Statistics Introduction to Data

Contents Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference Computers and Statistical Analysis

Applications in Business and Economics What areas need to use statistics?

Applications in Business and Economics Accounting Finance Marketing Production Economics Information Systems …………

Data Data and Data Sets Elements, Variables, and Observations Scales of Measurement Qualitative and Quantitative Data Cross-Sectional and Time Series Data

Data —Data and data set Data are the facts and figures collected, summarized, analyzed, and interpreted. The data collected in a particular study are referred to as the data set. Examples?

Data -- Elements, Variables, and Observations The are the entities on which data are collected. A is a characteristic of interest for the elements. The set of measurements collected for a particular element is called an . The total number of data values in a data set is the number of elements multiplied by the number of variables.

Data -- Elements, Variables, and Observations A data set with n elements contains n observations. The total number of data values in a data set is the number of elements multiplied by the number of variables.

Data -- Elements, Variables, and Observations the data set contains 8 elements. five variables: Exchange, Ticker Symbol, Market Cap, Price/Earnings Ratio, Gross Profit Margin. observations: the first observation (DeWolfe Companies) is AMEX, DWL, 36.4, 8.4, and 36.7.

Data -- Elements, Variables, and Observations Names Stock Annual Earn/ Exchange Sales($M) Share($) Company Dataram EnergySouth Keystone LandCare Psychemedics AMEX 73.10 0.86 OTC 74.00 1.67 NYSE 365.70 0.86 NYSE 111.40 0.33 AMEX 17.60 0.13 Data Set

Data-- Scales of Measurement Nominal scale When the data for a variable consist of labels or names used to identify an attribute of the element. For example, gender, ID number, “exchange variable” in Table 1.1 nominal data can be recorded using a numeric code. We could use “0” for female, and “1” for male.

Data-- Scales of Measurement Nominal scale example: Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on. Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).

Data-- Scales of Measurement Ordinal scale If the data exhibit the properties of nominal data and the order or rank of the data is meaningful. For example, questionnaire: a repair service rating of excellent, good, or poor. Ordinal data can be recorded using a numeric code. We could use 1 for excellent, 2 for good, and 3 for poor.

Data-- Scales of Measurement Ordinal scale example: Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).

Data-- Scales of Measurement Interval scale The data show the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Example: SAT scores, temperature. Interval data are always numeric.

Data-- Scales of Measurement Interval data example: Three students with SAT scores of 1120, 1050, and 970 can be ranked or ordered in terms of best performance to poorest performance. In addition, the differences between the scores are meaningful. For instance, student 1 scored 1120 – 1050 =70 points more than student 2, while student 2 scored 1050 – 970 = 80 points more than student 3.

Data-- Scales of Measurement Ratio scale The data have all the properties of interval data and the ratio of two values is meaningful. Ratio scale requires that a zero value be included to indicate that nothing exists for the variable at the zero point. For example, distance, height, weight, and time use the ratio scale of measurement.

Data-- Scales of Measurement Ratio scale example: Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.

Data --Qualitative and Quantitative Data Data can be further classified as either qualitative or quantitative. The statistical analysis appropriate for a particular variable depends upon whether the variable is qualitative or quantitative.

Data --Qualitative and Quantitative Data If the variable is qualitative, the statistical analysis is rather limited. In general, there are more alternatives for statistical analysis when the data are quantitative.

Data –Qualitative Data Labels or names used to identify an attribute of each element Qualitative data are often referred to as categorical data Use either the nominal or ordinal scale of measurement Can be either numeric or nonnumeric Appropriate statistical analyses are rather limited

Data --Quantitative Data Quantitative data indicate how many or how much: discrete, if measuring how many continuous, if measuring how much Quantitative data are always numeric. Ordinary arithmetic operations are meaningful for quantitative data.

Data-- Scales of Measurement Qualitative Quantitative Numerical Nonnumerical Numerical Nominal Ordinal Nominal Ordinal Interval Ratio

Data-- Cross-Sectional Data Cross-sectional data are collected at the same or approximately the same point in time. Example: data detailing the number of building permits issued in July 2016 in each of the districts of Tainan City

Data– Time series Data Time series data are collected over several time periods. Example: data detailing the number of building permits issued in Tainan City in each of the last 36 months

Time Series Data Graph of Time Series Data

Data Sources Existing Sources Statistical Studies Data Acquisition Errors

Data Sources Existing Sources Within a firm – almost any department Business database services – Dow Jones & Co. Government agencies - U.S. Department of Labor Industry associations – Travel Industry Association of America Special-interest organizations – Graduate Management Admission Council Internet – more and more firms

Data Sources

Data Sources Statistical Studies In experimental studies the variables of interest are first identified. Then one or more factors are controlled so that data can be obtained about how the factors influence the variables. In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest. a survey is a good example

Data Sources Time requirement Searching for information can be time consuming. Information may no longer be useful by the time it is available Cost of Acquisition Organizations often charge for information even when it is not their primary business activity.

Data Sources Data Errors Using any data that happens to be available or that were acquired with little care can lead to poor and misleading information

Descriptive Statistics – After collecting data Most of the statistical information in newspapers, magazines, company reports, and other publications consists of data that are summarized and presented in a form that is easy to understand. Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.

Descriptive Statistics – Example Next table is the data for different mini-systems. Brand & Model Price ($) Sound Quality CD Capacity FM Tuning Tape Decks Aiwa NSX-AJ800 250 Good 3 Fair 2 JVC FS-SD1000 500 Good 1 Very Good 0 JVC MX-G50 200 Very Good 3 Excellent 2 Panasonic SC-PM11 170 Fair 5 Very Good 1 RCA RS 1283 170 Good 3 Poor 0 Sharp CD-BA2600 150 Good 3 Good 2 Sony CHC-CL1 300 Very Good 3 Very Good 1 Sony MHC-NX1 500 Good 5 Excellent 2 Yamaha GX-505 400 Very Good 3 Excellent 1 Yamaha MCR-E100 500 Very Good 1 Excellent 0

Descriptive Statistics – Example Parts Cost ($) Parts Frequency Percent Frequency 2 13 16 7 5 50 4 26 32 14 10 100

Descriptive Statistics – Example Parts Cost ($) Parts Frequency Percent Frequency 2 13 16 7 5 50 4 26 32 14 10 100

Numerical Descriptive Statistics The most common numerical descriptive statistic is the average (or mean). The average price is ? Descriptive Statistics: Price ($) Total Sum of Variable Count Percent CumPct Mean StDev Sum Squares Minimum Price ($) 10 100 100 314.0 147.9 3 140.0 1182800.0 150.0 N for Variable Median Maximum Mode Mode Price ($) 275.0 500.0 500 3

Statistical inference Population - the set of all elements of interest in a particular study Sample - a subset of the population Statistical inference - the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population Census - collecting data for a population Sample survey - collecting data for a sample

Process of Statistical Inference 1. Population consists of all tune-ups. Average cost of parts is unknown. 2. A sample of 50 engine tune-ups is examined. 3. The sample data provide a sample average parts cost of $79 per tune-up. 4. The sample average is used to estimate the population average.

Computers and Statistical Analysis Statistical analysis often involves working with large amounts of data. Computer software is typically used to conduct the analysis. Statistical software packages such as Microsoft Excel and Minitab are capable of data management, analysis, and presentation.

Analytics Analytics is the scientific process of transforming data into insight for making better decisions. Techniques: Descriptive analytics: This describes what has happened in the past. Predictive analytics: Use models constructed from past data to predict the future or to assess the impact of one variable on another.

Analytics Techniques: Descriptive analytics Predictive analytics Prescriptive analytics: The set of analytical techniques that yield a best course of action.

Big data and Data Mining: Big data: Large and complex data set. Three V’s of Big data: Volume : Amount of available data Velocity: Speed at which data is collected and processed Variety: Different data types

Data warehousing Data warehousing is the process of capturing, storing, and maintaining the data. Organizations obtain large amounts of data on a daily basis by means of magnetic card readers, bar code scanners, point of sale terminals, and touch screen monitors.

Data warehousing Wal-Mart captures data on 20-30 million transactions per day. Visa credit card processes 6,800 payment transactions per second.

Data Mining Methods for developing useful decision-making information from large databases. Using a combination of procedures from statistics, mathematics, and computer science, analysts “mine the data” to convert it into useful information.

Data Mining The most effective data mining systems use automated procedures to discover relationships in the data and predict future outcomes prompted by general and even vague queries by the user.

Data Mining Applications The major applications of data mining have been made by companies with a strong consumer focus such as retail, financial, and communication firms. Data mining is used to identify related products that customers who have already purchased a specific product are also likely to purchase (and then pop-ups are used to draw attention to those related products).

Data Mining Applications Data mining is also used to identify customers who should receive special discount offers based on their past purchasing volumes.

Data Mining Requirements Statistical methodology such as multiple regression, logistic regression, and correlation are heavily used. Also needed are computer science technologies involving artificial intelligence and machine learning. A significant investment in time and money is required as well.

Data Mining Model Reliability Finding a statistical model that works well for a particular sample of data does not necessarily mean that it can be reliably applied to other data. With the enormous amount of data available, the data set can be partitioned into a training set (for model development) and a test set (for validating the model).

Data Mining Model Reliability There is, however, a danger of overfitting the model to the point that misleading associations and conclusions appear to exist. Careful interpretation of results and extensive testing is important.

Ethical Guidelines for Statistical Practice In a statistical study, unethical behavior can take a variety of forms including: Improper sampling Inappropriate analysis of the data Development of misleading graphs Use of inappropriate summary statistics Biased interpretation of the statistical results

Ethical Guidelines for Statistical Practice One should strive to be fair, thorough, objective, and neutral as you collect, analyze, and present data. As a consumer of statistics, one should also be aware of the possibility of unethical behavior by others.

Ethical Guidelines for Statistical Practice The American Statistical Association developed the report “Ethical Guidelines for Statistical Practice”.

Ethical Guidelines for Statistical Practice It contains 67 guidelines organized into 8 topic areas: Professionalism Responsibilities to Funders, Clients, Employers Responsibilities in Publications and Testimony Responsibilities to Research Subjects

Ethical Guidelines for Statistical Practice It contains 67 guidelines organized into 8 topic areas: Responsibilities to Research Team Colleagues Responsibilities to Other Statisticians/Practitioners Responsibilities Regarding Allegations of Misconduct Responsibilities of Employers Including Organizations, Individuals, Attorneys, or Other Clients