11.220: Quantitative Reasoning and Statistics for Planning IInformation about the test-out examThe exam will be held on Friday, February 3rd, time and room can be found at http://web.mit.edu/11.220/www06/brushup/. Please bring with you to the exam pens/pencils and a calculator. You may also bring up to 2 textbooks and 1 binder/set of *your* notes with you. We will supply copies of any statistical tables needed to complete the exam (although you’re welcome to use tables in your textbooks if you prefer).The QR staff will grade the exams over the weekend, and we hope to place the results in your mail files on Monday, February 6th. Please note that we will give partial credit for problems that you attempt but do not complete or make an error in completing. Thus, as you prepare for the exam, get in the habit of showing your work.The possible outcomes of the test-out exam are that (1) you pass out of 11.220 entirely; (2) you partially pass outand must complete one or more assignments and/or attend one or more specific lectures to address a particular deficiency; or (3) you must take QR.Information about the brush-up sessionsThe brush-up sessions will take place on January 30, 31, and February 1st, time and room can be found at http://web.mit.edu/11.220/www06/brushup/. The brush-up sessions are meant to refresh your memory and give you an opportunity to ask questions that arise while you are conducting your preparation for the exam over IAP. Please note that it is not designed to teach you QR/stats that you haven’t had before! The instructor will go through the topics covered in the QR syllabus (and the review below), and will have a few examples prepared for you. However, they will respond to student demand for assistance on particular topics—if you come prepared with questions the sessions will be much more valuable to you. By questions, we mean questions about QR/statsprinciples and tools, not questions about the test-out exam. You should review the sample test-out exam, as well as past midterm and final exams, on the class website for that type of information.The material covered on the 30th will not be the same as that covered on the 31st; that is, to take full advantage of the brush-up session you will need to come on all days. You are welcome, however, to come for as little or as much of the sessions as you like. We know that some of you are taking other IAP classes during this week. Feel free to leave the brush-up and come back when your other class finishes.Brush-up reviewThe following list of questions is meant to guide your preparation for the test-out exam. The answers to all these questions can be found by reviewing the class textbooks, and solution sets to past problem sets and exams. Note that a big part of 11.220 is developing the ability to explain a QR / stats concept in a way that someone with no training in statistics could understand. This is important for planners, and at least one third of the points on the test-out exam will be related to your ability to express concepts in clear, simple language. We know that this is not easy to do well, and it is a skill that many stats classes overlook. Make sure you understand the ideas behind the formulas and symbols, and that you can express them clearly for the exam.Argumentation:What is a premise? What is a conclusion?What is the difference between an inductive and a deductive argument? Which is more relevant to statistics and why?Types of data:Know the difference between ordinal, nominal, and interval/ratio data.Know which quantitative and statistical tools can be used with which kind of data.Measurement:What is a construct? What is an indicator?What is a valid indicator? What about a reliable indicator? Can you have one without the other?What is a biased indicator?Univariate data summary and analysis:Be able to look at summary statistics and/or a graph and say something about the argument summarized therein.Understand what a mean, median, quartile, and mode are and how to calculate them for grouped and ungrouped data.Understand what an outlier is and how to detect it.What kind of analysis might be affected by outliers? How might you deal with outliers in such cases?Understand what variance & standard deviation are and how to calculate them for grouped and ungrouped data.Know how to compute and interpret a Z-score.Bivariate data summary & analysis:Understand the conceptual distinctions between dependent and independent variables.Know how to interpret scatterplots, graphs, and contingency tables and say something about the argument summarized therein. Understand (Pearson’s) correlation: what it means, how to ‘eyeball’ values for a set of data, and the principlebehind how it’s computed (note that you will not have to compute it yourself).Understand the conceptual distinctions between causation and association or correlation. How is statistics related to “proving causality”?What is confounding and why is it a problem for quantitative analysis?Regression analysis:What is the purpose of OLS regression analysis? For what kind of data can this tool be used?What is the principle behind choosing where to put the OLS regression line through a set of data?Know how to interpret the values derived from a regression equation (slope, intercept, y-hat, error or residual). (You will not have to compute the slope or intercept values for a regression line.)Know how to compute and interpret predicted values of the dependent variable, as well as impacts of changes in the independent variable value, using a regression equation.Know how to compute and interpret errors (residuals) using a regression equation.Know what r2 is, the principle behind its computation (you will not have to compute it yourself), and how to interpret its value.Indices:Know what indices are and how to interpret index values relative to the base and to one another.Sampling:Know the terminology of sampling: target population, parent population, sample, census.What are the most frequent sources of bias in sampling? Know how to evaluate a sampling strategy described to you in terms of these types of bias.Be able to recognize the elements that comprise the most common sampling strategies: random sampling, systematic sampling, the use of stratification, etc., and their objectives.Why is the simple random sample often considered the “gold standard” in research that uses statistical analysis?Probability:Understand the concept of