Lab 9: Sampling Distributions
|
|
- Emery Thompson
- 6 years ago
- Views:
Transcription
1 Lab 9: Sampling Distributions Sampling from Ames, Iowa In this lab, we will investigate the ways in which the estimates that we make based on a random sample of data can inform us about what the population might look like. We re interested in formulating a sampling distribution of our estimate in order to get a sense of how good of an estimate it is. The Data The dataset that we ll be considering comes from the town of Ames, Iowa. The Assessor s Office records information on all real estate sales and the data set we re considering contain information on all residential home sales between 2006 and We will consider these data as our statistical population. In this lab we would like to learn as much as we can about these homes by taking smaller samples from the full population. Let s load the data. ames = read.delim(" source(" We see that there are quite a few variables in the data set, but we ll focus on the number of rooms above ground (TotRms.AbvGrd) and sale price (SalePrice). Let s look at the distribution of number of rooms in homes in Ames by calculating some summary statistics and making a histogram. summary(ames$totrms.abvgrd) hist(ames$totrms.abvgrd) Exercise 1 How would you describe this population distribution? The Unknown Sampling Distribution In this lab, we have access to the entire population, but this is rarely the case in real life. Gathering information on an entire population is often extremely costly or even impossible. Because of this, we often take a smaller sample survey of the population and use that to make educated guesses about the properties of the population. If we were interested in estimating the mean age number of rooms in homes in Ames based on a sample, we can use the following command to survey the population. samp1 = sample(ames$totrms.abvgrd,75) This command allows us to create a new vector called samp1 that is a simple random sample of size 75 from the population vector ames$totrms.abvgrd. At a conceptual level, you can imagine randomly choosing 75 entries from the Ames phonebook, calling them up, and recording the number of rooms in their houses. You would be correct in objecting that the phonebook probably doesn t contain phone numbers for all homes and that there will almost 1
2 certainly be people that don t pick up the phone or refuse to give this information. These are issues that can make gathering data very difficult and are a strong incentive to collect a high quality sample. Exercise 2 How would you describe the distribution of this sample? How does it compare to the distribution of the population? If we re interested in estimating the average number of rooms in homes in Ames, our best guess is going to be the sample mean from this simple random sample. mean(samp1) Exercise 3 How does your sample mean compare to your neighbors? Are the sample means the same? Why or why not? Depending which 75 homes you selected, your estimate could be a bit above or a bit below the true population mean of But in general, the sample mean turns out to be a pretty good estimate of the average number of rooms, and we were able to get it by sampling less than 3% of the population. Exercise 4 Take a second sample, also of size 75, and call it samp2. How does the mean of samp2 compare with the mean of samp1? If we took a third sample of size 150, intuitively would you expect the sample mean to be a better or worse estimate of the population mean? Not surprisingly, every time we take another random sample, we get a different sample mean. It s useful to get a sense of just how much variability we should expect when estimating the population mean this way. This is what is captured by the sampling distribution. In this lab, because we have access to the population, we can build up the sampling distribution for the sample mean by repeating the above steps 5000 times. We will use the function gen_samp_ means to do this, this function takes three arguments, pop: the population data, samp_size: the size of the sample to take when generating the samples, and niter: the number of sample means to generate. samp_means = gen_samp_means( ames$totrms.abvgrd, samp_size = 75, niter = 5000 ) hist(samp_means, probability = TRUE) Here we rely on the computational ability of R to quickly take 5000 samples of size 75 from the population, compute each of those sample means, and store them in a vector called samp _means. Exercise 5 How would you describe this sampling distribution? On what value is it centered? Would you expect the distribution to change if we instead collected 50,000 sample means? 2
3 Approximating the Sampling Distribution The sampling distribution that we computed tells us everything that we could hope for about the average number of rooms in homes in Ames. Because the sample mean is an unbiased estimator, the sampling distribution is centered at the true average number of rooms of the the population and the spread of the distribution indicates how much variability is induced by sampling only 75 of the homes. We computed the sampling distribution for mean number of rooms by drawing 5000 samples from the population and calculating 5000 sample means. This was only possible because we had access to the population. In most cases you don t (if you did, there would be no need to estimate!). Therefore, you have only your single sample to rely upon... that, and the Central Limit Theorem. The Central Limit Theorem states that, under certain conditions, the sample mean follows a normal distribution. This allows us to make the inferential leap from our single sample to the full sampling distribution that describes every possible sample mean you might come across. But we need to look before we leap. Exercise 6 Does samp1 meet the conditions for the sample mean to be approximately normally distributed according to the central limit theorem? If the conditions are met, then we can find the approximate sampling distribution by plugging in our best estimate for the population mean and standard error: x and s/ n. xbar = mean(samp1) se = sd(samp1)/sqrt(75) We can add a curve representing this approximation to our existing histogram using the command hist_curve. This function takes the arguments, sample_means the sample means used to generate the histogram, mean the mean of the normal curve to draw, and sd the standard deviation for normal curve to draw. hist_curve(samp_means, mean = xbar, sd = se) We can see that the line does a decent job of tracing the histogram that we derived from having access to the population. In this case, our approximation based on the CLT is a good one. Confidence Intervals In class this week we discussed how we can use the central limit theorem and the resulting normal distribution to describe a plausible range of values for the true population mean, we called these ranges confidence intervals. In the case of a sample mean we calculate the confidence interval using the following formula CI = X ± z CL s n 3
4 where X is the sample mean, z CL is the z-score for the appropriate confidence level (ie for a 95% CL), s is the sample standard deviation, and n is the sample size. We can calculate a 95% confidence interval in R for samp1 using the following code: mean(samp1)+c(-1,1)*1.96*sd(samp1)/sqrt(length(samp1)) Exercise 7 Does the confidence interval for samp1 include the true population mean 6.443? Does your neighbors confidence interval contain it? In class we also mentioned that the definition of a confidence level is that if we were collect additional samples of the same size and calculated a confidence interval based on their sample mean and sample standard deviation then we would expect CL% of those confidence intervals to contain the true population mean. We will confirm this by taking multiple samples and examining the resulting confidence intervals. We will do this using the check_ci function which will produce a graphical representation of 100 confidence intervals ranges relative to the true population mean. check_ci(ames$totrms.abvgrd, samp_size=75, CL = 0.95) Note that we can change both the size of the sample used as well as the confidence level. Exercise 8 What happens to the size of the confidence intervals when you increase the sample size? When you decrease it? What about when you change the confidence level? You will have also hopefully noticed that the color of the confidence intervals changes depending of if it includes the true population mean, which is indicated by the vertical black line. The confidence interval is represented in blue if it does contain the population mean, red if it does not. In practice when we can only take a single sample we would not necessarily know the value of the true population mean, which is why we have to use the language of confidence intervals / levels. Based on the resulting plot(s) it is possible to count the number of confidence intervals that do not include the true population mean, and if our definition of confidence level is correct this number should correspond to the confidence level you used when running the function. Exercise 9 Run the check_ci function several times with different values for the confidence level, CL, do the number of confidence intervals that contain the true population mean agree with the specified confidence level? 4
5 On Your Own So far we have only focused on estimating the mean number of rooms of the homes of Ames. Now we ll try to estimate the mean sale price. 1. Take a random sample of size 30 from ames$saleprice. Using this sample, what is your best point estimate of the population mean? Include a histogram of this sample in your answer. 2. Check the conditions for the sampling distribution of x SaleP rice to be nearly normal. 3. Since you have access to the population, compute the sampling distribution for x SaleP rice by taking 5000 samples from the population of size 30 and computing 5000 sample means. Describe the shape of this sampling distribution. Based on this sampling distribution, what would you guess the mean sale price of homes in Ames to be? Include a histogram of the sampling distribution. 4. Change your sample size from 30 to 150, then compute the sampling distribution using the same method as above. Describe the shape of this sampling distribution (where n = 150) and compare it to the sampling distribution from earlier (where n = 30). Based on this sampling distribution, what would you guess the mean sale price of the homes in Ames to be? Include a histogram of the sampling distribution. 5. Based on their shape, which sampling distribution would you feel more comfortable approximating by the normal model? 6. Which sampling distribution has a smaller spread? If we re concerned with making estimates that are consistently close to the true value, is having a sampling distribution with a smaller spread more or less desirable? 7. Generate plots of the confidence intervals for a sample sizes of 30 and 150 at confidence levels of 0.90, 0.95 and (6 plots in total) 8. Based on your plots how would describe the relationship of sample size and confidence level to the size of the confidence interval? Notes This is a product of OpenIntro that is released under a Creative Commons Attribution-NonCommercial- NoDerivs 3.0 Unported (creativecommons.org/ licenses/ by-nc-nd/ 3.0/ ). This lab was adapted for OpenIntro by Andrew Bray and Mine Çetinkaya-Rundel from a lab written by the faculty and TAs of UCLA Statistics. 5
Chapter 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 informationUnit3: Foundationsforinference. 1. Variability in estimates and CLT. Sta Fall Lab attendance & lateness Peer evaluations
Announcements Unit3: Foundationsforinference 1. Variability in estimates and CLT Sta 101 - Fall 2015 Duke University, Department of Statistical Science Lab attendance & lateness Peer evaluations Dr. Monod
More informationLecture 9 - Sampling Distributions and the CLT
Lecture 9 - Sampling Distributions and the CLT Sta102/BME102 February 15, 2016 Colin Rundel Variability of Estimates Mean Sample mean ( X): X = 1 n (x 1 + x 2 + x 3 + + x n ) = 1 n n i=1 x i Population
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 informationAP Stats ~ Lesson 8A: Confidence Intervals OBJECTIVES:
AP Stats ~ Lesson 8A: Confidence Intervals OBJECTIVES: DETERMINE the point estimate and margin of error from a confidence interval. INTERPRET a confidence interval in context. INTERPRET a confidence level
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 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 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 informationLecture 8: Introduction to sampling distributions
Lecture 8: Introduction to sampling distributions Statistics 101 Mine Çetinkaya-Rundel February 9, 2012 Announcements Announcements Due: Quiz 3 Monday morning 8am. OH change: Monday s office hours moved
More informationConfidence Intervals for Large Sample Means
Confidence Intervals for Large Sample Means Dr Tom Ilvento Department of Food and Resource Economics Overview Let s continue the discussion of Confidence Intervals (C.I.) And I will shift to the C.I. for
More informationprovided that the population is at least 10 times as large as the sample (10% condition).
8.2.1 Conditions for Estimating p As always, inference is based on the sampling distribution of a statistic. We described the sampling distribution of a sample proportion p-hat in section 7.2. Here is
More informationChapter 7: Sampling Distributions
+ Chapter 7: Sampling Distributions Section 7.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE + Chapter 7 Sampling Distributions 7.1 What is a Sampling Distribution? 7.2 Sample
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 informationChapter 7: Sampling Distributions
+ Chapter 7: Sampling Distributions Section 7.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE + Chapter 7 Sampling Distributions 7.1 What is a Sampling Distribution? 7.2 Sample
More informationSecondary Math Margin of Error
Secondary Math 3 1-4 Margin of Error What you will learn: How to use data from a sample survey to estimate a population mean or proportion. How to develop a margin of error through the use of simulation
More informationChapter 3: Distributions of Random Variables
Chapter 3: Distributions of Random Variables OpenIntro Statistics, 2nd Edition Slides developed by Mine Çetinkaya-Rundel of OpenIntro The slides may be copied, edited, and/or shared via the CC BY-SA license
More informationGame Theory & Firms. Jacob LaRiviere & Justin Rao April 20, 2016 Econ 404, Spring 2016
Game Theory & Firms Jacob LaRiviere & Justin Rao April 20, 2016 Econ 404, Spring 2016 What is Game Theory? Game Theory Intuitive Definition: Theory of strategic interaction Technical Definition: Account
More informationComment on A Macroeconomic Framework for Quantifying Systemic Risk by He and Krishnamurthy
Comment on A Macroeconomic Framework for Quantifying Systemic Risk by He and Krishnamurthy Chris Sims May 2, 2013 c 2013 by Christopher A. Sims. This document is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike
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 informationUntangling Correlated Predictors with Principle Components
Untangling Correlated Predictors with Principle Components David R. Roberts, Marriott International, Potomac MD Introduction: Often when building a mathematical model, one can encounter predictor variables
More informationStat 411/511 MORE ON THE RANDOM SAMPLING MODEL. Charlotte Wickham. stat511.cwick.co.nz. Sep
Stat 411/511 MORE ON THE RANDOM SAMPLING MODEL Sep 29 2015 Charlotte Wickham stat511.cwick.co.nz Announcements My office hours: Mondays 11am 255 Weniger Thursdays 3-5pm 3003 Cordley Help with Statistics
More information+? Mean +? No change -? Mean -? No Change. *? Mean *? Std *? Transformations & Data Cleaning. Transformations
Transformations Transformations & Data Cleaning Linear & non-linear transformations 2-kinds of Z-scores Identifying Outliers & Influential Cases Univariate Outlier Analyses -- trimming vs. Winsorizing
More informationChapter 8: Estimating with Confidence. Section 8.2 Estimating a Population Proportion
Chapter 8: Estimating with Confidence Section 8.2 Activity: The Beads Your teacher has a container full of different colored beads. Your goal is to estimate the actual proportion of red beads in the container.
More informationPopulation Genetics Simulations Heath Blackmon and Emma E. Goldberg last updated:
Population Genetics Simulations Heath Blackmon and Emma E. Goldberg last updated: 2016-04-02 Contents Introduction 1 Evolution Across Generations....................................... 1 Lauching the Population
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 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 informationEquipment and preparation required for one group (2-4 students) to complete the workshop
Your career today is a Pharmaceutical Statistician Leaders notes Do not give to the students Red text in italics denotes comments for leaders and example answers Equipment and preparation required for
More informationThe Financial and Insurance Advisor s Guide to Content Writing
The Financial and Insurance Advisor s Guide to Content Writing TABLE OF CONTENTS Introduction pg. 2 1. CRM 2 and the Rise of Content Marketing pg. 3 2. Write Creatively and Be Entertaining pg. 7 3. Read
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
= the number obtained when rolling one six sided die once. If we roll a six sided die once, the mean of the probability distribution is P( = x) Simulation: We simulated rolling a six sided die times using
More informationSection 7.3b Sample Means The Central Limit Theorem
We have seen in the previous investigation that even though the distribution of the population of the ages of the 1000 pennies was skewed to the right, the distribution of the sample means appeared to
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 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 informationChapter 7: Sampling Distributions
Chapter 7: Sampling Distributions Section 7.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 7 Sampling Distributions 7.1 What is a Sampling Distribution? 7.2 Sample Proportions
More informationAP Statistics Scope & Sequence
AP Statistics Scope & Sequence Grading Period Unit Title Learning Targets Throughout the School Year First Grading Period *Apply mathematics to problems in everyday life *Use a problem-solving model that
More informationThe 10 Parts of a Great Website Design Request for Proposal (RFP)
The 10 Parts of a Great Website Design Request for Proposal (RFP) 01. Intro / Project Overview The goal here is to grab the web design agency s attention and respect so that they ll keep reading. This
More informationVIDEO 1: WHY ARE FORMS IMPORTANT?
VIDEO 1: WHY ARE FORMS IMPORTANT? Hi there. Welcome to an introduction to forms. I m Angela from HubSpot Academy. We re going to discuss how to use a form to generate leads. After this class, you ll understand
More informationBloomberg s Supply Chain Algorithm: Providing Insight Into Company Relationships
Bloomberg s Supply Chain Algorithm: Providing Insight Into Company Relationships I. Bloomberg Supply Chain Algorithm (BSCA) In the SPLC diagram for Texas Instruments (TXN US Equity) below, we show WPG
More informationA GUIDE TO GETTING SURVEY RESPONSES
FROM EMAIL INVITATIONS TO PAID RESPONSES A GUIDE TO GETTING SURVEY RESPONSES CHOOSE SAMPLE CHOOSE MODE OF SURVEY SELECT PANEL IF NEEDED 1 2 SURVEY MODE: AN IMPORTANT CHOICE The way that you distribute
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 informationChapter 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 informationUtilizing Data Science To Assess Software Quality
Utilizing Data Science To Assess Software Quality Renato Martins renatopmartins@gmail.com Abstract Data Science is a "hip" term these days. Most people automatically associate Data Science with financial
More informationAGAINST ALL ODDS EPISODE 28 INFERENCE FOR PROPORTIONS TRANSCRIPT
AGAINST ALL ODDS EPISODE 28 INFERENCE FOR PROPORTIONS TRANSCRIPT 1 FUNDER CREDITS Funding for this program is provided by Annenberg Learner. 2 INTRO Hello, I m and this is Against All Odds, where we make
More informationSection 8.2 Estimating a Population Proportion. ACTIVITY The beads. Conditions for Estimating p
Section 8.2 Estimating a Population Proportion ACTIVITY The beads Conditions for Estimating p Suppose one SRS of beads resulted in 107 red beads and 144 beads of another color. The point estimate for the
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 informationHow to view Results with. Proteomics Shared Resource
How to view Results with Scaffold 3.0 Proteomics Shared Resource An overview This document is intended to walk you through Scaffold version 3.0. This is an introductory guide that goes over the basics
More informationEvaluation of Police Patrol Patterns
-1- Evaluation of Police Patrol Patterns Stephen R. Sacks University of Connecticut Introduction The Desktop Hypercube is an interactive tool designed to help planners improve police services without additional
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 informationTEACHER NOTES MATH NSPIRED
Math Objectives Students will recognize that the mean of all the sample variances for samples of a given size drawn with replacement calculated using n-1 as a divisor will give the population variance
More informationInstructions. AIRBUS A3XX: Developing the World s Largest Commercial Aircraft
Instructions AIRBUS A3XX: Developing the World s Largest Commercial Aircraft In this case, you will be analyzing the strategic interaction between Airbus and Boeing, the two leading producers of large
More informationApplying the central limit theorem
Patrick Breheny March 11 Patrick Breheny Introduction to Biostatistics (171:161) 1/21 Introduction It is relatively easy to think about the distribution of data heights or weights or blood pressures: we
More informationFrom Theory to Data Product
From Theory to Data Product Applying Data Science Methods to Effect Business Change KDD 2017 - August 13 Advanced Analytics Entry Points Strategy Organization Policies, Procedures & Standards Components
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 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 informationBroccolini Construction
CASE STUDY Broccolini Construction Challenge Broccolini Construction was using Newforma to manage parts of their projects, but needed a way to simplify and standardize their processes. Solution Using Procore
More informationHappyville. Kevin S. Robinson, PhD
Happyville Kevin S. Robinson, PhD krobinson@millersville.edu Department of Mathematics Millersville University of Pennsylvania Millersville, PA 17551 www.millersville.edu/~krobinson/happyville Happyville
More informationSEO Ranking Research Tools
Copyright All rights reserved worldwide. YOUR RIGHTS: This book is restricted to your personal use only. It does not come with any other rights. LEGAL DISCLAIMER: This book is protected by international
More informationChapter 19. Confidence Intervals for Proportions. Copyright 2012, 2008, 2005 Pearson Education, Inc.
Chapter 19 Confidence Intervals for Proportions Copyright 2012, 2008, 2005 Pearson Education, Inc. Standard Error Both of the sampling distributions we ve looked at are Normal. For proportions For means
More informationUnderstanding Inference: Confidence Intervals II. Questions about the Assignment. Summary (From Last Class) The Problem
Questions about the Assignment Part I The z-score is not the same as the percentile (eg, a z-score of 98 does not equal the 98 th percentile) The z-score is the number of standard deviations the value
More informationApplied Econometrics
Applied Econometrics Lecture 3 Nathaniel Higgins ERS and JHU 20 September 2010 Outline of today s lecture Schedule and Due Dates Making OLS make sense Uncorrelated X s Correlated X s Omitted variable bias
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 informationDECISION-MAKING 7/23/2018. Do not plant your dreams in the field of indecision, where nothing ever grows but the weeds of what-if.
DECISION-MAKING Moving Beyond Eeny, Meeny, Miny, Mo Innovation and Excellence in Advanced Illness at End of Life 42 nd Annual Hospice & Palliative Care Conference September 2018 Charlotte, NC DECISION-MAKING
More informationShape and Velocity Management. Stu Schmidt
Shape and Velocity Management by Stu Schmidt COO, Market-Partners Inc. www.market-partners.com I n the previous newsletter we took a look at sales measurements, asking the fundamental question, Are we
More informationEstimating With Objects - Part III
Estimating With Objects - Part III Contents The size estimating problem The comparison problem Estimating part size Selecting a proxy Relationship to development effort The proxy parts in a product can
More information= = Intro to Statistics for the Social Sciences. Name: Lab Session: Spring, 2015, Dr. Suzanne Delaney
Name: Intro to Statistics for the Social Sciences Lab Session: Spring, 2015, Dr. Suzanne Delaney CID Number: _ Homework #22 You have been hired as a statistical consultant by Donald who is a used car dealer
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 informationHappyville: Putting A Smile Into Statistical Ideas
Happyville: Putting A Smile Into Statistical Ideas Kevin S. Robinson, PhD krobinson@millersville.edu Department of Mathematics Millersville University of Pennsylvania Millersville, PA 17551 www.millersville.edu/~krobinson/happyville
More informationBiostatistics 208 Data Exploration
Biostatistics 208 Data Exploration Dave Glidden Professor of Biostatistics Univ. of California, San Francisco January 8, 2008 http://www.biostat.ucsf.edu/biostat208 Organization Office hours by appointment
More informationINTRODUCTION TO STATISTICS
INTRODUCTION TO STATISTICS Slides by Pierre Dragicevic WHAT YOU WILL LEARN Statistical theory Applied statistics This lecture GOALS Learn basic intuitions and terminology Perform basic statistical inference
More informationAComparisonTestforNetSensitivity
Global Journal of Researches in Engineering General Engineering Volume 13 Issue 3 Version 1.0 Year 2013 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA)
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 informationThree steps to joining and participating in unions
Anger hope action Three steps to joining and participating in unions 1. Anger The first condition for joining or becoming involved in the union is anger. Many people are uncomfortable about expressing
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 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 informationThe Art and Science of Bidding for Offshore License Blocks
By: George E. Danner Chief Technology Officer Business Laboratory LLC Abstract: A company s performance in a lease sale can have serious implications for future growth and sustained value. Therefore it
More informationEco 300 Intermediate Micro
Eco 300 Intermediate Micro Instructor: Amalia Jerison Office Hours: T 12:00-1:00, Th 12:00-1:00, and by appointment BA 127A, aj4575@albany.edu A. Jerison (BA 127A) Eco 300 Spring 2010 1 / 61 Monopoly Market
More informationGENETIC DRIFT INTRODUCTION. Objectives
2 GENETIC DRIFT Objectives Set up a spreadsheet model of genetic drift. Determine the likelihood of allele fixation in a population of 0 individuals. Evaluate how initial allele frequencies in a population
More informationClovis Community College Class Assessment
Class: Math 110 College Algebra NMCCN: MATH 1113 Faculty: Hadea Hummeid 1. Students will graph functions: a. Sketch graphs of linear, higherhigher order polynomial, rational, absolute value, exponential,
More informationLab 2: Mathematical Modeling: Hardy-Weinberg 1. Overview. In this lab you will:
AP Biology Name Lab 2: Mathematical Modeling: Hardy-Weinberg 1 Overview In this lab you will: 1. learn about the Hardy-Weinberg law of genetic equilibrium, and 2. study the relationship between evolution
More informationThe Market Economy. The Economy. Consumers, Producers, and the Market. Are You Motivated Yet? Name:
Name: The Economy You ve probably heard people say things like, The economy is down, or, Such-and-such would be good for the economy. Maybe you ve figured out that the economy has something to do with
More informationThe Language of Accountability
The Language of Accountability What s good, what s bad, and what it means PRACTICAL TOOLS The Language of Accountability / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /
More informationLIR 832: MINITAB WORKSHOP
LIR 832: MINITAB WORKSHOP Opening Minitab Minitab will be in the Start Menu under Net Apps. Opening the Data Go to the following web site: http://www.msu.edu/course/lir/832/datasets.htm Right-click and
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 information+? Mean +? No change -? Mean -? No Change. *? Mean *? Std *? Transformations & Data Cleaning. Transformations
Transformations Transformations & Data Cleaning Linear & non-linear transformations 2-kinds of Z-scores Identifying Outliers & Influential Cases Univariate Outlier Analyses -- trimming vs. Winsorizing
More informationData Visualization. Prof.Sushila Aghav-Palwe
Data Visualization By Prof.Sushila Aghav-Palwe Importance of Graphs in BI Business intelligence or BI is a technology-driven process that aims at collecting data and analyze it to extract actionable insights
More informationManaging Airline Customer Satisfaction
4333 Amon Carter Boulevard, MD 5675 Fort Worth, TX 76155 Managing Airline Customer Satisfaction American Airlines, Inc. is a major U.S. airline headquartered in Fort Worth, Texas. It operates an extensive
More informationClinical trials patient-education brochure
Released November 2005 Revised January 2008 Revised March 2012 Revised July 17, 2017 Clinical trials patient-education brochure Roslyn Mannon, MD David Rothstein, MD Maria Luisa Alegre, MD, PhD Giorgio
More informationMarketing Automation: One Step at a Time
Marketing Automation: One Step at a Time 345 Millwood Road Chappaqua, NY 10514 www.raabassociatesinc.com Imagine a wall. Your small business is on one side. A pot of gold is on the other. The gold is the
More informationMultiple Choice Questions Sampling Distributions
Multiple Choice Questions Sampling Distributions 1. The Gallup Poll has decided to increase the size of its random sample of Canadian voters from about 1500 people to about 4000 people. The effect of this
More informationProducer Theory - Monopoly
Producer Theory - Monopoly Mark Dean Lecture Notes for Fall 2009 Introductory Microeconomics - Brown University 1 Introduction Up until now, we have assumed that all the agents in our economies are price
More informationMonte Carlo Simulation Practicum. S. David Alley, P.E. ANNA, Inc (annainc.com)
Monte Carlo Practicum 1 Monte Carlo Simulation Practicum S. David Alley, P.E. ANNA, Inc (annainc.com) Monte Carlo Practicum 2 Abstract Monte Carlo analysis is commonly used to predict the cost of future
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 informationCHAPTER 21A. What is a Confidence Interval?
CHAPTER 21A What is a Confidence Interval? RECALL Parameter fixed, unknown number that describes the population Statistic known value calculated from a sample a statistic is used to estimate a parameter
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 informationBOOTSTRAPPING AND CONFIDENCE INTERVALS
BOOTSTRAPPING AND CONFIDENCE INTERVALS Fill out your reading report on Learning Suite MPA 630: Data Science for Public Management November 8, 2018 PLAN FOR TODAY Why are we even doing this? Confidence
More informationSession 7. Introduction to important statistical techniques for competitiveness analysis example and interpretations
ARTNeT Greater Mekong Sub-region (GMS) initiative Session 7 Introduction to important statistical techniques for competitiveness analysis example and interpretations ARTNeT Consultant Witada Anukoonwattaka,
More informationDIRECT MAIL: MASTERING THE LOGISTICS OF A SUCCESSFUL MAILING
DIRECT MAIL: MASTERING THE LOGISTICS OF A SUCCESSFUL MAILING INCREASE YOUR RESPONSE RATES AND PROFITABILITY WHITE PAPER - 2 - Before you develop the content for your next mailing, there are logistical
More information5 CHAPTER: DATA COLLECTION AND ANALYSIS
5 CHAPTER: DATA COLLECTION AND ANALYSIS 5.1 INTRODUCTION This chapter will have a discussion on the data collection for this study and detail analysis of the collected data from the sample out of target
More informationBusiness Analytics & Data Mining Modeling Using R Dr. Gaurav Dixit Department of Management Studies Indian Institute of Technology, Roorkee
Business Analytics & Data Mining Modeling Using R Dr. Gaurav Dixit Department of Management Studies Indian Institute of Technology, Roorkee Lecture - 02 Data Mining Process Welcome to the lecture 2 of
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 informationPersona Development How- To Guide
Persona Development How- To Guide Effective use of Personas in your business can lead to a stronger brand, increased conversions, a decrease in cost per acquisition, an increase in customer lifetime value,
More information