MGT201 Mathematical Models Salkind, Statistics for People Who (Think They) Hate Statistics 6th Edition, SAGE Inc. © 2017 What is Statistics?...and Why Statistics? Why You Need To Study Statistics: https://www.youtube.com/watch?v=wV0 Ks7aS7YI What is Statistics? So, what is statistics? What is Statistics? • Statistics is a way of reasoning, along with a collection of tools and methods, designed to help us understand the world. • A set of tools and techniques used for describing, organizing, and interpreting information or data. • Statisticians use tools and methods in statistics to: Analyze small and large amounts of data Analyze data real time Interpret the results and help organizations in their decision making How is Statistics used in Management? How is statistical analysis used in management? How is Statistics used in Management? Statistical analysis is used in almost every area in business decision making including: • Accounting – to audit a company’s accounts (“statistical audit” is conducted in which a representative sample of invoices is audited) • Finance – to decide on which investment alternatives to invest in (statistics can provide many ways of measuring risk and expected returns on investments) How is Statistics used in Management? • Marketing– to understand consumer purchasing patterns, marketers use statistical analysis to learn about the relationship between various variables including age group, income level, gender, postal code, etc. to design promotional campaigns focused on the appropriate target audience. • Human Resources Planning – to investigate the patterns of promotion, recruitment, retirement, transfers and resignation, an organization analyzes employee past data to forecast the number of employees at different levels of the management pyramid in the future. How Can I Learn Statistics? You need to be very proactive in doing the learning by putting into practice the concepts and methods the book teaches. Statistics is like most useful things in life: You must practise it to really learn it. Branches of Statistics What are the two major branches of statistics? Branches of Statistics Two major branches of statistics: a) descriptive statistics b) inferential statistics Descriptive Statistics Used to organize and describe the characteristics of a particular data set This collection of data is sometimes called a data set or just data. Descriptive Statistics Examples Average age of everyone in this class (i.e., mean) The most popular college major (i.e., mode) Practice (find the mean and mode) Inferential Statistics Used to make inferences based on a smaller group of data A sample is a subset of a population. A population is all of the occurrences with a certain characteristic. Inferential Statistics Examples Take 100 people with depression, and split them up into two groups randomly. With the first group, give them a sugar pill, and give the second group a new depression drug. If you find a statistically significant difference in both groups, you infer that you would find similar results in the entire population as well. Inferential Statistics Example Based on an analysis of students in MGT 201, would you infer that most business students at Stanford College take the bus to school every day? - Raise your hand if you do Inferential Statistics Why does statistics use samples to make assumptions about how the phenomenon presents itself in a population? Inferential Statistics It is often necessary to take a sample instead of studying every member of a population due to one or more of the following reasons: 1. The prohibitive cost of surveying the whole population. 2. The destructive nature of some tests. 3. The physical impossibility of capturing the population. Cases and Variables What are cases? What are variables? Cases A row of a data table corresponds to an individual case about Whom (or about Which – if they are not people) we record some characteristics. Purchase Order Number Cases Name Ship to Province Price Area Code Gift? ASIN 10675489 Katherine H. Alberta 10.99 403 N B0000015Y6 10783489 Samuel P. Nova Scotia 16.99 902 Y B000002BK9 12837593 Chris G. Quebec 15.98 819 N B000068ZVQ 15783947 Monique D. Ontario 11.99 905 N B000001OAA Variables The characteristics recorded about each individual or case are called variables. These are usually shown as the columns of a data table and identify What has been measured. Variables Purchase Order Number Name Ship to Province Price Area Code Gift? ASIN 10675489 Katherine H. Alberta 10.99 403 N B0000015Y6 10783489 Samuel P. Nova Scotia 16.99 902 Y B000002BK9 12837593 Chris G. Quebec 15.98 819 N B000068ZVQ 15783947 Monique D. Ontario 11.99 905 N B000001OAA Variable Types What are the types of variables? Variable Types When a variable names categories and answers questions about how cases fall into those categories, it is called a categorical variable (also called qualitative variable). When a variable has measured numerical values with units and the variable tells us about the quantity of what is measured, it is called a quantitative variable. Variable Types Categorical variables … • arise from descriptive responses to questions like “What kind of advertising do you use?” or “Do you invest in stock market?” • may only have two possible values (like “Yes” or “No”) • may be a number like a telephone area code Variable Types (Categorical) Question Categories or Responses Do you invest in the stock market? __Yes__No What kind of advertising do you use? __Magazines__Internet__Direct Mailings I would recommend this course to another student. __Strongly Disagree__Slightly Disagree__Slightly Agree__Strongly Agree How satisfied are you with this product? __Very Unsatisfied__Unsatisfied__Satisfied__Very Satisfied Variable Types (Quantitative) Some quantitative variables have units. The units indicate … • how each value has been measured • the corresponding scale of measurement • how much of something we have • how far apart two values are Other quantitative variables have no units, such as … • Number of visits to a web site • Number of shares of a company traded in Toronto Stock Exchange Variable Types • Some variables can be both categorical and quantitative • How data are classified depends on Why we are collecting the data For example, variable Age is obviously the quantitative value, measured in years, that may be used for finding the average age of customers. Age categories such as Child, Teen, Adult, or Senior can be the categorical value used to decide in which music to offer in a special deal – folk, jazz, hip hop or reggae. May take on any value within a given range of real numbers and usually arises from a measurement (not a counting) process. Eg. Height, weight, time, etc. May have a finite number. Mostly comes from a counting process. Their values are mostly whole numbers (counts). Eg. Numbers of students, number of university credits, etc. Indicates the rank ordering of items. Eg. Customer product review. Where, 1: very satisfied, 2: Satisfied, 3: Neutral, 4= Unsatisfied, 5= Very unsatisfied. Words that describe the categories or classes of response. Eg. 1=Male 2=Female. Numerical variables Nominal vs. ordinal categorical variables A nominal variable is one that has two or more categories, but there is no intrinsic ordering to the categories. For example, gender is a categorical variable having two categories (male and female) and there is no intrinsic ordering to the categories. Hair color is also a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) and again, there is no agreed way to order these from highest to lowest. A purely categorical variable is one that simply allows you to assign categories but you cannot clearly order the variables. If the variable has a clear ordering, then that variable would be an ordinal variable. An ordinal variable is similar to a categorical variable. The difference between the two is that there is a clear ordering of the variables. For example, suppose you have a variable, economic status, with three categories (low, medium and high). In addition to being able to classify people into these three categories, you can order the categories as low, medium and high. Now consider a variable like educational experience (with values such as elementary school graduate, high school graduate, some college and college graduate).
