statistics are used when the population from which the samples are selected is not normally distributed. These statistics are also known as distribution free statistics. Nonparametric statistics can also be used to test hypotheses that do not involve specific population parameters.

Use of Nonparametric Statistics in Data Analysis:

Nonparametric tests are used when assumptions of nonparametric tests cannot be met, when very small numbers of data are used and when no basis exists for assuming certain types or shapes of distribution.

They can also be used for nominal and ordinal levels of measurement. Nominal data is a set of data in which values or observations belonging to it can be assigned a code or a label, e.g. In a data set, males could be coded as 0, females as1; marital status of an individual could be coded as ‘Y’ if married and ‘N’ if single. Ordinal data on the other hand is a set of data in which the values or observations belonging to it can be ranked or have a rating scale attached e.g. a set of survey answers can be listed as very satisfactory, satisfactory, neutral, unsatisfactory, very unsatisfactory. As a result, nonparametric tests can be used if data can only be classified, counted or ordered.

Examples of nonparametric tests include Wilcoxon Mann-Whitney Test, Sign Test and Ruskal-Wallis Test.

Advantages of nonparametric statistics:

Nonparametric tests are simple and easy to understand

They are designed for small numbers of data

Nonparametric statistics do not involve complicated sampling theories

No assumption is made regarding the parent population

Nonparametric statistics can be used when data is nominal or ordinal

They can be used to test population parameters when the variable is not normally distributed

They can be used effectively for determining relationships and significance of differences using behavioral research methods

Disadvantages of nonparametric statistics:

They are less efficient than parametric tests when the assumptions of the parametric methods are met.

They tend to use less information than parametric tests

They are less sensitive that parametric tests when the assumptions of the parametric methods are met.

iii. Differences between Parametric Tests and Nonparametric Tests:

Parametric Tests Nonparametric Tests

Information about the population is completely known Information about the population is not completely known

Specific assumptions are made regarding the population No assumptions are made regarding the population

Null hypothesis is made on parameters of the population distribution The null hypothesis is free from parameters

Test statistics is based on the distribution Test statistics is arbitrary

No parametric tests exist for nominal data Nonparametric tests exist for nominal and ordinal data

References:

Allan G. Bluman. (2004) Elementary Statistics, A Step by Step Approach, 5th Edition

Angela Hebel. (2002) Parametric versus Nonparametric statistics- when to use them and which is more powerful. [Presentation] University of Maryland Eastern Shore, 5th April.

Sai Prakesh (n.d) Parametric and Nonparametric Test. [Presentation] MBA Insurance Management, Pondicherry University.

L. Don Lehmukhul. (1996) Nonparametric Statistics: Methods for Analyzing Data Not Meeting Assumptions Required for the Application of Parametric Test. [Online] 8 (3).…...

Premium Essay

...empec, Vol. 13, 1988, page 223-249 Nonparametric Estimation and Hypothesis Testing in Econometric Models By A. Ullah ~ Abstract: In this paper we systematically review and develop nonparametric estimation and testing techniques in the context of econometric models. The results are discussed under the settings of regression model and kernel estimation, although as indicated in the paper these results can go through for other econometric models and for the nearest neighbor estimation. A nontechnical survey of the asymptotic properties of kernel regression estimation is also presented. The technique described in the paper are useful for the empirical analysis of the economic relations whose true functional forms are usually unknown. 1 Introduction Consider an economic model y =R(x)+u where y is a dependent variable, x is a vector o f regressors, u is the disturbance and R(x) = E ( y l x ) . Often, in practice, the estimation o f the derivatives o f R(x)are o f interest. For example, the first derivative indicates the response coefficient (regression coefficient) o f y with respect to x, and the second derivauve indicates the curvature o f R(x). In the parametric econometrics the estimation o f these derivatives and testing 1 Aman Ullah, Department of Economics, University of Western Ontario, London, Ontario, N6A 5C2, Canada. I thank L Ahmad, A. Bera, A. Pagan, C. Robinson, A. Zellner, and the participants of the workshops at the Universities of......

Words: 5119 - Pages: 21

Premium Essay

...Application of Bootstrap method in spectrometric data analysis By XIAO Jiali, Jenny ( 0830300038) A Final Year Project thesis (STAT 4121; 3 Credits) submitted in partial fulﬁllment of the requirements for the degree of Bachelor of Science in Statistics at BNU-HKBU UNITED INTERNATIONAL COLLEGE December, 2011 DECLARATION I hereby declare that all the work done in this Project is of my independent eﬀort. I also certify that I have never submitted the idea and product of this Project for academic or employment credits. XIAO Jiali, Jenny (0830300038) Date: ii Application of Bootstrap method in spectrometric data analysis XIAO Jiali, Jenny Science and Technology Division Abstract In this project the bootstrap methodology for spectrometric data is considered. The bootstrap can also compare two populations, without the normality condition and without the restriction to comparison of means. The most important new idea is that bootstrap resampling must mimic the separate samples design that produced the original data. Bootstrap in mean, bootstrap in median, and bootstrap in conﬁdence interval are three kinds of eﬀective way to handle mass spectrometric data. Then,we need to reduce dimension based on bootstrap method. It may allow the data to be more easily visualized. Afterwards, using results obtained by bootstrap, we use data mining method to predict a patient has ovarian cancer or not. Decision tree induction and neural network are usual way to...

Words: 7049 - Pages: 29

Premium Essay

...A Stochastic Approach to Indian Banking Sector : Technical Analysis of Private Sector Banks Dr. Rahul Rajan Abhilasha Srivastava Abstract The objective of this paper is to present a method for estimating the cost efficiency of Indian banks in order to study the degree of technical and cost performance of the Indian banking sector and to analyze how the banking sector has been affected by technical efficiency and cost efficiency. Initially, the evolution in the technical front in the banks between 2005 to 2012 is measured. For this analysis purpose a sample of 101 Indian banks including 28 public ,29 private and 44 foreign banks operating in India is taken for the period 2005-2012. For analysis purpose both the parametric method of productive efficiency frontier (Stochastic Frontier Analysis ) and nonparametric method (Data Envelopment Analysis) are taken. Introduction The financial system is the lifeline of the economy. The changes in the economy get mirrored in the performance of the financial system, more so of the banking industry. The banking system in India is significantly different from that of other Asian nations because of the country’s unique geographic, social, and economic characteristics. India has a large population and land size, a diverse culture, and extreme disparities in income, which are marked among its regions. There are high levels of illiteracy among a large percentage of its population but, at the same time, the country has a large......

Words: 5433 - Pages: 22

Premium Essay

...Systems 30 (2012) 67–77 Contents lists available at SciVerse ScienceDirect Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys Bankruptcy prediction models based on multinorm analysis: An alternative to accounting ratios Javier de Andrés ⇑, Manuel Landajo, Pedro Lorca University of Oviedo, Spain a r t i c l e i n f o a b s t r a c t In this paper we address the bankruptcy prediction problem and outline a procedure to improve the performance of standard classiﬁers. Our proposal replaces traditional indicators (accounting ratios) with the output of a so-called multinorm analysis. The deviations of each ﬁrm from a battery of industry norms (computed by nonparametric quantile regression) are used as input variables for the classiﬁers. The approach is applied to predict bankruptcy of ﬁrms, and tested on a representative data set of Spanish ﬁrms. Results indicate that the approach may provide signiﬁcant improvements in predictive accuracy, both in linear and nonlinear classiﬁers. Ó 2011 Elsevier B.V. All rights reserved. Article history: Received 9 February 2011 Received in revised form 2 October 2011 Accepted 3 November 2011 Available online 30 December 2011 Keywords: Bankruptcy prediction Classiﬁcation techniques Nonparametric methods Quantile regression Accounting ratios 1. Introduction Under the current economic conditions, bankruptcy early warning systems have become tools of key importance in order to guarantee the stability of......

Words: 10207 - Pages: 41

Premium Essay

...PLANNING AND MANAGEMENT COURSE: LDP 603: RESEARCH METHODS ASSIGNMENT STUDENT; GITHUNDI BEDAN. ADMISSION REF-27086/2013 LECTURER; Dr. Lilian Otieno, Resident Lecturer I am tasked to distinguish between parametric and non-parametric statistics and explain when to use each method in analysis of data. I shall first seek to define what parametric and non-parametric statistics mean and then compare and contrast them in the analysis of data. Parametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric. (According to Wikipedia, the online dictionary). In statistical analysis, parametric significance tests are only valid if certain assumptions are met. If they are not, nonparametric tests can be used. A parameter is a measure of an entire population, such as the mean height of every man in London. In statistical analysis, one practically never has measurements from a whole population and has to infer the characteristics of the population from a sample. Generally speaking parametric methods make more assumptions than non-parametric methods. If those extra assumptions are correct, parametric methods can produce more accurate and precise estimates. They are said to have more statistical power. However, if assumptions are incorrect, parametric methods can be very misleading. For that reason they......

Words: 3625 - Pages: 15

Premium Essay

...Statistics Practical 2a Comments on Z-tests and t-tests 1. You should have realized from the lectures that in practice, a z-test is seldom used, while the ‘default’ test for single sample or two-samples mean(s) is the ttest. This is because in most practical situations, the population variance is seldom known and therefore we need to estimate that by the sample variance, thus justifying a t-test rather than a z-test. It is always good to perform the standard exploratory data analysis before commencing any hypothesis testing involving t-tests. It is often useful to check through summary statistics (like the minimum and maximum of the data), as well as a quick plot of the data (box-plots), to check for any problematic data or outliers. The use of a t-test requires the assumption that the data is distributed like a normal distribution – essentially a bell-shaped curve for the histogram. Therefore it is extremely informative to look at the histogram of the data before commencing on testing, as this will indicate whether the use of the t-test is justified. Before commencing any testing, evaluate what are your hypotheses that you are interested in. If you are testing the mean for a single sample, are you testing the mean to be 0, or are you testing the mean against some non-zero value. If so, do remember to change the input in SPSS correspondingly. Similarly if you are testing the means for two samples, are you testing for the difference to be zero, or against a non-zero......

Words: 755 - Pages: 4

Free Essay

...Methods of Collecting Job Analysis Data A variety of methods are used to collect information about jobs. None of them, however, is perfect. In actual practice, therefore, a combination of several methods is used for obtaining job analysis data. These are discussed below. Job performance In this method the job analyst actually performs the job in question. The analyst, thus, receives first hand experience of contextual factors on the job including physical hazards, social demands, emotional pressures and mental requirements. This method is useful for jobs that can be easily learned. It is not suitable for jobs that are hazardous (e.g., fire fighters) or for jobs that require extensive training (e.g., doctors, pharmacists). Personal observation The analyst observes the worker(s) doing the job. The tasks performed, the pace at which activities are done, the working conditions, etc., are observed during a complete work cycle. During observation, certain precautions should be taken The analyst must observe average workers during average conditions. The analyst should observe without getting directly involved in the job. The analyst must make note of the specific job needs and not the behaviors specific to particular workers. The analyst must make sure that he obtains a proper sample for generalization. This method allows for a deep understanding of job duties. It is appropriate for manual, short period job activities. On the negative side, the methods fail to take note of the......

Words: 852 - Pages: 4

Premium Essay

...STATISTICAL METHODS STATISTICAL METHODS Arnaud Delorme, Swartz Center for Computational Neuroscience, INC, University of San Diego California, CA92093-0961, La Jolla, USA. Email: arno@salk.edu. Keywords: statistical methods, inference, models, clinical, software, bootstrap, resampling, PCA, ICA Abstract: Statistics represents that body of methods by which characteristics of a population are inferred through observations made in a representative sample from that population. Since scientists rarely observe entire populations, sampling and statistical inference are essential. This article first discusses some general principles for the planning of experiments and data visualization. Then, a strong emphasis is put on the choice of appropriate standard statistical models and methods of statistical inference. (1) Standard models (binomial, Poisson, normal) are described. Application of these models to confidence interval estimation and parametric hypothesis testing are also described, including two-sample situations when the purpose is to compare two (or more) populations with respect to their means or variances. (2) Non-parametric inference tests are also described in cases where the data sample distribution is not compatible with standard parametric distributions. (3) Resampling methods using many randomly computer-generated samples are finally introduced for estimating characteristics of a distribution and for statistical inference. The following section deals with methods......

Words: 4718 - Pages: 19

Premium Essay

...“Virtue ethics is of little use when dealing with practical ethics.” Discuss. It is often argued that virtue ethics is of little use when dealing with practical ethics. Virtue ethics does not focus on actions being right or wrong, but on how to be a good person. Virtue ethics raises three questions “who am I?”, “Who I ought to become?” and “How do I get there?”. On the other hand Practical ethics describes situations where an action is needed. Firstly virtue ethics goes back to Plato and Aristotle. Plato’s moral theory centres on the achievement of man’s highest good, which involves the right cultivation of his soul and the harmonious wellbeing of his life (Eudaimonia). Plato seemed to consider that certain virtues such as temperance, courage, prudence and justice (cardinal Virtues) are in balance a person’s actions will be good. It motivates people to want to be good. It shows the importance of education in showing that good actions are their own rewards. When these virtues are in balance a person’s actions will be good and therefore would disagree that virtue ethics is of little use. Aristotle’s ethical theory is known as virtue ethics because at the centre of his description of the good, which are the virtues which shape human character and ultimately human behaviour. However this good human life is one lived in harmony and co-operation with other people, since Aristotle saw people as not only rational beings but also as social beings. Aristotle saw two types of......

Words: 1557 - Pages: 7

Premium Essay

...Introductory STATISTICS 9TH EDITION This page intentionally left blank Introductory STATISTICS 9TH EDITION Neil A. Weiss, Ph.D. School of Mathematical and Statistical Sciences Arizona State University Biographies by Carol A. Weiss Addison-Wesley Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo On the cover: Hummingbirds are known for their speed, agility, and beauty. They range in size from the smallest birds on earth to several quite large species—in length from 2 to 8.5 inches and in weight from 0.06 to 0.7 ounce. Hummingbirds ﬂap their wings from 12 to 90 times per second (depending on the species) and are the only birds able to ﬂy backwards. Normal ﬂight speed for hummingbirds is 25 to 30 mph, but they can dive at speeds of around 60 mph. Cover photograph: Hummingbird, Editor in Chief: Deirdre Lynch Acquisitions Editor: Marianne Stepanian Senior Content Editor: Joanne Dill Associate Content Editors: Leah Goldberg, Dana Jones Bettez Senior Managing Editor: Karen Wernholm Associate Managing Editor: Tamela Ambush Senior Production Project Manager: Sheila Spinney Senior Designer: Barbara T. Atkinson Digital Assets Manager: Marianne Groth Senior Media Producer: Christine Stavrou Software Development: Edward Chappell, Marty Wright C iDesign/Shutterstock Marketing Manager: Alex Gay Marketing......

Words: 377092 - Pages: 1509

Premium Essay

... The terms "statistical analysis" and "data analysis" can be said to mean the same thing -- the study of how we describe, combine, and make inferences based on numbers. A lot of people are scared of numbers (quantiphobia), but data analysis with statistics has got less to do with numbers, and more to do with rules for arranging them. It even lets you create some of those rules yourself, so instead of looking at it like a lot of memorization, it's best to see it as an extension of the research mentality, something researchers do anyway (i.e., play with or crunch numbers). Once you realize that YOU have complete and total power over how you want to arrange numbers, your fear of them will disappear. It helps, of course, if you know some basic algebra and arithmetic, at a level where you might be comfortable solving the following equation There are three (3) general areas that make up the field of statistics: descriptive statistics, relational statistics, and inferential statistics. 1. Descriptive statistics fall into one of two categories: measures of central tendency (mean, median, and mode) or measures of dispersion (standard deviation and variance). Their purpose is to explore hunches that may have come up during the course of the research process, but most people compute them to look at the normality of their numbers. Examples include descriptive analysis of sex, age, race, social class, and so forth. 2. Relationalstatistics fall into one of three categories: univariate...

Words: 4590 - Pages: 19

Premium Essay

...areas of basic statistics including: descriptive statistics, correlations, t-tests for independent samples, t-test of dependent samples and data mining used during the research process. In this 2 pages summary of those listed methods, I will identify the keys aspects of its usage, importance in the research process, provide examples of its usage and value and how it will be used my future research projects throughout this coursework. Meaning Use of Statistics Understanding the use of statistics requires one to understand the experimental design or how the research is conducted. Knowledge about the methodology allows use to input and interpret the results of the values. Statistics values are not just random numbers but values that have been generated out of research. Basic statistic values are tools utilized to assist with answering the questions of what, why, and how. Understanding the reasoning for using statistics will better help one’s understanding of basic statistics. Descriptive statistics is a quantitative description of data collection sometimes referred to as inferential statistics. Descriptive statistics are used to summarize the sample and measures of values as they form the basis of quantitative analysis of data (Criswell, 2009). Utilizing descriptive statistics draws conclusions by extending beyond the data known. It utilizes judgments of the probability that are observed between groups and reduces that data into a......

Words: 879 - Pages: 4

Premium Essay

...Nonparametric Hypothesis Testing RES/342 Nonparametric Hypothesis Testing During the course of the last three weeks, the team explored the hypothesis testing segment of statistics research. The first part of this assignment was the one sample hypothesis testing. The second was the two or more sample hypothesis testing, and finally in this third week, we will look at nonparametric hypothesis testing. This week’s project is a continuation of the previous projects and entails to build on the identical research question that we will frame a research hypothesis from the same provided data sets (Wage and Wage Earners) using ratio or interval numerical data; however, this week we will use a nonparametric hypothesis test to find our answer. In the next following paragraphs, the team will clearly affirm a hypothesis statement that will provide the base for our survey, perform a five-step hypothesis test on information concerning our choice and apply the concepts of nonparametric testing learned in this course, and describe how the results of our findings answer our research question. Finally, we will conclude this study with a brief summary that will examine the main points, the purpose, and conclusions of this final third week’s study on nonparametric testing. Perform the five-step hypothesis test on the data Nonparametric tests are statistical tests that analyze data that does not require assumptions about the distribution of shape of the population from......

Words: 1530 - Pages: 7

Premium Essay

...Data Gathering Method Evidence-based Practices in Corrections Clarence S. Lasana MGMT 568: Organizational Development & Change Tarleton State University Summer 2012 Cover letter July 22, 2012 Dear Participants: Mr. Robert, Sala, Area Manager: The Hertz Corporation Austin Bergstrom International AP, Austin, Texas Respected Mr. Robert Sala, I am a student from Texas A&M University, Central Texas doing my MS in Management & Leadership, as per the Data Gathering project requirement I am conducting an Employee Satisfaction Survey on The Hertz Corporation at Austin, Texas. The purpose of the Employee Satisfaction Survey is to gather data on the Hertz Corporation at Austin Bergstrom International Airport with the intention of solving employee relation problems. This is a “Skip level” survey. This survey includes all employees and excludes all internal managers. The survey will consist of open ended and close ended questions. The answers are expected to be answered with integrity as I use these answers to analyze the overall data. Once the analysis has been completed, the data will be kept confidential. Sincerely, Mr. Lasana ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- Survey Introduction During the spring of 2012, I Clarence Lasana noticed a lack of......

Words: 1253 - Pages: 6

Premium Essay

...Applying Analysis of Variance (ANOVA) and Nonparametric Tests Simulation RES 342 William Modey Applying Analysis of Variance (ANOVA) and Nonparametric Tests Simulation ANOVA and Non Parametric tests can help in business endeavors wherever there is two or more variables or hypothesis. The ANOVA and Non Parametric Tests Simulation showed the various ways to do hypothesis testing with two or more hypothesis. Being able to do the various types of testing that come along with ANOVA and Non Parametric data sets is key to making the right decision when having two or more choices. The three lessons that I have learned after doing the ANOVA and Non Parametric Tests Simulation were to thoroughly analyze the presented problem before attempting to make a decision, enlist the help of others when making a decision or choosing a course of action, and to continually improve on decision making skills based on learning from past mistakes made. As a result of using this simulation the concepts and analytic tools that I would be able to use in my workplace are that I am now able to approach a decision making scenario with appropriate knowledge and testing procedures to help make the best decision. The skills that I learned in the simulation, such as the different hypothesis testing procedures, could be key to helping me improve my managerial skills. Based on my passed experiences and current knowledge, I would recommend that the key decision maker take his or her time when......

Words: 396 - Pages: 2