Chapter 1: Data and Statistics GBS221, Class January 28, 2013 Notes Compiled by Nicolas C. Rouse, Instructor, Phoenix College

Transcription

1 Chapter Objectives 1. Obtain an appreciation for the breadth of statistical applications in business and economics. 2. Understand the meaning of the terms elements, variables, and observations as they are used in statistics. 3. Obtain an understanding of the difference between qualitative, quantitative, cross-sectional and time series data. 4. Learn about the sources of data for statistical analysis both internal and external to the firm. 5. Be aware of how errors can arise in data. 6. Know the meaning of descriptive statistics and statistical inference. 7. Be able to distinguish between a population and a sample. 8. Understand the role a sample plays in making statistical inferences about the population. 1. Statistical Applications in Business and Economics Statistics is defined as the art and science of collecting, analyzing, presenting, and interpreting data. In accounting, public firms use statistical sampling procedures when conducting audits for their clients. For example, suppose an accounting firm wants to determine whether the amount of accounts receivable shown on a client s balance sheet fairly represents the actual amount of accounts receivable. Usually the large number of individual accounts receivable makes reviewing and validating every account too time-consuming and expensive, so instead the audit staff selects a subset of the accounts, which we call a sample. After reviewing the accuracy of the sample accounts, the auditors draw a conclusion as to whether or not the accounts receivable amount on the balance sheet is acceptable. In economics, economists frequently provide forecasts about the future of the economy or some aspect of it. They use a variety of statistical information in making such forecasts. For example, in forecasting inflation rates, economists use statistical information such as the Producer Price Index, the unemployment rate, and manufacturing capacity utilization. In marketing, electronic point-of-sale scanners at the checkout stand is used to collect data for a variety of marketing research applications. For example, data suppliers such as AC Nielsen and Information Resources, Inc. purchase point-of-sale scanner data from grocery stores, process the data, and then sell statistical summaries of the data to manufacturers. Manufacturers spend a lot of money (in the hundreds of thousands) per product category to obtain this scanner data. Manufacturers also purchase data and statistical summaries on promotional activities such as special pricing and the use of in-store displays. Brand managers can use the scanner statistics and promotional activity statistics to gain a better understanding of the relationship between promotional activities and sales. In production, a variety of statistical quality control charts are used to monitor the output of a production process. In particular an x-bar chart can be used to monitor the average output. For example, suppose a machine fills containers with 12 ounces of a soft drink. Periodically, a production worker selects a sample of containers and computes the average number of ounces in the sample. This average, or x-bar value, is plotted on the x-bar chart. A plotted value over the upper control limit indicates overfilling, and a plotted value below the lower control limit indicates underfilling. In finance, financial analysts use a variety of statistical information to guide their investment recommendations. In the case of stocks, the analysts review a variety of financial data including price/earnings ratios and dividend yields. By comparing the information for an individual stock with information about the stock market averages, a financial analyst can begin to draw a conclusion as to whether an individual stock is over- or underpriced. These conclusions help analysts make buy, sell, or hold recommendations for stocks. 2. Elements, Variables, and Observations Data are facts and figures collected, analyzed, and summarized for presentation and interpretation. All the data collected in a particular study are referred to as the data set for the study. In table 1.1 on page 5, a data set containing information on 25 companies that are part of the S&P 500 is presented. Page 1 of 5

2 Elements are entities on which data is collected. For this data set, each individual company s stock is an element and these element names appear in the first column. So how many elements does the data set have? It has 25! A variable is a characteristic of interest for the elements. There are five variables in the data set from table 1.1. These include exchange (where the stock is traded N is for NY Stock Exchange and NQ is for NASDAQ Nat l. Market), ticker symbol (abbreviation to identify stock on exchange listing), BusinessWeek Rank (a number to measure company strength), Share Price ($) (The closing price on 2/28/05), and Earnings Per Share ($) (For most recent 12 months). Measurements collected on each variable for every element in a study provide the data. The set of measurements obtained for a particular element is called an observation. The set of measurements for the first observation (Abbott Laboratories) is N, ABT, 90, 46, and The total # of data values in table 1.1 is 25X5=125. Data collection often requires one of the following scales of measurement: nominal, ordinal, interval, or ratio. The scale of measurement determines the amount of information contained in the data and indicates the most appropriate data summarization and statistical analyses. When the data for a variable consist of labels or names used to identify an attribute of the element, the scale of measurement is considered a nominal scale. For example, referring back to the data in Table 1.1, we see that the scale of measurement for the exchange variable is nominal since N and NQ are labels used to determine where the company s stock is traded. Keep in mind that where nominal scales are used, in addition to non-numeric codes (such as N and NQ), numeric codes may also be used. For example a 1 could be used to denote NYSE and 2 could be used to denote NASDAQ. The scale of measurement is called an ordinal scale if the data exhibit the properties of nominal data and the order or rank of the data is meaningful. Again, a numeric or non-numeric code may be used. In table 1.1, the BusinessWeek rank is from This shows that a non-numeric code may be used. Another example would be when a customer rates a company s customer service as excellent, good, fair, or poor. Because the data obtained are the labels of excellent, good, fair, or poor, the data have the properties of nominal data. In addition, the data can be ranked or ordered with respect to the service quality. The quality of service by employee can be ranked in order. The scale of measurement for a variable becomes an interval scale if the data show the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Keep in mind that interval data are always numeric. SAT scores are an example of interval-scaled data. The scale of measurement for a variable is a ratio scale if the data have all the properties of interval data and the ratio of the two values is meaningful. Variables such as distance, height, weight, and time use the ratio scale of measurement. This scale requires that a zero value be included to indicate that nothing exists for the variable at the zero point. Let s compare the cost of a luxury SUV to the cost of a hybrid automobile. If the cost of the luxury SUV is $57,000 and the cost of the hybrid is $19,000, the ratio property shows that the SUV is $57K/$19K = 3 times the cost of the hybrid. 3. Qualitative, Quantitative, Cross-sectional, and Time Series Data Data can be classified as either categorical/qualitative or quantitative. The statistical analysis that is appropriate depends on whether the data for the variable are qualitative (categorical) or quantitative. There are more alternatives for statistical analysis when the data are quantitative. Data that can be grouped by specific categories are referred to as categorical (or qualitative) data. Categorical data use either the nominal or ordinal scale of measurement. Data that use numeric values to indicate how much or how many are referred to as quantitative data. Quantitative data are obtained using either the interval or ratio scale of measurement. Values can be numeric or non-numeric. Appropriate statistical analyses are rather limited. We can summarize categorical data by counting the number of observations in each category or by computing the proportion of the observations in each category. Even when categorical data has a numeric code, you cannot use arithmetic operations since no meaningful results would arise. Page 2 of 5

3 Data that use numeric values to indicate how much or how many are referred to as quantitative data. Quantitative data are obtained using either the interval or ratio scale of measurement. Arithmetic operations provide meaningful results for quantitative variables. For example, quantitative data may be added and then divided by the number of observations to compute the average value. This average is usually meaningful and easily interpreted. In general, more alternatives for statistical analysis are possible when data are quantitative. Data can be numeric or non-numeric, and uses the nominal or ordinal scales of measurement. Quantitative data on the other hand only comprises of numeric data and uses the interval or ratio scales of measurement. Cross-sectional data are data collected at the same or approximately the same point in time. The data in table 1.1 are cross-sectional because they describe the five variables for the 25 S&P 500 companies at the same point in time. Another example of this would be data detailing the number of building permits issued in June 2006 in each of the counties of Ohio. Time series data on the other hand are data collected over several time periods. For example, figure 1.1 provides a graph of the U.S. city average price per gallon for conventional regular gasoline. The graph shows the price rising the first half of 2005 then falling the second half of Gas prices increased until September 2005 and decreased thereafter. Graphs of time series data help analysts understand what happened in the past, identify any trends over time, and project future levels for the time series. Figure 1.2 shows the variety of forms time-series data graphs. 4. Sources of Data Data can be obtained from existing sources or from statistical studies designed to collect new data. In some cases, data needed for a particular application already exist. Companies maintain a variety of databases about their employees, customers, and business operations. Data on employee salaries, ages, and years of experience can be obtained from internal personnel records. In Table 1.2 on page 10, you can see that production records, inventory records, sales and credit records, and customer profiles may also be found within internal records. There are also organizations that specialize in collecting and maintaining data. Dun and Bradstreet, Bloomberg, and Dow Jones & Company are three firms that provide extensive business database services to clients. The U.S. Department of Labor maintains considerable data on employment rates, wage rates, size of the labor force, and union membership. Table 1.3 on page 11 shows governmental agencies and the data they provide. Industry associations, such as the Travel Industry Association of America maintains travel-related information such as the number of tourists and travel expenditures by states. Such data would be of interest to firms and individuals in the travel industry. The Graduate Management Admission Council maintains data on test scores, student characteristics, and graduate management education programs. Data from industry and special-interest organizations are available to qualified users at a modest cost. Almost all companies maintain Web sites that provide general information about the company as well as data on sales, number of products, product prices, and product specifications. There are a number of companies that specialize in making information available on the Net. 5. How Errors Arise Keep in mind that when attempting to acquire data, there is a time requirement. If data needs to be obtained in a short period of time, would you use existing data or spend time performing an observational study? Using existing data makes sense; however, the cost involved is also a major consideration. Many organizations charge for data. Data acquisition errors can also occur. This happens whenever the data value obtained is not equal to the true or actual value that would be obtained with a correct procedure. For example, an interviewer could make a recording error, such as a transposition in writing the age of a 24 year old person as 42. This can also happen if the person interviewed misinterprets a question and provides an incorrect answer. Special procedures can be used to check for internal consistency of the data. For example, such procedures would indicate that the analyst should review the accuracy of data for a respondent shown to be 22 years of age but reporting 20 years of work experience. Taking steps to acquire accurate data can help ensure reliability and valuable decision making information. Page 3 of 5

4 6. Descriptive Statistics and Statistical Inference Most statistical information in newspapers, magazines, company reports, and other publications consist of data that are summarized and presented in a form that is easy for the reader to understand. Such summaries of data, which may be tabular, graphical, or numerical, are referred to as descriptive statistics. The most common numerical descriptive statistic is the average (or mean). Many situations require information about a large group of elements (individuals, companies, voters, households, products, customers, etc.). Because of time, cost, and other considerations, data can only be collected from a small portion of the group. The larger group of elements in a particular study is called the population. The smaller group is called the sample. The process of conducting a survey to collect data for the entire population is called a census. The process of conducting a survey to collect data for a sample is called a sample survey. As one of its major contributions, statistics uses data from a sample to make estimates and test hypotheses about the characteristics of a population through a process referred to as statistical inference. 7. Population and Sample Many situations require information about a large group of elements (individuals, companies, voters, households, products, customers, etc.). Because of time, cost, and other considerations, data can only be collected from a small portion of the group. The larger group of elements in a particular study is called the population. The smaller group is called the sample. 8. Sample and Statistical Inference As one of its major contributions, statistics uses data from a sample to make estimates and test hypotheses about the characteristics of a population through a process referred to as statistical inference. Because statistical analysis typically involves working with large amounts of data, computer software is frequently used to conduct the analysis. Often the data to be analyzed reside in a spreadsheet. It is now possible to conduct sophisticated statistical analyses using modern spreadsheet packages and in this class, we will be using Microsoft Excel, which is currently the most widely available spreadsheet software in business organizations. In using Excel for statistical analysis, three tasks are needed: Enter Data, Enter Functions and Formulas, and Apply Tools. When you enter data, you simply select the cell locations for the data and enter data along with appropriate descriptive labels. When you enter functions and formulas, you select the cell locations, enter Excel functions and formulas, and provide descriptive materials to identify the results. When you apply tools, you use Excel s tools for data management, data analysis, and presentation. An example of this is StatTools, which is an Excel add-in. Keep in mind that to display formulas, you use the keyboard combination Ctrl and ` Page 4 of 5

5 KEY TERMS Census A survey to collect data on the entire population. Cross-sectional data Data collected at the same or approximately the same point in time. Data The facts and figures collected, analyzed, and summarized for presentation and interpretation. Data set All the data collected in a particular study. Descriptive statistics Tabular, graphical, and numerical summaries of data. Elements The entities on which data are collected. Formula worksheet A worksheet that displays the Excel formulas used to create the results shown in the value worksheet. Interval scale The scale of measurement for a variable if the data demonstrate the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Interval data are always numeric. Nominal scale The scale of measurement for a variable when the data are labels or names used to identify an attribute of an element. Nominal data may be nonnumeric or numeric. Observation The set of measurements obtained for a particular element. Ordinal scale The scale of measurement for a variable if the data exhibit the properties of nominal data and the order or rank of the data is meaningful. Ordinal data may be nonnumeric or numeric. Population The set of all elements of interest in a particular study. Qualitative data Labels or names used to identify an attribute of each element. Qualitative data use either the nominal or ordinal scale of measurement and may be nonnumeric or numeric. Qualitative variable A variable with qualitative data. Quantitative data Numeric values that indicate how much or how many of something. Quantitative data are obtained using either the interval or ratio scale of measurement. Quantitative variable A variable with quantitative data. Ratio scale The scale of measurement for a variable if the data demonstrate all the properties of interval data and the ratio of two values is meaningful. Ratio data are always numeric. Sample A subset of the population. Sample survey A survey to collect data on a sample. Statistical inference The process of using data obtained from a sample to make estimates or test hypotheses about the characteristics of a population. Statistics The art and science of collecting, analyzing, presenting, and interpreting data. Time series data Data collected over several time periods. Value worksheet A worksheet that displays the data for the problem and shows the results of the analysis. ***TIP: THE STEPS TO CREATE A HISTOGRAM FOR PROBLEM 25 ARE ON PAGES IN THE FIFTH EDITION, AND PAGES IN THE 6 TH EDITION*** Page 5 of 5