Chapter 1 Basic Concepts PDF

Business Statistics (COM 508) Second Term, AY 2024- 2025 Prof. Belinda V. de Castro, Ph.D. UST College of Commerce and Business Administration Research Cent...

Business Statistics (COM 508) Second Term, AY 2024- 2025 Prof. Belinda V. de Castro, Ph.D. UST College of Commerce and Business Administration Research Center for Social Sciences and Education [email protected]  Basic Concepts in Statistics  STATISTICS C Collection O Organization D Description A Analysis I Interpretation  A collection of all the elements under consideration in POPULATION any statistical study. SAMPLE Random Sampling A subset of the population from which the information is collected.  Population and Sample Population Sample Use statistics to summarize features Use parameters to summarize features Inference on the population from the sample Population VS Sample Population – Contains all the items or individual about which you want to reach conclusion. – It is the universe of the study. – it includes all of the elements from a set of data. – The measurable characteristics of a population is called PARAMETER. Sample – it is portion of the population selected for analysis. – data set contains a part, or a subset of a population. – The measurable characteristics of a sample is called STATISTIC  Parameter vs Statistics Sample Population (drawn from the population) , 2 x, s 2 Parameters Statistics Mean  x Variance 2 s2  a summary measure computed PARAMETER to describe a characteristic of the population -a summary measure computed STATISTICS to describe a characteristic of the sample * The mean values of two or more samples, drawn from the same population, will not necessarily be equal.  Two Major Fields of Statistics Descriptive statistics - provides a summary of the data collected (e.g., averages, charts, and measures of variability) to describe the characteristics of a group. Inferential statistics – a set of procedures used to draw conclusions or make predictions about the population characteristics from the information contained in a sample.  Descriptive Statistics Collect data – e.g. Survey Present data – e.g. Tables and graphs Characterize data – e.g. Sample mean = X i n  Inferential Statistics Estimation – e.g.: Estimate the population mean weight using the sample mean weight Hypothesis testing – e.g.: Test the claim that the population mean weight is 120 pounds Drawing conclusions and/or making decisions concerning a population based on sample results. Descriptive Statistics vs Inferential Statistics Identify if the following situations involves descriptive or inferential statistics 1. A retailer analyzes the average stock levels, standard deviation, and frequency distribution of products sold weekly. 1. A company tests two pricing models on different customer groups to determine which generates higher revenue. 1. A company wants to predict delivery delays based on a sample of historical shipment data.  Descriptive statistics vs Inferential statistic These examples highlight how descriptive statistics provide a snapshot of business data, while inferential statistics enable decision-making by uncovering trends, testing hypotheses, and predicting future outcomes. Steps in Statistical Inquiry Problem Research identification design & hypothesis formulation formulation Results interpretation / Data Collection drawing conclusions Data Processing and Data Coding analysis  Data and Data Sets Data are the 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. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 15  Elements, Variables, and Observations Elements are the entities on which data are collected. A variable is a characteristic of interest for the elements. The set of measurements obtained for a particular element is called an observation. A data set with n elements contains n observations. The total number of data values in a complete data set is the number of elements multiplied by the number of variables. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 16 Data, Data Sets, Elements, Variables, and Observations ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 17  Types of Data according to Nature Quantitative data – any attribute that we measure in numbers. Examples: Height: 100cm, 5m, 5ft Weight: 60kg, 140 lb, Qualitative data – observations in the form of categorical labeling of a characteristic Examples: Sex: male, female color: red, blue, yellow Types of Variable Categorical/ Qualitative Variable Numerical/ Quantitative Variable Have data/values that can Have data/values that represent represents categories or quantities characterization.  Discrete Variables o Have numerical values arising from counting process  Continuous Variable o produce numerical responses that arises from measuring process.  Types of Data according to Continuous data Measurement Data that can take on any value within a continuum measurable and can take on any value within a given range whether in a finite or infinite interval. Examples: Passing rate Percentage of retention Time, distance, speed  Types of Data according to Discrete data Measurement Data which results from a process of counting take on whole, distinct values Examples: Number of children Amount of tuition (rounded to the nearest peso) Number of students in the class Types of Data according to Measurement Continuous measurement data Discrete data counting * Continuous data such as length, age, weight, height and time are given discrete values but statistically considered as continuous data,  Categorize each of the following as discrete or continuous a.Number of Products Sold b.Daily revenue c.Customer Satisfaction Rating d.Number of Employees in a Department MEASUREMENT SCALES  PRIMARYCONSIDERATIONS IN SELECTING APPROPRIATE STATISTICAL TECHNIQUES scheme for numerical Measurement representation of the values Scale of the variables Measurement Scales Categorical Variable Numerical/ Quantitative Variable Nominal Interval – Can be measured or counted – has 2 or more categories, no intrinsic – Zero point is arbitrary; that is, the ordering of categories, categories are number zero does not imply the distinct, non-overlapping, & exhaustive absence of characteristics under consideration.  Ordinal Ratio – Categories can be ranked or ordered – has true zero point; that is, the number – difference between each pair of zero indicates the absence of the categories are not equal characteristics under consideration. Determine the variable and the measurement scale used for the following questions in a survey. Determine the variable and the measurement scale used for the following questions in a survey.  Identify the measurement scale a. Customer Satisfaction Ratings b. Department Names c. Temperature in Office Spaces d. Job Applicant Priority e. Product Categories f. Customer Feedback Scores g. Total revenue earned Scale Characteristics Examples Gender, School Type, Nominal Categories without order Subjects Studied Categories with order, Class Rankings, Letter Ordinal no uniform difference Grades, Ratings Equal intervals, no true Test Scores, IQ, Interval zero Temperature Equal intervals, true zero Attendance, Exam Scores, Ratio exists Study Time  MANIFEST VARIABLE Variable LATENT Typologies VARIABLE Other Classifications of Variable Manifest Variable Latent Variable A manifest variable is a Variables that cannot be measured or observed directly variable that can be directly A latent variable is a variable measured using only 1 that can be measured using question. several indicators. It is also known as Latent variable models use manifest variables as a means observed/observable to determine whether latent variable variables exist. Categorize each of the following as either latent or manifest variables a. Highest educational attainment b. Job mismatch c. Occupation d. Job satisfaction e. Civil status f. Statistics anxiety g. Advertising Budget Aspect Latent Variables Manifest Variables Not directly measurable; Directly measurable Definition inferred from data. and observable. Customer satisfaction, Sales revenue, Examples employee engagement. customer complaints. Requires statistical models Measurement (e.g., factor analysis, Simple counts or Method structural equation direct observations. modeling). Other Classifications of Variable Exogenous Variable Endogenous Variable Similar to independent Similar to dependent variables variables The one that causes the They are the one influenced fluctuation in the values of by the exogenous variables other observable/latent in the model, either directly variable or indirectly.  Variables Independent Dependent Exogenous Endogenous Predictor Criterion Cause Effect Stimulus Response Adopted from Writing for International Publication by Prof. Allan B. de Guzman, Ph.D. Categorize each of the following as either exogenous or endogenous variables a.Advertising spending has a significant positive impact on sales revenue. b.A higher emotional intelligence will lead to a better self esteem. c. The more evident the job-skill mismatch, the higher the intent to leave. d.Better work-life balance will lead to less burnout. Data Classification according to Source Primary Secondary Data Collection Data Compilation Print or Electronic Observation Survey Experimentation  Categorize if the following situations needs primary or secondary data Customer Satisfaction Surveys o Situation: A company wants to assess customer satisfaction with its products or services. o Data Collection Method: Surveys or interviews directly from customers after purchase or service use. o Purpose: To gather specific feedback on product features, customer service, or the overall experience, which helps the company improve offerings and customer relationships. Categorize if the following situations needs primary or secondary data Industry Reports and Market Analysis Situation: A company wants to analyze industry trends and market conditions before entering a new market. Data Source: Published market research reports from firms like Nielsen, Statista, or government publications. Purpose: To understand market size, growth trends, competitor analysis, and customer demographics without the need to gather new data. Aspect Primary Data Secondary Data Data collected directly by the Data that has been previously Definition business or researcher for a specific collected, processed, and published by purpose. others. Market reports, government Surveys, interviews, focus groups, Data Source publications, industry statistics, direct observations, experiments. academic studies. Time-consuming and expensive to Quick and inexpensive to obtain, Time and Cost collect. often publicly available. Highly specific to the business's May not be fully tailored to the Customization needs and research questions. specific business needs. Can be highly accurate and Accuracy and relevance depend on Accuracy and relevant to the business's unique the quality of the original data and its Relevance context. applicability to the business context. Customer satisfaction surveys, Industry reports, government Examples market research for new products, economic data, competitor analysis. employee performance appraisals.  Data Acquisition Considerations 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 Errors Using any data that happen to be available or were acquired with little care can lead to misleading information. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 42  Descriptive Statistics Most of the statistical information in newspapers, magazines, company reports, and other publications consist of data that are summarized and presented in a form that is easy to understand. Such summaries of data, which may be tabular, graphical, or numerical, are referred to as descriptive statistics. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 43  Data Classification according to Arrangement Ungrouped Data – raw data - data without any specific order or arrangement Grouped Data – organized set of data - arranged and tabulated raw data  Tabulating Numerical Data: Frequency Distributions Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Relative Class Interval Frequency Frequency Percentage 10 – 19 3.15 15 20 - 29 6.30 30 30 - 39 5.25 25 40 - 49 4.20 20 50 - 59 2.10 10 Total 20 1.00 100 Profile of Respondents 1st year 4th year Count % Count % Male 64 39.3 32 25.6 Gender Female 99 60.7 93 74.4 Eldest 78 47.9 51 40.8 Ordinal Middle 56 34.4 51 40.8 Position Youngest 21 12.9 15 12.0 Only Child 6 3.7 6 4.8 Missing 2 1.2 2 1.6 Total (N) 163 100 125 100  Example: Hudson Auto Repair (1 of 2) The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune- ups performed in her shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 48  Example: Hudson Auto Repair (2 of 2) Sample of Parts Cost ($) for 50 Tune-ups 91 78 93 57 75 52 99 80 97 62 71 69 72 89 66 75 79 75 72 76 104 74 62 68 97 105 77 65 80 109 85 97 88 68 83 68 71 69 67 74 62 82 98 101 79 105 79 69 62 73 ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 49  Tabular Summary: Frequency and Percent Frequency Parts Cost ($) Frequency Percent Frequency 50 to 59 2 4% 60 to 69 13 26% 70 to 79 16 32% 80 to 89 7 14% 90 to 99 7 14% 100 to 109 5 10% TOTAL 50 100% ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 50  Graphical Summary: Bar Chart Example: Hudson Auto ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 51  Cross-Sectional Data Cross-sectional data are collected at the same or approximately the same point in time. Example: Data detailing different variables like status, Per capita GDP, Fitch rating for 60 different WTO nations at the same point in time.  Time Series Data (1 of 2) Time series data are collected over several time periods. Example: U.S average price per gallon of conventional regular gasoline between 2012 and 2018 Graphs of time series help analysts understand: what happened in the past, identify any trends over time, and project future values for the time series. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 53  Time Series Data (2 of 2) Graph of Time Series Data ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 54 Categorize whether each situation needs a cross-sectional data or time series data Sales Forecasting Situation: A retail company wants to forecast future sales for the upcoming quarters based on historical sales data. Data: Monthly sales data over the past 5 years. Purpose: Time series analysis can help the company identify seasonal trends, growth patterns, and potential future sales based on historical trends. Categorize whether each situation needs a cross-sectional data or time series data Market Research and Consumer Behavior Situation: A company conducts a survey to understand customer preferences for a new product. Data: Responses from 1,000 customers gathered in a single month about their preferences for product features, pricing, and quality. Purpose: To predict future enrollment and allocate resources accordingly. Aspect Time Series Data Cross-Sectional Data Data collected over time Data collected at a single point Definition (periodically, sequentially). in time. Analyze trends, patterns, and Compare different entities or Purpose make forecasts. characteristics at one time. Sales data, stock prices, Survey data, financial reports, Data Source production levels, GDP, etc. market share data, etc. Covers long periods (e.g., Represents a snapshot at one Time Frame monthly, quarterly, annually). point in time. Benchmarking, comparing Forecasting, trend analysis, Usage groups, analyzing cross- seasonality analysis. sectional differences.  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 the entire population. Sample survey: Collecting data for a sample. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 58  Analytics Scientific process of transforming data into insight for making better decisions. Descriptive analysis—Analytical techniques that describe what happened in the past. Predictive analysis Analytical techniques that use models constructed from past data to predict future. Helps assess the impact the impact of one variable on another Prescriptive analysis—Analytical techniques that yield a best course of action to take. ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 59 Categorize whether each situation needs a descriptive, predictive or prescriptive analysis Problem Situation: A retail company wants to analyze its sales data for the past quarter to understand overall sales performance across different regions and product categories.  Descriptive Analysis Needed:  Summarize total sales by region, product category, and time period.  Identify trends in sales performance over the last quarter.  Calculate average sales per day, week, or month.  Visualize sales trends using charts and graphs. Categorize whether each situation needs a descriptive, predictive or prescriptive analysis Problem Situation: A manufacturing company wants to optimize its inventory levels to minimize costs while ensuring product availability.  Prescriptive Analysis Needed:  Use optimization algorithms to recommend optimal reorder points and order quantities.  Suggest the best mix of suppliers based on delivery times and cost considerations.  Propose strategies for minimizing storage costs while avoiding stockouts. Categorize whether each situation needs a descriptive, predictive or prescriptive analysis Problem Situation: A company wants to predict its sales for the next quarter to plan production and inventory needs.  Predictive Analysis Needed:  Use historical sales data to forecast future sales trends.  Identify factors (e.g., seasonality, promotions) that impact sales.  Predict the expected sales volume for the upcoming months to optimize production and stock levels.  Business Statistics (COM 508) Second Term, AY 2024- 2025 Prof. Belinda V. de Castro, Ph.D. UST College of Commerce and Business Administration Research Center for Social Sciences and Education [email protected]