Chapter 1 - Kαλι M²ρα!1 Introduction (p. 1)What is statistics? It consist of three major areas:• Data Collection: sampling plans and experimental designs• Descriptive Statistics: numerical and graphical summaries of the data collected from asample• Inferential Statistics: estimation, confidence intervals and hypothesis testing of parametersof interestStatistical procedures are part (steps 2-5 below) of the Scientific Method first espoused bySir Francis Bacon (1561-1626), who wrote “to learn the secrets of nature involves collecting dataand carrying out experiments.” The modern methodology:1. Observe some phenomenon2. State a hypothesis explaining the phenomenon3. Collect data4. Test: Does the data support the hypothesis?5. Conclusion. If the test fails, go back to step 2.Application of statistical thinking does not include whining or emotional arguments. If youencounter a “scientific claim” that you disagree with, scrutinize the steps of the scientific methodused. “Statistics don’t lie, but liars do statistics.” - Mark Twain.What is mathematical statistics?: The study of the theoretical foundation of statistics.What is probability theory?: The theoretical foundation of statistics.POPULATION vs. SAMPLE:Individuals, subjects, units: The objects from which data is collected.Individuals may be people, places, animals, things, even time periods.Population: The entire group of individuals, which can be either existent orconceptual, that we want information about. For example: all grizzly bears inYellowstone National Park; all G.E. light bulbs (made now and in the future);all tosses with a weighted dieSample: A subset of the population from which data is collected. For example:22 tagged grizzly bears in Yellowstone National Park; 1 box G.E. light bulbs; 100tosses with a weighted die.Typically, it is unrealistic to obtain data from the entire population of interest. Soone collects data from a sample and uses the sample results to draw conclusionsabout the population. This process is called Inference.1GOAL OF STATISTICS: To make an inference about a population based on informationcontained in a sample from that population and to provide an associated measure of goodnessfor the inference.1Variable: Any characteristic of an individual which can be measured.Two Types of Variables:• Categorical (or Qualitative) - The possible values are categories. Beware, some categorynames are actually numbers (e.g. zip codes and dates)• Numerical (or Quantitative) - The possible values are numbers so that mathematicaloperations, such as averaging, make sense!QUESTION: Categorical or Numerical? Individuals? Population ofinterest?1. Lifetime of a battery:2. Type of battery:3. Distance to school:4. UPC:Two Types of Numerical Variables:• Discrete - The possible values are isolated points on the number line. Discrete variablescan be either:– finite (e.g. the number of beers left in a six pack: 0, 1, 2, 3, 4, 5 or 6)– infinite (e.g. the number of (full) minutes until the next terrorist attack: 0, 1, 2, 3,. . . , ∞).• Continuous - The possible values are an interval on the number line (e.g. the distancebetween any two students in this classroom (in feet) is in the interval [0,50) - all realnumbers between 0 and 50, including 0 and excluding 50).QUESTION: Discrete or Continuous?1. Amount of money on you:2. Your height:3. Reaction time:4. Number of children you have:1p.2-321.1 The statistical software package RThe authors of your textbook offer a set of applets for use online athttp://www.thomsonedu.com/statistics/book_content/0495110817_wackerly/applets/seeingstats/index.htmlFeel free to use these! However, students last semester reported problems accessing these appletsfrom the computers available in Math. I am not aware of Windows machines having anyproblems. We’ll be using the software package R whenever convenient. It’s free, powerful,and ubiquitous.1.1.1 Obtaining and Installing RHere’s some install instructions:21. Get on the Internet and go to the web address http://cran.r-project.org. This is the“official” site of the The Comprehensive R Archive Network (CRAN). Bookmark thisaddress. Lots of information (manuals, answers to frequently asked questions, etc) can bedownloaded from this site.2. The first box on this page is labeled Download and Install R. In that box, click on theappropriate link. For example, MAC users will click on MAC OS X and Microsoft Windowsusers will click on the link Windows. The rest of these instructions are specific to Windowsusers.3. On the new page, click on the link named base.4. Click on the link Download R 2.13.1 for Windows. Download the setup program R-2.13.1-win.exe to the hard drive on your computer.5. Exit from your Internet Browser and open Windows Explorer. Go to the folder in whichyou saved R-2.13.1-win32.exe and run the program.6. You will be guided through the installation by a Setup Wizard.There are many excellent resources for using R. For example, check out http://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf written by John Veranzi.Special-purpose software routines are bundled as separate “packages.” Some packages areautomatically downloaded when base R is downloaded. To download additional packages,execute R on your PC and then click on the tab Packages from one of the tabs at the topof the screen. From the drop down menu, click on Install package(s) ... and then choose thepackage(s) that you want to download. The packages that we may need to download for thiscourse are the following:• lattice• pastecsMASS is another package which we will be using which you do NOT need to download becauseit is a part of base R.2Revised from what appears in Chapter 7.1 of Robert Boik’s Course Notes: Statistics for ResearchersSTAT401 FALL 2006.31.1.2 Entering Data into RA researcher is interested in determining whether adding a certain type of bacteria, called PC,helps increase the firmness of cottage cheese. Seven dairies make two identical batches of cottagecheese, one with and one without the bacteria PC. The results of the experiment are in a textfile called “dairy.txt” which is shown below (and available at the course web site):Farm Treatment FirmnessA withPC 68A withoutPC 61B withPC 75B withoutPC 69C withPC 62C withoutPC 64D withPC 86D withoutPC 76E withPC 52E withoutPC 52F withPC 46F withoutPC 38G withPC 72G withoutPC 68Text data files that are tab or space delimited can be imported into R (xls can also be