MA 331 Intermediate StatisticsSlide Number 2GradesGrades (cont.)Grades (cont.)TextbooksRData, Data, Data, all around us !ExampleWhat is statistics?Structure of the courseChapter 1Variable types:Information on employees of CyberstatnetDistribution of a variable: For the Categorical VariablesBar GraphPie ChartEXAMPLE - Child poverty before and after government intervention—UNICEF, 1996 ExerciseGraphical tools for quantitative dataStemplot example (FYI)Stemplot (FYI)Back-to-back stemplot (FYI)Histograms (example)Histogram (cont)Frequency TableUsing RExamining distributionsInterpreting histogramsMost common distribution shapesSlide Number 32What do you see?Quantitative Variables-Graphical DisplaySlide Number 35Newcomb’s data (dealing with outliers)OutliersTime plots. Newcomb’s data.Slide Number 39OutliersHow to create a histogramSlide Number 42IMPORTANT NOTE: Your data are the way they are. Do not try to force them into a particular shape.Time seriesSlide Number 45Slide Number 46Slide Number 47Exercises: Learn to input data in RSummaryMA 331 Intermediate StatisticsFall 2008Webpage:http://www.math.stevens.edu/~ifloresc/Teaching/2008-2009/index331.html Instructor : Ionut Florescu Office: Kidde 227 Phone 201-216-5452 Office hours: TTh 11:00-12:00, or by appointment. Please print off the course information posted on web. Email: [email protected] Mailbox: in Math. Dept office.Grades Homework (30%) – almost every week, usually due on Thursdays.  Quizzes and attendance (10%) – there will be a few quizzes given during the course of the semester. Attendance is not mandatory, however if you get into the habit of skipping the lecture I will deduct points. Participation in the lecture is rewarded here as well. Final exam (30%) – during the finals week, closed books/notes.Grades (cont.) Project (30%) There are two parts of the project. The students are supposed to work in groups of maximum 4. For the first part of the project you will be required to find an interesting dataset suitable for analysis. You will write a proposal detailing a description and interesting features of the dataset, questions that would be useful to answer, and proposed methods. For the second part of the project you will implement methods learned in class to analyze the dataset from the first part of the project.Grades (cont.) You should assume regular cutoffs (90%-100% A etc.), however depending on the performance of the class the final percentages may be curved. R is needed for the class. You will need to use it for the project and homework problems and I may test your knowledge of R in the exam and quizzes.TextbooksIntroduction to the Practice of Statistics, 4th edition, by David S. Moore and George P. McCabe.Introductory Statistics with R, by Peter Dalgaard.R Please see the Introduction to R files on the website. You are expected to read the second textbook and familiarize yourself with R If you need help ask questions and seek answers from your project mates, class mates and myselfData, Data, Data, all around us ! We use data to answer research questions What evidence does data provide?Example 1:Subject SBP HR BG Age Weight Treatment1 120 84 100 45 140 12 160 75 233 52 160 13 95 63 92 44 110 2. . . . . . . How do I make sense of these numbers without some meaningful summary?Example Study to assess the effect of exercise on cholesterol levels. One group exercises and other does not. Is cholesterol reduced in exercise group? people have naturally different levels respond differently to same amount of exercise (e.g. genetics) may vary in adherence to exercise regimen diet may have an effect exercise may affect other factors (e.g. appetite, energy, schedule)What is statistics?• Recognize the randomness, the variability in data.• “the science of understanding data and making decisions in face of variability”• Design the study• Analyze the collected Data *• Discover what data is telling you…Structure of the course Part I: Data: Analysis and production Examine, organize and summarize Part II: Statistical Inference Formal Method of drawing conclusions Formal Statistical Tests Testing the reliability of conclusions Part III: Advanced Statistical Inference Analyzing relationships between 2 or more variablesChapter 1 Individuals – objects described by a set of data (people, animals, things) Variable – characteristic of an individual, takes different values for different subjects. The three questions to ask :  Why: Purpose of study? Who: Members of the sample, how many? What: What did we measure (the variables) and in what units? Example:  In a study on how the time spent partying affects the GPAvariables like age, student’s major, height, weight were also recorded…Variable types: Categorical – outcomes fall into categories Quantitative – outcome is a numberContinuous: height, weight, distanceCan take any value within a rangeDiscrete : number of phone calls made every week, number of accidents on I 1/9, number of students getting A in Math 331 this Fall Can not take all possible values (integers here) Arithmetic operations like addition subtraction, etc. are meaningfulInformation on employees of CyberstatnetDistribution of a variable: What values a variable takes How often the variable takes those values (frequency)Preliminary Analysis of Variables and their distributions: Display variables graphically (with pictures) Basic Descriptive Statistics (with numbers)For the Categorical Variables Graphical Displays: enable us to see the distribution of the variable Bar Graphs (height of each column represents the counts in the respective category). Pie charts (each slice of the pie represents the percent from the total). To find the distribution of the categorical variable: List Categories Indicate count or percent of individuals in each category Read pages 75-80 from the R textbookBar GraphPie ChartEXAMPLE - Child poverty before and after government intervention—UNICEF, 1996 What does this chart tell you?•The United States has the highest rate of child poverty among developed nations (22% of under 18).•Its government does the least—through taxes and subsidies—to remedy the