Lecture 2: Introduction to Data and Sampling - EC 220 Business Statistics PDF

EC 220: Business Statistics INTRODUCTION TO DATA AND SAMPLING I. Introduction Recall: Statistics is the art and science of collecting, analyzing, presenting and interpreting data. It provides us with tools to analyze data in order to help us make informed decisions. Example: Choosing th...

EC 220: Business Statistics INTRODUCTION TO DATA AND SAMPLING I. Introduction Recall: Statistics is the art and science of collecting, analyzing, presenting and interpreting data. It provides us with tools to analyze data in order to help us make informed decisions. Example: Choosing the right graduate program We can analyze this problem through the following series of steps What is the issue? What variables/information do we need or have? Define variables? How do we measure this information (measure variables)? Where do we get the data from? Analysis (describing and summarizing the data, called Descriptive statistics) Interpretation (Inferential statistics) Implementation or decision This process is how statistical project is conducted. 1  EC 220: Business Statistics II. Business application Business Week writes that “Congress is currently considering lowering the 35% federal tax rate. But a lot of companies don't need help from Washington; they've been finding legal ways to shrink their tax bill for years. We asked the analysts at Capital IQ (a division of Standard & Poor's) to cull the cash taxes (i.e. actual checks) that the companies of the S&P 500 paid to the tax collector over the past five years and then look at how that compares to their earnings before income taxes 1.” Business Week compiled a list of 100 companies that sent in the smallest checks. A portion of the data set is shown below: Rank Cash based on 5 yr avg taxes Effective 5 yr avg Company (in %) paid tax rate Sector 1 CMS ENERGY 0 0 NM Utilities 2 CHESAPEAKE ENERGY 0.3 0.3 38.5 Energy 3 BOEING 0.7 28 30.9 Industrials 4 BROADCOM 1.1 3.9 NM Information Technology 5 FPL GROUP 1.2 30 23.7 Utilities 6 ALLEGHENY ENERGY 1.3 3.2 35.1 Utilities CITIZENS 7 COMMUNICATIONS 1.6 5.4 35 Telecommunication Services AMERICAN CAPITAL 8 STRATEGIES 1.8 21 1.2 Financials 9 AKAMAI TECHNOLOGIES 1.9 3.5 41.7 Information Technology 10 DIRECTV GROUP 2 30.3 37.7 Consumer Discretionary 11 NVIDIA 2.2 26.6 9.4 Information Technology 12 XCEL ENERGY 2.3 -13.3 24.2 Utilities 13 AMAZON.COM 2.8 15 49.6 Consumer Discretionary 14 YAHOO! 2.9 66 37.8 Information Technology 15 SOUTHWEST AIRLINES 3.2 15 36.8 Industrials 16 EBAY 3.3 179.2 27.2 Information Technology 17 LSI LOGIC 3.4 8 8.5 Information Technology 18 NETWORK APPLIANCE 4.3 34.7 17.2 Information Technology 19 HOSPIRA 4.8 28.6 26.8 Healthcare L-3 COMMUNICATIONS 20 HOLDINGS 5.2 61.3 35.7 Industrials 21 ALTERA 6.2 38.9 10.1 Information Technology 22 TERADYNE 6.3 6.8 12 Information Technology COGNIZANT TECHNOLOGY 23 SOLUTIONS 6.6 14.1 16.2 Information Technology 24 ENTERGY 6.7 -147.4 28.1 Utilities 25 CITRIX SYSTEMS 7 2.3 24.7 Information Technology 1 http://bwnt.businessweek.com/interactive_reports/corporate_taxes/ 2  EC 220: Business Statistics Concepts Elements – entities on which data are collected. Variable – a characteristic of interest for the element. Observation – the set of measurements obtained for a particular element. Population – the set of all the elements of interest in a study. Is it possible to collect information on the entire population? Why? Data can be classified as one of the following types: Qualitative data Quantitative data Scales of measurement To collect data you must be able to measure it. There are four scales of measurement: two associated with qualitative data and two with quantitative data Nominal: Where names or numbers are used as identifiers. E.g. M/F, states, major, sports jersey numbers Ordinal: An ordinal scale represents an ordered series of relationships or rank order. E.g. pain measurement, rankings of tennis players or professional golfers Interval: A scale that represents quantity and has equal units but which zero is simply an arbitrary point. E.g. temperature, sea level Ratio: A scale that represents a quantity and has equal units (similar to interval in that regard), but the scale has an absolute zero. E.g. $ in your bank account, height, weight, area. 3  EC 220: Business Statistics III. Sampling Sample – a subset of the population. There are two types of sample: Non-random sample- select items or individuals without knowing their probability of selection (i.e. a non-probability sample) Random sample- items are selected based on known probabilities of selection (i.e. a probability sample of some kind) Example: Suppose I select a sample of five students from a class of 25. What is the likelihood of any one of you being selected? Sampling Issues Coverage error – when there is selection bias in the sample it results in coverage error Non-response error –in a survey, people sometimes do not respond to the survey Measurement error –it is usually the result of mistakes in recording the data (observational error) Sampling error – this is the result of random variations in the sample Descriptive Statistics Descriptive statistics are methods of organizing, summarizing, and presenting sample data in an informative way. Examples: Inferential Statistics Inferential statistics are the methods used to determine something about a population based on a sample. Examples: Sample Statistics versus Population Parameters 4