Chapter 1 – Stats Starts Here
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Regression Summary Project Analysis for Today Review Questions: Categorical Variables
Statistics 102 Regression Summary Spring, 2000 - 1 - Regression Summary Project Analysis for Today First multiple regression • Interpreting the location and wiring coefficient estimates • Interpreting interaction terms • Measuring significance Second multiple regression • Deciding how to extend a model • Diagnostics (leverage plots, residual plots) Review Questions: Categorical Variables Where do those terms in a categorical regression come from? • You cannot use a categorical term directly in regression (e.g. 2(“Yes”)=?). • JMP converts each categorical variable into a collection of numerical variables that represent the information in the categorical variable, but are numerical and so can be used in regression. • These special variables (a.k.a., dummy variables) use only the numbers +1, 0, and –1. • A categorical variable with k categories requires (k-1) of these special numerical variables. Thus, adding a categorical variable with, for example, 5 categories adds 4 of these numerical variables to the model. How do I use the various tests in regression? What question are you trying to answer… • Does this predictor add significantly to my model, improving the fit beyond that obtained with the other predictors? (t-ratio, CI, p-value) • Does this collection of predictors add significantly to my model? Partial-F (Note: the only time you need partial F is when working with categorical variables that define 3 or more categories. In these cases, JMP shows you the partial-F as an “Effect Test”.) • Does my full model explain “more than random variation”? Use the F-ratio from the Anova summary table. Statistics 102 Regression Summary Spring, 2000 - 2 - How do I interpret JMP output with categorical variables? Term Estimate Std Error t Ratio Prob>|t| Intercept 179.59 5.62 32.0 0.00 Run Size 0.23 0.02 9.5 0.00 Manager[a-c] 22.94 7.76 3.0 0.00 Manager[b-c] 6.90 8.73 0.8 0.43 Manager[a-c]*Run Size 0.07 0.04 2.1 0.04 Manager[b-c]*Run Size -0.10 0.04 -2.6 0.01 • Brackets denote the JMP’s version of dummy variables. -
10 Questions Opinion Polls
Questions you might have on 10opinion polls 1. What is an opinion poll? An opinion poll is a survey carried out to measure views on a certain topic within a specific group of people. For example, the topic may relate to who Kenyans support in the presidential race, in which case, the group of people interviewed will be registered voters. 2. How are interviewees for an opinion poll selected? The group of people interviewed for an opinion poll is called a sample. As the name suggests, a sample is a group of people that represents the total population whose opinion is being surveyed. In a scientific opinion poll, everyone has an equal chance of being interviewed. 3. So how come I have never been interviewed for an opinion poll? You have the same chance of being polled as anyone else living in Kenya. However, chances of this are very small and are estimated at about 1 in 14,000. This is because there are approximately 14 million registered voters in Kenya and, for practical and cost reasons, usually only between 1,000 and 2,000 people are interviewed for each survey carried out. 4. How can such a small group be representative of the entire population? In order to ensure that the sample/survey group is representative of the population, the surveyors must ensure that the group reflects the characteristics of the whole. For instance, to get a general idea of who might win the Kenyan presidential election, only the views of registered voters in Kenya will be surveyed as these are the people who will be able to influence the election. -
Random Selection in Politics
Random selection in politics Lyn Carson and Brian Martin Published in 1999 by Praeger Publishers, Westport, CT Available for purchase from Praeger This is the text submitted to Praeger in February 1999. It differs from the published version in minor ways, including formatting, copy-editing changes, page numbering (100 pages instead of 161) and omission of the index. This version prepared August 2008 Contents 1. Introduction 1 2. Random selection in decision making 10 3. Direct democracy 26 4. Citizen participation without random selection 36 5. Citizen participation with random selection: the early days 43 6. Citizen participation with random selection: yesterday, today, and tomorrow 52 7. Sortition futures 65 8. Strategies 76 Appendix: Examples of citizen participation 84 Bibliography 93 Acknowledgments Brownlea, John Burnheim, Ned Crosby, Many people we’ve talked to find the Jim Dator, Mary Lane, Marcus Schmidt, idea of random selection in politics and Stuart White. Their input was unnatural and unwelcome. This didn’t valuable even when we decided on an deter us! Fortunately, there were a few alternative approach. Helpful comments enthusiasts who got and kept us going. were also received from Ted Becker, Alan Davies, Fred Emery, and Merrelyn Stephen Healy, Lars Klüver, and Ken Emery provided the original inspiration Russell. Others who provided many years ago as well as ongoing information are acknowledged in the conversations. text. The process of obtaining comments Ted Becker encouraged us to write has been stimulating because not all this book. On drafts, we received readers go with us all the way on extensive comments from Arthur randomness. -
13 Collecting Statistical Data
13 Collecting Statistical Data 13.1 The Population 13.2 Sampling 13.3 Random Sampling 1.1 - 1 • Polls, studies, surveys and other data collecting tools collect data from a small part of a larger group so that we can learn something about the larger group. • This is a common and important goal of statistics: Learn about a large group by examining data from some of its members. 1.1 - 2 Data collections of observations (such as measurements, genders, survey responses) 1.1 - 3 Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data 1.1 - 4 Population the complete collection of all individuals (scores, people, measurements, and so on) to be studied; the collection is complete in the sense that it includes all of the individuals to be studied 1.1 - 5 Census Collection of data from every member of a population Sample Subcollection of members selected from a population 1.1 - 6 A Survey • The practical alternative to a census is to collect data only from some members of the population and use that data to draw conclusions and make inferences about the entire population. • Statisticians call this approach a survey (or a poll when the data collection is done by asking questions). • The subgroup chosen to provide the data is called the sample, and the act of selecting a sample is called sampling. 1.1 - 7 A Survey • The first important step in a survey is to distinguish the population for which the survey applies (the target population) and the actual subset of the population from which the sample will be drawn, called the sampling frame. -
Using Survey Data Author: Jen Buckley and Sarah King-Hele Updated: August 2015 Version: 1
ukdataservice.ac.uk Using survey data Author: Jen Buckley and Sarah King-Hele Updated: August 2015 Version: 1 Acknowledgement/Citation These pages are based on the following workbook, funded by the Economic and Social Research Council (ESRC). Williamson, Lee, Mark Brown, Jo Wathan, Vanessa Higgins (2013) Secondary Analysis for Social Scientists; Analysing the fear of crime using the British Crime Survey. Updated version by Sarah King-Hele. Centre for Census and Survey Research We are happy for our materials to be used and copied but request that users should: • link to our original materials instead of re-mounting our materials on your website • cite this as an original source as follows: Buckley, Jen and Sarah King-Hele (2015). Using survey data. UK Data Service, University of Essex and University of Manchester. UK Data Service – Using survey data Contents 1. Introduction 3 2. Before you start 4 2.1. Research topic and questions 4 2.2. Survey data and secondary analysis 5 2.3. Concepts and measurement 6 2.4. Change over time 8 2.5. Worksheets 9 3. Find data 10 3.1. Survey microdata 10 3.2. UK Data Service 12 3.3. Other ways to find data 14 3.4. Evaluating data 15 3.5. Tables and reports 17 3.6. Worksheets 18 4. Get started with survey data 19 4.1. Registration and access conditions 19 4.2. Download 20 4.3. Statistics packages 21 4.4. Survey weights 22 4.5. Worksheets 24 5. Data analysis 25 5.1. Types of variables 25 5.2. Variable distributions 27 5.3. -
Analysis of Variance with Categorical and Continuous Factors: Beware the Landmines R. C. Gardner Department of Psychology Someti
Analysis of Variance with Categorical and Continuous Factors: Beware the Landmines R. C. Gardner Department of Psychology Sometimes researchers want to perform an analysis of variance where one or more of the factors is a continuous variable and the others are categorical, and they are advised to use multiple regression to perform the task. The intent of this article is to outline the various ways in which this is normally done, to highlight the decisions with which the researcher is faced, and to warn that the various decisions have distinct implications when it comes to interpretation. This first point to emphasize is that when performing this type of analysis, there are no means to be discussed. Instead, the statistics of interest are intercepts and slopes. More on this later. Models. To begin, there are a number of approaches that one can follow, and each of them refers to a different model. Of primary importance, each model tests a somewhat different hypothesis, and the researcher should be aware of precisely which hypothesis is being tested. The three most common models are: Model I. This is the unique sums of squares approach where the effects of each predictor is assessed in terms of what it adds to the other predictors. It is sometimes referred to as the regression approach, and is identified as SSTYPE3 in GLM. Where a categorical factor consists of more than two levels (i.e., more than one coded vector to define the factor), it would be assessed in terms of the F-ratio for change when those levels are added to all other effects in the model. -
MRS Guidance on How to Read Opinion Polls
What are opinion polls? MRS guidance on how to read opinion polls June 2016 1 June 2016 www.mrs.org.uk MRS Guidance Note: How to read opinion polls MRS has produced this Guidance Note to help individuals evaluate, understand and interpret Opinion Polls. This guidance is primarily for non-researchers who commission and/or use opinion polls. Researchers can use this guidance to support their understanding of the reporting rules contained within the MRS Code of Conduct. Opinion Polls – The Essential Points What is an Opinion Poll? An opinion poll is a survey of public opinion obtained by questioning a representative sample of individuals selected from a clearly defined target audience or population. For example, it may be a survey of c. 1,000 UK adults aged 16 years and over. When conducted appropriately, opinion polls can add value to the national debate on topics of interest, including voting intentions. Typically, individuals or organisations commission a research organisation to undertake an opinion poll. The results to an opinion poll are either carried out for private use or for publication. What is sampling? Opinion polls are carried out among a sub-set of a given target audience or population and this sub-set is called a sample. Whilst the number included in a sample may differ, opinion poll samples are typically between c. 1,000 and 2,000 participants. When a sample is selected from a given target audience or population, the possibility of a sampling error is introduced. This is because the demographic profile of the sub-sample selected may not be identical to the profile of the target audience / population. -
A Computationally Efficient Method for Selecting a Split Questionnaire Design
Iowa State University Capstones, Theses and Creative Components Dissertations Spring 2019 A Computationally Efficient Method for Selecting a Split Questionnaire Design Matthew Stuart Follow this and additional works at: https://lib.dr.iastate.edu/creativecomponents Part of the Social Statistics Commons Recommended Citation Stuart, Matthew, "A Computationally Efficient Method for Selecting a Split Questionnaire Design" (2019). Creative Components. 252. https://lib.dr.iastate.edu/creativecomponents/252 This Creative Component is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Creative Components by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. A Computationally Efficient Method for Selecting a Split Questionnaire Design Matthew Stuart1, Cindy Yu1,∗ Department of Statistics Iowa State University Ames, IA 50011 Abstract Split questionnaire design (SQD) is a relatively new survey tool to reduce response burden and increase the quality of responses. Among a set of possible SQD choices, a design is considered as the best if it leads to the least amount of information loss quantified by the Kullback-Leibler divergence (KLD) distance. However, the calculation of the KLD distance requires computation of the distribution function for the observed data after integrating out all the missing variables in a particular SQD. For a typical survey questionnaire with a large number of categorical variables, this computation can become practically infeasible. Motivated by the Horvitz-Thompson estima- tor, we propose an approach to approximate the distribution function of the observed in much reduced computation time and lose little valuable information when comparing different choices of SQDs. -
Describing Data: the Big Picture Descriptive Statistics Community
The Big Picture Describing Data: Categorical and Quantitative Variables Population Sampling Sample Statistical Inference Exploratory Data Analysis Descriptive Statistics Community Coalitions (n = 175) In order to make sense of data, we need ways to summarize and visualize it. Summarizing and visualizing variables and relationships between two variables is often known as exploratory data analysis (also known as descriptive statistics). The type of summary statistics and visualization methods to use depends on the type of variables being analyzed (i.e., categorical or quantitative). One Categorical Variable Frequency Table “What is your race/ethnicity?” A frequency table shows the number of cases that fall into each category: White Black “What is your race/ethnicity?” Hispanic Asian Other White Black Hispanic Asian Other Total 111 29 29 2 4 175 Display the number or proportion of cases that fall into each category. 1 Proportion Proportion The sample proportion (̂) of directors in each category is White Black Hispanic Asian Other Total 111 29 29 2 4 175 number of cases in category pˆ The sample proportion of directors who are white is: total number of cases 111 ̂ .63 63% 175 Proportion and percent can be used interchangeably. Relative Frequency Table Bar Chart A relative frequency table shows the proportion of cases that In a bar chart, the height of the bar corresponds to the fall in each category. number of cases that fall into each category. 120 111 White Black Hispanic Asian Other 100 .63 .17 .17 .01 .02 80 60 40 All the numbers in a relative frequency table sum to 1. -
Third Party Election Spending and the Charter
ELECTIONSPENDING AND THE CHARTER 429 LIBERTE, EGALITE, ARGENT: THIRD PARTY ELECTION SPENDING AND THE CHARTER 0 ANDREW GEDDIS Both the federal government and the courts have le gouvernementfederal et /es cours de Justice ont brought about changes in election law. The author apportedes modificationsa la loi electorate.l 'auteur reviews these recent changes In the legal landscape revolt le.r recents changementsdans le cadre legal that surroundelection mies. Inparticular third party entourant/es reg/es electorates, tout particulierement electionspending. Thequestions of "whatrules exist" /es depenseselectorates de tiers. la question,a savoir and "who shall make them" are particularly « quelles sont les reg/es qui existent II et « qui les importantto the discussionas this area of law tries to me/Ira en place ,, est particulierement importante reconcile individual interestsin liberty and equality dans celle discussionetant donne que ce domainedu in a democracy.The trio of SupremeC our/ of Canada droit teme de reconcilierles interets individuelset la decisions, Libman v. Quebec (A.G.), Thomson notion de liberte et d'egalite d'une democralie.Les Newspapersv. Canada (A.G.) and Sauve v. Canada trois dkisions de la Cour supreme du Canada. (Chief Electoral Officer), reveal ambiguity In the notamment Libman c. le Quebec (A.G.). Thomson Court's rationalefor limiting Individual liberty at Newspapersc. le Canada (A.G.)et Sauve c. le Canada electiontime. Thisambiguity Is broachedIn the recent (Directeur general des elections), manlfestent Supreme Court of Canada case of Harper v. Canada I 'amblg1111erelativement au raisonnementde la Cour (A.G.)where the Courtaccepted that Parliamentmay de limiter la liberte individuellependant un scrutm. -
Collecting Data
Statistics deal with the collection, presentation, analysis and interpretation of data.Insurance (of people and property), which now dominates many aspects of our lives, utilises statistical methodology. Social scientists, psychologists, pollsters, medical researchers, governments and many others use statistical methodology to study behaviours of populations. You need to know the following statistical terms. A variable is a characteristic of interest in each element of the sample or population. For example, we may be interested in the age of each of the seven dwarfs. An observation is the value of a variable for one particular element of the sample or population, for example, the age of the dwarf called Bashful (= 619 years). A data set is all the observations of a particular variable for the elements of the sample, for example, a complete list of the ages of the seven dwarfs {685, 702,498,539,402,685, 619}. Collecting data Census The population is the complete set of data under consideration. For example, a population may be all the females in Ireland between the ages of 12 and 18, all the sixth year students in your school or the number of red cars in Ireland. A census is a collection of data relating to a population. A list of every item in a population is called a sampling frame. Sample A sample is a small part of the population selected. A random sample is a sample in which every member of the population has an equal chance of being selected. Data gathered from a sample are called statistics. Conclusions drawn from a sample can then be applied to the whole population (this is called statistical inference). -
Questionnaire Analysis Using SPSS
Questionnaire design and analysing the data using SPSS page 1 Questionnaire design. For each decision you make when designing a questionnaire there is likely to be a list of points for and against just as there is for deciding on a questionnaire as the data gathering vehicle in the first place. Before designing the questionnaire the initial driver for its design has to be the research question, what are you trying to find out. After that is established you can address the issues of how best to do it. An early decision will be to choose the method that your survey will be administered by, i.e. how it will you inflict it on your subjects. There are typically two underlying methods for conducting your survey; self-administered and interviewer administered. A self-administered survey is more adaptable in some respects, it can be written e.g. a paper questionnaire or sent by mail, email, or conducted electronically on the internet. Surveys administered by an interviewer can be done in person or over the phone, with the interviewer recording results on paper or directly onto a PC. Deciding on which is the best for you will depend upon your question and the target population. For example, if questions are personal then self-administered surveys can be a good choice. Self-administered surveys reduce the chance of bias sneaking in via the interviewer but at the expense of having the interviewer available to explain the questions. The hints and tips below about questionnaire design draw heavily on two excellent resources. SPSS Survey Tips, SPSS Inc (2008) and Guide to the Design of Questionnaires, The University of Leeds (1996).