Summary STA1610 - Introduction To Portage Statistics Module 1.

STA1610 - Introduction To Portage Statistics Module 1. Introduction to Statistics Note: For access to statistical tables and equations, please click "Help Files" on the upper right of any module/exam page. "Figures never lie, but liars will figure!" - attributed to Samuel Clemens (aka Mark Twain) How many times have we heard this famous quote? How many times does this quote come to mind when we hear the results to a poll and completely disagree with the results? Here in lies the difficulty with statistics. Not only do statistics need to be properly tabulated, they also have to properly address what is being analyzed. Statistics touch our lives every day of the year. Virtually every endeavor people are involved in uses statistical analysis to explain what has happened, what is currently going on or how to proceed in the future. Economics, politics, production, marketing, accounting, sports, and so on; all rely on statistics. Here are a few specifics where statistical analysis is used … Managers use statistics to understand and eliminate variations in production systems, Financial advisors use statistics to determine portfolio changes by studying stock market trends, Talk show pundits use statistics to determine public policy in response to political polls, Manufacturers use statistics to evaluate which gum most dentists recommend, Pittsburgh Pirate's fans use statistics to know what centerfielder Andrew McCutchen's batting average is with men in scoring position, Etc., etc., etc. With this said, everyone might as well give in and learn how to not only proper statistical analysis is calculated, but everyone should also understand how to properly collect and interpret the results. NursingABC - Module 4 of 17 8/6/2018, 9:17 AM What is Data? To begin the study of statistics, every student needs to first understand what is data. Data (plural of the word datum) are basically things about which information can be collected and analyzed. These "things" can be further characterized as people, numerical information, geographical areas, etc. A data set is an arranged collection of information that contains the various categories of data which were collected for a specific study. The element of a data set is simply the individual and unique entry in a data set about which data has been collected, analyzed and presented in the same manner. A variable is a particular, measurable attribute that the researcher believes is needed to describe the element in their study. Like the element, a variable can include categories characterized as people, numerical information, geographical areas, etc. While in some cases there will be only one variable needed to provide measurable information about the element, most of the time there will be many variables used in the study. All the information collected for each element in a study is called an observation. Table One is an example of a data set. Last Name First Name Student ID Class Campus Major MidTerm Exam Grade Final Exam Grade Final Grade Anderson Aubrey 13-3457 Junior Lafayette Nursing 87.00% 87.25% 87.13% Brown Avery 13-6427 Junior Brickland Literature 72.50% 69.25% 70.88% Clark Matthew 15-4497 Freshman Main Literature 46.00% 44.25% 45.13% Davis Hannah 13-3760 Junior Downtown Engineering 55.25% 52.50% 53.88% Garcia James 13-1698 Junior Brickland Nursing 83.25% 91.75% 87.50% Harris Isabella 14-3925 Sophomore Brickland Nursing 90.25% 86.25% 88.25% Jackson Ethan 15-8970 Freshman Main Engineering 100.00% 100.00% 100.00% Johnson Chloe Dec-70 Senior Downtown Engineering 80.50% 81.25% 80.88% Jones Jacob 14-4427 Sophomore Main Nursing 99.75% 100.00% 99.88% Lewis Connor 15-2062 Freshman Main Business 71.25% 83.00% 77.13% Martin Addison Dec-58 Senior Downtown Engineering 91.55% 95.10% 93.33% Martinez Nicholas 15-8951 Freshman Lafayette Engineering 98.75% 94.50% 96.63% Miller William 15-4488 Freshman Lafayette Business 86.00% 87.75% 86.88% Moore Ryan Dec-44 Senior Brickland Business 40.00% 54.25% 47.13% Robinson Charlotte 13-9471 Junior Lafayette Business 81.00% 82.50% 81.75% Rodriguez Hailey 14-9523 Sophomore Brickland Engineering 80.75% 89.00% 84.88% Smith John 14-4873 Sophomore Downtown Business 71.75% 61.25% 66.50% Smith John 15-1922 Freshman Main Engineering 94.25% 85.25% 89.75% Taylor Benjamin 15-3457 Freshman Downtown Engineering 95.25% 88.75% 92.00% Thomas Logan 14-7457 Sophomore Brickland Engineering 81.25% 76.25% 78.75% Thompson Landon Dec-03 Senior Main Business 73.00% 79.00% 76.00% Williams Emma 15-8413 Freshman Lafayette Nursing 88.50% 91.75% 90.13% Wilson Sophia Dec-93 Senior Main Literature 67.75% 71.25% 69.50% Table One: A sample of student grades from the Intro to Statistics course at Analysis State University at the end of the 2012 Spring Semester. Table One contains information from a random selection of students at the fictional Analysis State University. The researcher wants to investigate how students at different campuses, and in different majors, performed in the university's Intro to Statistics course. Looking at the table, it is easy to figure out what the elements of this study are … the students. The students (or elements) are identified not only by their first and last names but also their student ID number. The need for the student ID becomes evident upon closer inspection of the table: there are two John Smiths listed. As mentioned earlier in the definition of an element, there needs to be a unique characteristic to an element in order to differentiate one element from another and to also avoid duplicating information in a study. In this case, the university issues a unique student ID to every student in order to differentiate them and thus alleviate the potential error of mistaking one student for NursingABC - Module 5 of 17 8/6/2018, 9:17 AM another. In this study, each row of information is an observation taken at that moment about that element. Now let's will take a closer look at the different variables in the table: #1 Student ID As already discussed, this variable would be used to help to uniquely identify the element. #3 Class & #5 Major Both of these variables could be used as a way to effectively compare the different elements. Simply stated, they provide a means to either "compare apples to apples and oranges to oranges" or to determine if there is are any differences between the groups. #4 Campus This variable is could be used to determine if a geographical or spatial attribute has an influence on the element. #6 Mid-term Exam Grade, #7 Final Exam Grade & #8 Final Grade Each of these variables would be collected as way to evaluate the ability of the student. In this study, it is possible to randomly select different students (or elements) that possess one or more variable that have the same values. In other words … it is possible in this study that there could be two or more students which have the same name AND are in the same graduating class AND are attending classes on the same campus AND are majoring in same curriculum. The fact is, virtually every study has a potential where ALL the variables between the differing elements will have identical values. A further way of classifying data is to categorize it as either qualitative or quantitative. Qualitative data basically describes something about the element. Here are a few examples of qualitative data: where is it located, what is its color or size, or in the case of Table One what is the student's major, what graduating class is the student in, etc. Quantitative data always answers the questions of how much or how many. Examples of quantitative data from Table One would be the student's Mid-term Exam grade and Final GPA … other quantitative data could be the number of DVDs sold, gross profit earned, etc. While quantitative data is ALWAYS numerical, qualitative data can be either numerical or non-numerical. The key difference between qualitative and quantitative data is that mathematical operations only make sense when performed on quantitative data. There are also two different types of data collection. Cross-sectional data is where a researcher would collect information or measurements for each variable on an element at the same (or roughly same) point. The point of reference could be a time or date, a point in space (such as a split or lap time in a race) or anything else that provides a basis of when the data stopped being collected of measure. The cross-sectional data point of reference for Table One is the end of the Spring Semester in 2012. Time series data are data that is collected over a specific period of time. Chart One shown below is a simple example of a time series. The data collected is a 2 ½ year review of the average monthly stock price of U.S. Steel Corporation. Each data point represents the average value of the stock for the given month calculated by averaging the daily closing price of the stock over the given month. NursingABC - Module 6 of 17 8/6/2018, 9:17 AM NursingABC - Module 7 of 17 8/6/2018, 9:17 AM Where to Find Data Research data can be gathered in one of two ways: 1) Through existing information that was already collected and is stored somewhere. 2) Through direct collection of information by conducting surveys, sending out questionnaires, performing experimental testing, etc. Since the dawn of civilization, every well run organization has collected and maintained information. It is well known that tax collectors in ancient Rome kept detailed records of who paid their taxes … and that was over 2000 years ago!! Today, with the advent of computers in everyday life, data is collected and stored every minute of every day. Businesses keep records on employees, suppliers, customers, inventory, accounts receivable, etc. The United States government keeps records on general population information through the census every 10 years, yearly tax collections, the money supply, business activity, etc. Schools keep records on current students, alumni, benefactors, research projects, grants, student loans, etc. A person can find a wealth of free information if they only know where to look. Nearly every department of the U.S. government has a website where citizens can get information: The Census Bureau ( the U.S. population. The World Factbook run by the CIA ( information on countries around the world. The U.S. Department of Commerce ( The Centers for Disease Control has compiled an entire library of healthcare related information for the public( /nchs/fastats/). A person can also find a wealth of free data from various news sources such as the Associated Press, the Wall Street Journal and Investor's Business Daily. Another key way to gather information is to simply buy it. There are also lots of companies who collect data and offer the information for sale. A simple internet search will list hundreds, if not thousands, of reputable (and some not so reputable) companies that are willing to share the information they have collected for a fee. One of the most famous of these for profit companies is called A.C. Nielsen. This company has been the primary collector of market information for the radio and television industries for over 75 years. Another well known data collection company is called the Dow Jones Company. Dow Jones provides businesses and investors with up-to-the-minute financial information on companies across the globe. Even though there are thousands of places where people can get existing data, more times than not, the information a researcher needs is not found anywhere. In cases like this, the researcher needs to collect the necessary data themselves through a statistical study. There are two basic types of statistical studies: experimental and observational. An experimental study begins with a researcher making a thorough review of the given situation. During this review, the researcher identifies the variables that have an influence on the individual elements in the study. During the actual study, the researcher will then attempt to manipulate some of the variables in the study while holding others constant. The researcher will then compare the elements in the study to each other in order to understand how the manipulated variables impacted the element being studied. In an observational study, the researcher collects information not by influencing the variables in the study, but by simply observing the variable in action. The observation can be passive or active. A passive observation is when the researcher has no interaction with the subject but collects information from a distance. An active observation is when the researcher interacts with the subject to some degree. This interaction can be as non-obtrusive as simply handing out a survey for the subject to fill out or can be highly interactive as is the case for the researcher asking a slew of questions on a questionnaire or by conducting a focus group analysis. Now let's look at a few simple applications using these research principles. Mr. Benn is a fictitious small business owner who owns Gentle Benn's Bakeries. He currently has two bakeries that are located across the street from the front gates of the Downtown and Lafayette campuses of Analysis State University. Mr. Benn is considering expanding not only his business operations but also would like to add items to his menu. To determine if it is feasible to expand his business, Mr. Benn first gathered information on his current customer base and also organized his NursingABC - Module 8 of 17 8/6/2018, 9:17 AM current sales data. Through simply counting how many customers purchase goods at his store each day for a couple weeks and also observing the types of customers entering his shops over that period, he has determined that each shop gets 300 - 400 customers a day and his customers are roughly 60% college students, roughly 20% are business owners with shops located close to his bakery and the remaining 20% are customers who come in without any detectable regularity. Now that he has some customer data, Mr. Benn will then review his current sales data to determine what sales levels are necessary to produce a profit level high enough to make the new shop cost effective. Mr. Benn can now go to the U.S. government websites to gather demographic information on the population around his current locations and the areas he is considering expanding into. These websites will provide information on the population such as age groups, income levels, types of businesses in the area, etc. By comparing the collected business information he has collected to the various local populations, Mr. Benn can decide whether the populations at his proposed expansion locations are capable of generating the necessary sales required to run a successful business.