Descriptive Statistics Tutorial
|
|
- Paulina Porter
- 6 years ago
- Views:
Transcription
1 Descriptive Statistics Tutorial Measures of central tendency Mean, Median, and Mode Statistics is an important aspect of most fields of science and toxicology is certainly no exception. The rationale behind the importance of statistics in a field such as this is that no two individuals are the same. There is a lot of variation in the population. In trying to make sense of this variation in a population, it is sometimes important to generalize. This is often done by providing an average. Given the range of salaries for the safety and health profession, for instance, one might argue that the average salary in the US is around $70,000 per year. There are some questions that might be asked about this figure, however. For instance, how was this average determined? There are actually a number of ways to determine an average and each is used for a different reason. Usually when somebody discusses salaries, they use an average known as the median. The median is determined by lining up all the salaries in numerical order and picking the middle number. If there are an even number of values in the sample, the median will equal the sum of the middle two values divided by two. The reason one would use the median for salaries is because there are often extreme outliers in salary data. There may be safety professionals, for instance, who have made millions of dollars as a result of owning a very successful consulting firm. If a person is looking for a measure of central tendency here, the median allows folks to not have to account for these extreme values because one is simply lining up the numbers and picking the one in the middle. Here is an example: Calculate the median for the following data that represents the number of hours rodents in a sample went before positively responding to a specific experimental treatment: 2, 11, 14, 15, 15, 17, 17, 17, 17, 19, 19, 20, 20, 21, 22, 378 There are 16 numbers here. The two middle numbers (8 th and 9 th number) are 17 and X 2 = /2 = 17 Notice that if we were to calculate an average known as the Mean, which would essentially be calculated by adding all the numbers together and dividing by the total number in the sample, we would get an average of 624/16 = 39 Notice how that large number (378) moved the average from the middle value of 17 to something much larger. This is why, when we know there might be unusual outliers, we often consider using the median as the reported value of central tendency. Sometimes, outliers are also removed in order to conduct standard statistical analysis. Perhaps something unusual was going on with our rodent that failed to respond for 378 hours that did not really reflect the response of the general population. One other measure of central tendency that is sometimes used is the mode. This is used when a person wants to know what value is repeated the most in a sample. Looking at our example above, for instance, we can see that the number 17 is repeated 4 times. No other number is repeated that many times, so the mode would be 17. With this said, it should be obvious that a given sample can have more than one mode. Measures of Dispersion
2 The Range When we talk about measures of dispersion, we are typically referring to how wide the data is spread. There are a number of ways to do this. One way to do this is to report the range. The range is basically the difference between the highest value and the lowest value. Let s look at our sample above again with the outlier removed. 2, 11, 14, 15, 15, 17, 17, 17, 17, 19, 19, 20, 20, 21, 22 In this situation, the highest number is 22 and the lowest number is 2, so the range would be 20. Note, if we kept the outlier in the sample, the range would be much larger. The range is the most basic measure of dispersion and does not really convey a lot of information. It is like asking someone to describe his or her daily driving habits and getting a response like Sometimes I do not drive at all and the most I drive is 20 miles on a given day. This does not convey much information about driving habits, does it? However, if the person indicated he or she drove an average of 10 miles a day and also reported the range, we would have a much better idea as to driving habits. Two more commonly used measures of dispersion are the variance and the standard deviation. They are related because the latter is the square root of the former. That is, take the square root of the variance and you get the standard deviation. In order to discuss these concepts further, it is important to first consider the concept of the normal distribution or what is commonly known as the Bell Curve. Chances are you have seen something like this or at least heard of the bell curve somewhere along the way: Often when we take a measurement of different subjects in a sample, we see the distribution best represented as a bell curve as depicted above. Let s consider a variable like weight, for example, and its relationship with blood alcohol dosages. If we take the weight measurement of 3000 randomly selected adult males, we will likely note that there are a few individuals who are much lighter than average and a few people who are much heavier, but most people will be somewhere in the middle, much closer to the average. This is why the bell curve is shaped the way it is. The left tail would represent the few very light individuals in the population and the right tail would represent the few very heavy individuals, but most males would fall somewhere in the middle, around the mean average which is represented by the middle, and the highest point on the curve.
3 Variance and Standard Deviation: A more commonly used measure of dispersion used in most sciences is the standard deviation. This value basically represents the average distance most of the data falls from the mean. Let s take a look at the normal distribution diagram below where we set our mean average to zero. Please note that the Greek letter σ, or sigma is used here to represent the population standard deviation. Standard Deviation. (n.d.) In a normally distributed sample, one standard deviation on either side of the mean typically accounts for 68.2% of the variation around the mean. Considering our adult male sample above, that would mean that 68.2 % of all males, or 1860 individuals, weighed in within one standard deviation. It is also important to note that the standard deviation is a calculation that depends on the data in the sample and so this value can fluctuate depending on the variation within the sample. Let s say we have two samples of 3,000 individuals from different countries we will weigh for a study. We calculate a standard deviation of 35 pounds for group A and 10 pounds for group B. What these two standard deviations tell us is that there is a lot more variation in Group A than there is in group B. In group B, most people (68.2% in fact) are within 10 pounds of the average. In group A, however, most people are within 35 pounds of the average. We can say, therefore, that there is a lot more variation in group A as compared to group B. This is why the standard deviation is frequently reported along with the mean. It gives the reader an idea as to how much variation exists in the population or sample being considered. If one hears, for instance, that the average weight of a group is 170 pounds with a standard deviation of 10.7 pounds, it gives the person a much better picture than reporting the mean average alone. Calculating Standard Deviation We pretty much know how to calculate the mean average but as indicated above, but it is also good to be able to determine the standard deviation of a sample. It is quite a bit of work to calculate the standard deviation of a sample, but it is doable if it is undertaken step by step. The first step in calculating the standard deviation is to calculate the variance. The variance is essentially the square of the standard deviation. Once the variance is calculated, one only needs to click the square root button on the calculator to get to the standard deviation. Also, above we pointed out that the standard deviation of a population is typically depicted with the Greek letter σ. When dealing with samples (as opposed to an entire population), the value is reported as an italicized letter s. Since the sample variance is simply the square of the sample standard deviation, it is commonly depicted as follows s 2. For the purposes of this tutorial, we will not get into too much
4 discussion regarding the usefulness of the variance value except to indicate that it needs to be calculated first in order to determine the standard deviation. Here is how we calculate the variance of a sample. And here is the formula for calculating the standard deviation of a sample: (Formula images from Standard Deviation (n.d.)) Again, both of these look like fairly scary formulas, but it is nothing to be overly concerned about. For our purposes, we will calculate the variance using a step-by-step process and we will save deciphering these seemingly complex mathematical equations for another time. Here are the steps for calculating a sample standard deviation (the formulas above actually instruct us to perform these steps): 1. Calculate the mean average. 2. List all of the values of the sample in a column. 3. Subtract the mean average from each row. 4. Square the result in each row. 5. Add all of these squared values together. 6. Divide the squared values by the number of values in the sample minus 1 to get the variance. 7. Take the square root of the variance to get the standard deviation. OK, now that you know the steps, let s give this a whirl. Say we are going to do a preliminary study on the diameter of a skin rash exhibited on rodents after being treated with a very small quantity of chemical A. Since we are just trying to get a general idea as to the response, we only treat eight individuals. We get the following values in millimeters: 10, 8, 10, 8, 6, 4, 12, 6 The first step is to find the mean average. So we add them all together and divide the total by the number in the sample (8). We end up with an average of 8 mm (64/8=8). The next step is to list each value in the sample and subtract the mean
5 10-8 = = = = = = = = -2 The next step is to square each result we just obtained: 2 2 = = = = = = = = 4 The next step is to add these results: = 48 Finally, to get our variance, we divide this total by N-1 (the sample size minus 1). 48/7 = 6.86 So 6.86 is our variance. Now do you remember how to determine the sample standard deviation from the sample variance? Correct! You just hit the square root button on your calculator. SqRt of 6.86 = 2.62 Based on this information, we would report our sample mean as 8.0 and our standard deviation as This is, of course, a very small sample and clearly does not reflect a perfect normally distributed sample. A larger sample needs to be obtained. It is possible, and likely that a much larger sample will be much more normally distributed. But regardless, you now know the steps to calculating the mean, variance, and standard deviation. References: Standard Deviation. (n.d.). Wikipedia. Retrieved from: Note: Although using Wikipedia sources is typically discouraged as they have the potential to be unreliable, this tutorial utilized such sources primarily to obtain images. However, the writer of this tutorial is well versed in the use of statistics and therefore able to evaluate the reliability of the images used.
Chapter 8 Script. Welcome to Chapter 8, Are Your Curves Normal? Probability and Why It Counts.
Chapter 8 Script Slide 1 Are Your Curves Normal? Probability and Why It Counts Hi Jed Utsinger again. Welcome to Chapter 8, Are Your Curves Normal? Probability and Why It Counts. Now, I don t want any
More informationIntroduction to Control Charts
Introduction to Control Charts Highlights Control charts can help you prevent defects before they happen. The control chart tells you how the process is behaving over time. It's the process talking to
More informationChapter 1 Data and Descriptive Statistics
1.1 Introduction Chapter 1 Data and Descriptive Statistics Statistics is the art and science of collecting, summarizing, analyzing and interpreting data. The field of statistics can be broadly divided
More informationGETTING READY FOR DATA COLLECTION
3 Chapter 7 Data Collection and Descriptive Statistics CHAPTER OBJECTIVES - STUDENTS SHOULD BE ABLE TO: Explain the steps in the data collection process. Construct a data collection form and code data
More informationChapter 12 Module 3. AMIS 310 Foundations of Accounting
Chapter 12, Module 3 AMIS 310: Foundations of Accounting Slide 1 CHAPTER 1 MODULE 1 AMIS 310 Foundations of Accounting Professor Marc Smith Hi everyone, welcome back. Let s continue our discussion on cost
More informationDDBA8437: Central Tendency and Variability Video Podcast Transcript
DDBA8437: Central Tendency and Variability Video Podcast Transcript JENNIFER ANN MORROW: Today's demonstration will review measures of central tendency and variability. My name is Dr. Jennifer Ann Morrow.
More informationIntroduction to Statistics. Measures of Central Tendency
Introduction to Statistics Measures of Central Tendency Two Types of Statistics Descriptive statistics of a POPULATION Relevant notation (Greek): µ mean N population size sum Inferential statistics of
More informationIntroduction to Statistics. Measures of Central Tendency and Dispersion
Introduction to Statistics Measures of Central Tendency and Dispersion The phrase descriptive statistics is used generically in place of measures of central tendency and dispersion for inferential statistics.
More informationThe Dummy s Guide to Data Analysis Using SPSS
The Dummy s Guide to Data Analysis Using SPSS Univariate Statistics Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved Table of Contents PAGE Creating a Data File...3 1. Creating
More informationDay 1: Confidence Intervals, Center and Spread (CLT, Variability of Sample Mean) Day 2: Regression, Regression Inference, Classification
Data 8, Final Review Review schedule: - Day 1: Confidence Intervals, Center and Spread (CLT, Variability of Sample Mean) Day 2: Regression, Regression Inference, Classification Your friendly reviewers
More informationSTAT/MATH Chapter3. Statistical Methods in Practice. Averages and Variation 1/27/2017. Measures of Central Tendency: Mode, Median, and Mean
STAT/MATH 3379 Statistical Methods in Practice Dr. Ananda Manage Associate Professor of Statistics Department of Mathematics & Statistics SHSU 1 Chapter3 Averages and Variation Copyright Cengage Learning.
More informationLECTURE 17: MULTIVARIABLE REGRESSIONS I
David Youngberg BSAD 210 Montgomery College LECTURE 17: MULTIVARIABLE REGRESSIONS I I. What Determines a House s Price? a. Open Data Set 6 to help us answer this question. You ll see pricing data for homes
More informationHow to do Statistics in Excel
How to do Statistics in Excel Introduction The best answer is Don t. Get someone else to do it. But since there is no American who has a life and also likes statistics, this may not be easy. And it likely
More information1. Contingency Table (Cross Tabulation Table)
II. Descriptive Statistics C. Bivariate Data In this section Contingency Table (Cross Tabulation Table) Box and Whisker Plot Line Graph Scatter Plot 1. Contingency Table (Cross Tabulation Table) Bivariate
More informationMathematics in Contemporary Society - Chapter 5 (Spring 2018)
City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College Spring 218 Mathematics in Contemporary Society - Chapter (Spring 218) Patrick J. Wallach
More informationChapter 3. Displaying and Summarizing Quantitative Data. 1 of 66 05/21/ :00 AM
Chapter 3 Displaying and Summarizing Quantitative Data D. Raffle 5/19/2015 1 of 66 05/21/2015 11:00 AM Intro In this chapter, we will discuss summarizing the distribution of numeric or quantitative variables.
More informationLecture-16. Data Tables, Scenarios & Goal Seek in Excel 2007
Lecture-16 Data Tables, Scenarios & Goal Seek in Excel 2007 In Excel, a Data Table is a way to see different results by altering an input cell in your formula. As an example, we're going to alert the interest
More informationGush vs. Bore: A Look at the Statistics of Sampling
Gush vs. Bore: A Look at the Statistics of Sampling Open the Fathom file Random_Samples.ftm. Imagine that in a nation somewhere nearby, a presidential election will soon be held with two candidates named
More informationHow to Use Excel for Regression Analysis MtRoyal Version 2016RevA *
OpenStax-CNX module: m63578 1 How to Use Excel for Regression Analysis MtRoyal Version 2016RevA * Lyryx Learning Based on How to Use Excel for Regression Analysis BSTA 200 Humber College Version 2016RevA
More informationMath 1 Variable Manipulation Part 8 Working with Data
Name: Math 1 Variable Manipulation Part 8 Working with Data Date: 1 INTERPRETING DATA USING NUMBER LINE PLOTS Data can be represented in various visual forms including dot plots, histograms, and box plots.
More informationMath 1 Variable Manipulation Part 8 Working with Data
Math 1 Variable Manipulation Part 8 Working with Data 1 INTERPRETING DATA USING NUMBER LINE PLOTS Data can be represented in various visual forms including dot plots, histograms, and box plots. Suppose
More informationBar graph or Histogram? (Both allow you to compare groups.)
Bar graph or Histogram? (Both allow you to compare groups.) We want to compare total revenues of five different companies. Key question: What is the revenue for each company? Bar graph We want to compare
More informationKING ABDULAZIZ UNIVERSITY FACULTY OF COMPUTING & INFORMATION TECHNOLOGY DEPARTMENT OF INFORMATION SYSTEM. Lab 1- Introduction
Lab 1- Introduction Objective: We will start with some basic concept of DSS. And also we will start today the WHAT-IF analysis technique for decision making. Activity Outcomes: What is what-if analysis
More informationTwo Way ANOVA. Turkheimer PSYC 771. Page 1 Two-Way ANOVA
Page 1 Two Way ANOVA Two way ANOVA is conceptually like multiple regression, in that we are trying to simulateously assess the effects of more than one X variable on Y. But just as in One Way ANOVA, the
More informationModule - 01 Lecture - 03 Descriptive Statistics: Graphical Approaches
Introduction of Data Analytics Prof. Nandan Sudarsanam and Prof. B. Ravindran Department of Management Studies and Department of Computer Science and Engineering Indian Institution of Technology, Madras
More informationSuper-marketing. A Data Investigation. A note to teachers:
Super-marketing A Data Investigation A note to teachers: This is a simple data investigation requiring interpretation of data, completion of stem and leaf plots, generation of box plots and analysis of
More informationExcel #2: No magic numbers
Excel #2: No magic numbers This lesson comes from programmers who long ago learned that everything entered into code must be defined and documented. Placing numbers into an equation is dangerous because
More informationCapability on Aggregate Processes
Capability on Aggregate Processes CVJ Systems AWD Systems Trans Axle Solutions edrive Systems The Problem Fixture 1 Fixture 2 Horizontal Mach With one machine and a couple of fixtures, it s a pretty easy
More informationSurvey Question Analysis (Draft )
The purpose of this tutorial is to analyze two types of questions commonly found on surveys: proportion (yes/no) questions and Likert scale (preferences) questions. (This tutorial doesn t tell you how
More informationMultiple Regression. Dr. Tom Pierce Department of Psychology Radford University
Multiple Regression Dr. Tom Pierce Department of Psychology Radford University In the previous chapter we talked about regression as a technique for using a person s score on one variable to make a best
More informationEliminating waste isn t enough; you have to reduce inputs to save money. lean accounting. By Reginald Tomas Yu-Lee.
Eliminating waste isn t enough; you have to reduce inputs to save money Proper lean accounting By Reginald Tomas Yu-Lee October 2011 39 proper lean accounting rom its inception, lean has been about cost
More informationOperations and Supply Chain Management Prof. G. Srinivisan Department of Management Studies Indian Institute of Technology, Madras
Operations and Supply Chain Management Prof. G. Srinivisan Department of Management Studies Indian Institute of Technology, Madras Module No - 1 Lecture No - 22 Integrated Model, ROL for Normal Distribution
More informationCHAPTER 8 T Tests. A number of t tests are available, including: The One-Sample T Test The Paired-Samples Test The Independent-Samples T Test
CHAPTER 8 T Tests A number of t tests are available, including: The One-Sample T Test The Paired-Samples Test The Independent-Samples T Test 8.1. One-Sample T Test The One-Sample T Test procedure: Tests
More informationDescriptive Statistics
Descriptive Statistics Let s work through an exercise in developing descriptive statistics. The following data represent the number of text messages a sample of students received yesterday. 3 1 We begin
More informationSlide 1 Hello this is Carrie Tupa with the Texas Workforce Commission and I want to welcome you to part two of
Welcome to TEAMS 3.2 An Introduction Carrie Tupa Texas Workforce Commission December 6, 2017 Slide 1 Hello this is Carrie Tupa with the Texas Workforce Commission and I want to welcome you to part two
More informationComputing Descriptive Statistics Argosy University
2014 Argosy University 2 Computing Descriptive Statistics: Ever Wonder What Secrets They Hold? The Mean, Mode, Median, Variability, and Standard Deviation Introduction Before gaining an appreciation for
More informationChapter 2 Part 1B. Measures of Location. September 4, 2008
Chapter 2 Part 1B Measures of Location September 4, 2008 Class will meet in the Auditorium except for Tuesday, October 21 when we meet in 102a. Skill set you should have by the time we complete Chapter
More informationChapter 10 Regression Analysis
Chapter 10 Regression Analysis Goal: To become familiar with how to use Excel 2007/2010 for Correlation and Regression. Instructions: You will be using CORREL, FORECAST and Regression. CORREL and FORECAST
More informationTutorial Formulating Models of Simple Systems Using VENSIM PLE System Dynamics Group MIT Sloan School of Management Cambridge, MA O2142
Tutorial Formulating Models of Simple Systems Using VENSIM PLE System Dynamics Group MIT Sloan School of Management Cambridge, MA O2142 Originally prepared by Nelson Repenning. Vensim PLE 5.2a Last Revision:
More informationMarginal Costing Q.8
Marginal Costing. 2008 Q.8 Break-Even Point. Before tackling a marginal costing question, it s first of all crucial that you understand what is meant by break-even point. What this means is that a firm
More informationAnd the numerators are the shaded parts We talking fractions. Hook
Understanding fractions Common Core Standard 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity
More informationSPSS 14: quick guide
SPSS 14: quick guide Edition 2, November 2007 If you would like this document in an alternative format please ask staff for help. On request we can provide documents with a different size and style of
More informationGuest Concepts, Inc. (702)
Guest Concepts, Inc. (702) 998-4800 Welcome to our tutorial on the Lease End Renewal Process The process you will see here is extremely effective and has been used successfully with thousands of renewal
More informationEnterprise Diversification: Will It Reduce Your Risk?
Enterprise Diversification: Will It Reduce Your Risk? By: Chris Bastian and Larry Held University of Wyoming Weather, diseases, pests, and infertility are all factors which cause yield variability or production
More informationPRINCIPLES AND APPLICATIONS OF SPECIAL EDUCATION ASSESSMENT
PRINCIPLES AND APPLICATIONS OF SPECIAL EDUCATION ASSESSMENT CLASS 3: DESCRIPTIVE STATISTICS & RELIABILITY AND VALIDITY FEBRUARY 2, 2015 OBJECTIVES Define basic terminology used in assessment, such as validity,
More informationBasic Statistics, Sampling Error, and Confidence Intervals
02-Warner-45165.qxd 8/13/2007 5:00 PM Page 41 CHAPTER 2 Introduction to SPSS Basic Statistics, Sampling Error, and Confidence Intervals 2.1 Introduction We will begin by examining the distribution of scores
More informationWinning more business in professional services firms
Winning more business in professional services firms A Guest Article by Chris Matthews June 2013 Shocking statistics What do you think is an acceptable level of new business success for a professional
More informationOnline Student Guide Types of Control Charts
Online Student Guide Types of Control Charts OpusWorks 2016, All Rights Reserved 1 Table of Contents LEARNING OBJECTIVES... 4 INTRODUCTION... 4 DETECTION VS. PREVENTION... 5 CONTROL CHART UTILIZATION...
More informationSection 9: Presenting and describing quantitative data
Section 9: Presenting and describing quantitative data Australian Catholic University 2014 ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced or used in any form
More informationStatistics Chapter 3 Triola (2014)
3-1 Review and Preview Branches of statistics Descriptive Stats: is the branch of stats that involve the organization, summarization, and display of data Inferential Stats: is the branch of stats that
More informationModelling buyer behaviour - 2 Rate-frequency models
Publishing Date: May 1993. 1993. All rights reserved. Copyright rests with the author. No part of this article may be reproduced without written permission from the author. Modelling buyer behaviour -
More informationMAS187/AEF258. University of Newcastle upon Tyne
MAS187/AEF258 University of Newcastle upon Tyne 2005-6 Contents 1 Collecting and Presenting Data 5 1.1 Introduction...................................... 5 1.1.1 Examples...................................
More informationOperations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras
Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Module - 01 Lecture - 08 Aggregate Planning, Quadratic Model, Demand and
More informationManaging stock levels: materials management and inventory control
16 Managing stock levels: materials management and inventory control Prerequisites Objectives Introduction For part of this chapter you will find it useful to have some knowledge of the normal distribution
More informationChapter 5. Statistical Reasoning
Chapter 5 Statistical Reasoning Measures of Central Tendency Back in Grade 7, data was described using the measures of central tendency and range. Central tendency refers to the middle value, or perhaps
More informationStrong Interest Inventory Certification Program Program Pre-Reading Assignment
Strong Interest Inventory Certification Program Program Pre-Reading Assignment Strong Interest Inventory is a registered trademark of CPP, Inc. Readings: Strong Manual, Chapter 1, Strong User s Guide,
More informationScript for 408(b)(2) Disclosure Focus Groups
Script for 408(b)(2) Disclosure Focus Groups Introduction Thank you for coming and agreeing to participate in this discussion. What we are doing here today is called a focus group. My name is [insert moderator
More informationPivot Table Tutorial Using Ontario s Public Sector Salary Disclosure Data
Pivot Table Tutorial Using Ontario s Public Sector Salary Disclosure Data Now that have become more familiar with downloading data in Excel format (xlsx) or a text or csv format (txt, csv), it s time to
More informationAP Statistics Test #1 (Chapter 1)
AP Statistics Test #1 (Chapter 1) Name Part I - Multiple Choice (Questions 1-20) - Circle the answer of your choice. 1. You measure the age, marital status and earned income of an SRS of 1463 women. The
More informationModule 55 Firm Costs. What you will learn in this Module:
What you will learn in this Module: The various types of cost a firm faces, including fixed cost, variable cost, and total cost How a firm s costs generate marginal cost curves and average cost curves
More informationCentral Tendency. Ch 3. Essentials of Statistics for the Behavior Science Ch.3
Central Tendency Ch 3 Ch. 3 Central Tendency 3.1 Introduction 3.2 Mean 3.3 Median 3.4 Mode 3.5 Selecting a Measure of Central Tendency 3.6 Central Tendency & Shape of the Distribution Summary 3.1 Introduction
More informationTHE NORMAL CURVE AND SAMPLES:
-69- &KDSWHU THE NORMAL CURVE AND SAMPLES: SAMPLING DISTRIBUTIONS A picture of an ideal normal distribution is shown below. The horizontal axis is calibrated in z-scores in terms of standard deviation
More informationSTEP BY STEP INTRODUCTION TO STATISTICS FOR BUSINESS. Edition. Second. Richard N. Landers
A STEP BY STEP INTRODUCTION TO STATISTICS FOR BUSINESS Second Edition Richard N. Landers 00_LANDER_STEP_FM.indd 3 16/11/2018 11:49:24 AM SAGE Publications Ltd 1 Oliver s Yard 55 City Road London EC1Y 1SP
More informationModule 1: Fundamentals of Data Analysis
Using Statistical Data to Make Decisions Module 1: Fundamentals of Data Analysis Dr. Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business S tatistics are an important
More informationChapter 4: Foundations for inference. OpenIntro Statistics, 2nd Edition
Chapter 4: Foundations for inference OpenIntro Statistics, 2nd Edition Variability in estimates 1 Variability in estimates Application exercise Sampling distributions - via CLT 2 Confidence intervals 3
More informationGlossary of Standardized Testing Terms https://www.ets.org/understanding_testing/glossary/
Glossary of Standardized Testing Terms https://www.ets.org/understanding_testing/glossary/ a parameter In item response theory (IRT), the a parameter is a number that indicates the discrimination of a
More informationPoint Sampling (a.k.a. prism cruising)
Point Sampling (a.k.a. prism cruising) The following is a (simple?) explanation of the principles behind prism cruising. This is not meant as a stand alone paper; it is intended to supplement lecture/lab
More informationMeasuring Performance with Objective Evaluations
PERFORMANCE MANAGEMENT FOR HIGH-PERFORMANCE CULTURES PART 3 of 5 Measuring Performance with Objective Evaluations TABLE OF CONTENTS I CREATING A CULTURE OF HIGH PERFORMANCE Decouple performance development
More informationUsing Key Principles to Build Rapport
Using Key Principles to Build Rapport Were you ever interviewed by someone who had little regard for your feelings? What did this person say or do, and how did you feel? How open were you with this person,
More informationForecasting Introduction Version 1.7
Forecasting Introduction Version 1.7 Dr. Ron Tibben-Lembke Sept. 3, 2006 This introduction will cover basic forecasting methods, how to set the parameters of those methods, and how to measure forecast
More informationGLOSSARY OF COMPENSATION TERMS
GLOSSARY OF COMPENSATION TERMS This compilation of terms is intended as a guide to the common words and phrases used in compensation administration. Most of these are courtesy of the American Compensation
More informationCorrelation and Simple. Linear Regression. Scenario. Defining Correlation
Linear Regression Scenario Let s imagine that we work in a real estate business and we re attempting to understand whether there s any association between the square footage of a house and it s final selling
More informationStudents will understand the definition of mean, median, mode and standard deviation and be able to calculate these functions with given set of
Students will understand the definition of mean, median, mode and standard deviation and be able to calculate these functions with given set of numbers. Also, students will understand why some measures
More informationConfidence Intervals
Confidence Intervals Example 1: How prevalent is sports gambling in America? 2007 Gallup poll took a random sample of 1027 adult Americans. 17% of the sampled adults had gambled on sports in the past year.
More informationBenchmarking with international partners: an interview with Robert Camp
Benchmarking with international partners: an interview with Robert Camp Interview by James Nelson R obert Camp is a leading authority on benchmarking and its use to obtain best practice knowledge and superior
More informationModule 5: Production and costs
Module 5: Production and costs 5.2.1: Demonstration - production of tennis balls Production of anything is essentially a three step process: Inputs are combined Production process Output is produced Activity
More informationCHAPTER 10 REGRESSION AND CORRELATION
CHAPTER 10 REGRESSION AND CORRELATION SIMPLE LINEAR REGRESSION: TWO VARIABLES (SECTIONS 10.1 10.3 OF UNDERSTANDABLE STATISTICS) Chapter 10 of Understandable Statistics introduces linear regression. The
More informationHIMSS ME-PI Community. Quick Tour. Sigma Score Calculation Worksheet INSTRUCTIONS
HIMSS ME-PI Community Sigma Score Calculation Worksheet INSTRUCTIONS Quick Tour Let s start with a quick tour of the Excel spreadsheet. There are six worksheets in the spreadsheet. Sigma Score (Snapshot)
More informationPhysics 141 Plotting on a Spreadsheet
Physics 141 Plotting on a Spreadsheet Version: Fall 2018 Matthew J. Moelter (edited by Jonathan Fernsler and Jodi L. Christiansen) Department of Physics California Polytechnic State University San Luis
More informationVIII. STATISTICS. Part I
VIII. STATISTICS Part I IN THIS CHAPTER: An introduction to descriptive statistics Measures of central tendency: mean, median, and mode Measures of spread, dispersion, and variability: range, variance,
More informationICTCM 28th International Conference on Technology in Collegiate Mathematics
Need a Graphing Calculator/CAS App? You re in the Right Place! 2016 ICTCM Atlanta, GA John C.D. Diamantopoulos, Ph.D. Northeastern State University diamantj@nsuok.edu Sometimes, having the right technology
More informationThe Human Tendency to Infer the Worst: Why the Absence of a Proper Cover Letter Can Severely Damage Your Candidacy
The Human Tendency to Infer the Worst: Why the Absence of a Proper Cover Letter Can Severely Damage Your Candidacy One of the most important lessons I learned as a legal headhunter was taught to me just
More informationHUD-US DEPT OF HOUSING & URBAN DEVELOPMENT: Understanding Internal Controls. Ladies and gentlemen, thank you for standing by and welcome to the
Final Transcript HUD-US DEPT OF HOUSING & URBAN DEVELOPMENT: Understanding Internal Controls SPEAKERS Petergay Bryan PRESENTATION Moderator Ladies and gentlemen, thank you for standing by and welcome to
More information10.2 Correlation. Plotting paired data points leads to a scatterplot. Each data pair becomes one dot in the scatterplot.
10.2 Correlation Note: You will be tested only on material covered in these class notes. You may use your textbook as supplemental reading. At the end of this document you will find practice problems similar
More informationDon t We Need to Remove the Outliers?
Quality Digest Daily, October 6, 2014 Manuscript 274 Characterization and estimation are different. Donald J. Wheeler Much of modern statistics is concerned with creating models which contain parameters
More informationLecture 10. Outline. 1-1 Introduction. 1-1 Introduction. 1-1 Introduction. Introduction to Statistics
Outline Lecture 10 Introduction to 1-1 Introduction 1-2 Descriptive and Inferential 1-3 Variables and Types of Data 1-4 Sampling Techniques 1- Observational and Experimental Studies 1-6 Computers and Calculators
More informationChapter 9 Assignment (due Wednesday, August 9)
Math 146, Summer 2017 Instructor Linda C. Stephenson (due Wednesday, August 9) The purpose of the assignment is to find confidence intervals to predict the proportion of a population. The population in
More informationTHE GUIDE TO SPSS. David Le
THE GUIDE TO SPSS David Le June 2013 1 Table of Contents Introduction... 3 How to Use this Guide... 3 Frequency Reports... 4 Key Definitions... 4 Example 1: Frequency report using a categorical variable
More informationThe most frequent question that I am asked after
The economic importance of meat yield in processing Introdução Cobb-Vantress, Inc The most frequent question that I am asked after I am introduced as someone knowledgeable in product testing for Cobb is
More information1/26/18. Averages and Variation. Measures of Central Tendency. Focus Points. Example 1 Mode. Measures of Central. Median, and Mean. Section 3.
3 Averages and Variation Section 3.1 Measures of Central Tendency: Mode,, and Focus Points Compute mean, median, and mode from raw data. Interpret what mean, median, and mode tell you. Explain how mean,
More informationLet us introduce you to Course Match
1 Let us introduce you to Course Match 2 In order to understand course match you need to know three terms. Utilities We re using utility here as an economic term. If you aren t already you ll be very familiar
More informationChapter 8: Exchange. 8.1: Introduction. 8.2: Exchange. 8.3: Individual A s Preferences and Endowments
Chapter 8: Exchange 8.1: Introduction In many ways this chapter is the most important in the book. If you have time to study just one, this is the one that you should study (even though it might be a bit
More informationAn Introduction to Descriptive Statistics (Will Begin Momentarily) Jim Higgins, Ed.D.
An Introduction to Descriptive Statistics (Will Begin Momentarily) Jim Higgins, Ed.D. www.bcginstitute.org Visit BCGi Online While you are waiting for the webinar to begin, Don t forget to check out our
More informationDesigning with LRFD for Wood by Robert J. Taylor, Ph.D., P.Eng., M.ASCE, Assoc. AIA
Designing with LRFD for Wood by Robert J. Taylor, Ph.D., P.Eng., M.ASCE, Assoc. AIA Many engineers (especially seasoned engineers) ask, "Why should I switch from allowable stress design (ASD) to LRFD design
More informationApplying Statistical Techniques to implement High Maturity Practices At North Shore Technologies (NST) Anand Bhatnagar December 2015
Applying Statistical Techniques to implement High Maturity Practices At North Shore Technologies (NST) Anand Bhatnagar December 2015 For our audience some Key Features Say Yes when you understand Say No
More informationStatistical Pay Equity Analyses: Data and Methodological Overview
Statistical Pay Equity Analyses: Data and Methodological Overview by Paul F. White, Ph.D. Resolution Economics, LLC Washington, DC for American Bar Association 10 th Annual Labor and Employment Law Conference
More informationUsing the Percent Equation
Using the Percent Equation LAUNCH (7 MIN) Before How can your personality affect a decision like this one? During What are the advantages of Offer A? Offer B? After Which option would you choose? KEY CONCEPT
More informationMSMGT 782 Lesson 2 Important note: Transcripts are not substitutes for textbook assignments.
MSMGT 782 Lesson 2 Important note: Transcripts are not substitutes for textbook assignments. Supply chain cost to serve analysis is really the powerful tool that we use to weed out alternatives on how
More informationApplied Multivariate Statistical Modeling Prof. J. Maiti Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur
Applied Multivariate Statistical Modeling Prof. J. Maiti Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur Lecture - 19 Tutorial - ANOVA (Contd.) (Refer Slide
More informationWeka Evaluation: Assessing the performance
Weka Evaluation: Assessing the performance Lab3 (in- class): 21 NOV 2016, 13:00-15:00, CHOMSKY ACKNOWLEDGEMENTS: INFORMATION, EXAMPLES AND TASKS IN THIS LAB COME FROM SEVERAL WEB SOURCES. Learning objectives
More information