Ka-fu Wong © 2003 Chap 1-1 Dr. Ka-fu Wong ECON1003 Analysis of Economic Data

Ka-fu Wong © 2003 Chap 1-2 Chapter One What is Statistics? GOALS 1.Understand why we study statistics. 2.Populations and Samples Sampling a Population of Existing Units Sampling a Process 3.Explain what is meant by descriptive statistics and inferential statistics. 4.Distinguish between a qualitative variable and a quantitative variable. 5.Distinguish between a discrete variable and a continuous variable. 6.Distinguish among the nominal, ordinal, interval, and ratio levels of measurement. 7.Define the terms mutually exclusive and exhaustive.

Ka-fu Wong © 2003 Chap 1-3 What is Meant by Statistics? Statistics is the science of 1.collecting, 2.organizing, 3.presenting, 4.analyzing, and 5.interpreting numerical data to assist in making more effective decisions.

Ka-fu Wong © 2003 Chap 1-4 Who Uses Statistics? Statistical techniques are used extensively by Economists, marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc...

Ka-fu Wong © 2003 Chap 1-5 Who Uses Statistics? As economists, We must verifying our models with data. We need to provide forecast of the economy (GDP growth). We need quantitative estimates of How individual decisions are influenced by policy variables (such as unemployment benefits, education subsidy) in order to forecast the impact of public policies. How macro policies (government expenditure) will affect output.

Ka-fu Wong © 2003 Chap 1-6 Who Uses Statistics? In the business community, managers must make decisions based on what will happen to such things as demand, costs, and profits. These decisions are an effort to shape the future of the organization. If the managers make no effort to look at the past and extrapolate into the future, the likelihood of achieving success is slim.

Ka-fu Wong © 2003 Chap 1-7 Why do we need to understand Statistics? We are constantly deluged with statistics in the media (newspapers, magazines, journals, text books, etc.). We need to have a means to condense large quantities of information into a few facts or figures. We need to predict what will likely occur given what has occurred in the past. We need to generalize what we have learned in specific situations to the more general case.

Ka-fu Wong © 2003 Chap 1-8 We are users of statistics We do not want to become professors of statistics. We do not want to develop advanced statistics theory. We are users of statistics To be effective users, we need to have a good grip of basic statistics theory. We need to practice using the tools. This course will give you the basic, enough for you to move on to your next Econometrics class.

Ka-fu Wong © 2003 Chap 1-9 Populations and Samples A population is a collection of all possible individuals, objects, or measurements of interest. A sample is a portion, or part, of the population of interest.

Ka-fu Wong © 2003 Chap 1-10 Populations and Samples Population Sample

Ka-fu Wong © 2003 Chap 1-11 Sampling a Population of Existing Units Random Sampling A procedure for selecting a subset of the population units in such a way that every unit in the population has an equal chance of selection Sampling with replacement When a unit is selected as part of the sample, its value is recorded and placed back into the population for possible reselection Sampling without replacement Units are not placed back into the population after selection

Ka-fu Wong © 2003 Chap 1-12 Approximate Random Samples Frame A list of all population units. Required for random sampling, but not for approximate random sampling methods like systematic and voluntary response sampling. Systematic Sample Every k-th element of the population is selected for the sample Voluntary Response Sample Sample units are self-selected (as in radio/TV surveys)

Ka-fu Wong © 2003 Chap 1-13 Process A sequence of operations that takes inputs (labor, raw materials, methods, machines, and so on) and turns them into outputs (products, services, and the like.) Process Inputs Outputs Sampling a Process A process is in statistical control if it displays constant level and constant variation.

Ka-fu Wong © 2003 Chap 1-14 Runs Plot A runs plot is a graph of individual process measurements over time.

Ka-fu Wong © 2003 Chap 1-15 Runs Plot – Payment Time Example

Ka-fu Wong © 2003 Chap 1-16 Types of Statistics Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way. Examples: 1.A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer. 2.According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during The statistic 9 describes the number of problems out of every 100 machines. 3.In our class, xx are female out of yy. 4.On 2 January, xx% of stocks listed in HK closed lower than the previous trading day.

Ka-fu Wong © 2003 Chap 1-17 Types of Statistics Inferential Statistics: A decision, estimate, prediction, or generalization about a population, based on a sample.

Ka-fu Wong © 2003 Chap 1-18 Types of Statistics (examples of inferential statistics) 1.TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers. 2.The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company. 3.Wine tasters sip a few drops of wine to make a decision with respect to all the wine waiting to be released for sale. 4.Unemployment rate in December Consumer price index in December 2002.

Ka-fu Wong © 2003 Chap 1-19 Gender (female/male). Religious affiliation. Type of automobile owned. Place of birth, Eye color. Secondary school attended. Grades of your AL Examination. Whether you have tasted Vanilla Coca Cola (Yes/No). Types of Variables For a Qualitative or Attribute variable the characteristic being studied is nonnumeric in nature. Sometimes we will convert qualitative variables to numbers for convenience of calculating summary statistics. For example, Yes may be coded 1, No may be coded 0. But the coding does not change the nature of the variable.

Ka-fu Wong © 2003 Chap 1-20 Balance in your checking account. Minutes remaining in class. Number of children in a family. Heights. Income. Age. Number of hours spent on ICQ. Types of Variables In a Quantitative variable information is reported numerically.

Ka-fu Wong © 2003 Chap 1-21 Types of Variables Quantitative variables can be classified as either discrete or continuous. Discrete variables: can only assume certain values and there are usually “gaps” between values. The number of bedrooms in a house. The number of car accidents per year (1,2,3,…,etc). The number of students in a class. The number of ten-cents coin in your pocket today. The number of sexual partners you have in the past 12 months.

Ka-fu Wong © 2003 Chap 1-22 Types of Variables Quantitative variables can be classified as either discrete or continuous. A continuous variable can assume any value within a specified range. The pressure in a tire. The weight of a pork chop. The height of students in a class. The amount of water (litre) you drink today. Time spent on commuting between school and home.

Ka-fu Wong © 2003 Chap 1-23 Summary of Types of Variables Data Qualitative or attribute (type of car owned) Quantitative or numerical Discrete (Number of children) Continuous (Hours of sleep last night)

Ka-fu Wong © 2003 Chap 1-24 Levels of Measurement There are four levels of data. 1.Nominal, 2.Ordinal, 3.Interval, and 4.Ratio Level.

Ka-fu Wong © 2003 Chap 1-25 Levels of Measurement Nominal level: Data that is classified into categories and cannot be arranged in any particular order. Eye color. Gender. Religious affiliation Marital status (single, married, divorced, separated, windowed). Place of birth. Secondary school attended. Mode of labor force participation (self- employed, unemployed, employee, employer, etc.).

Ka-fu Wong © 2003 Chap 1-26 Levels of Measurement Ordinal level: involves data arranged in some order, but the differences between data values cannot be determined or are meaningless. During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4. The ranking of MBA programs around the world. In rating the examples and illustrations given in class “Very helpful” “Helpful” “Of some help” “Of little help” “Of no help” Moody’s country ratings (Aaa, Baa, etc.)

Ka-fu Wong © 2003 Chap 1-27 Levels of Measurement Interval level: similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point. Temperature on the Fahrenheit scale. Wealth (may be negative and positive). Profit of a company.

Ka-fu Wong © 2003 Chap 1-28 Levels of Measurement Ratio level: the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement. Hours spent on studying per week. Weight in kilograms. Height in centimeters. Monthly income of surgeons. distance traveled by manufacturer’s representatives per month. Age.

Ka-fu Wong © 2003 Chap 1-29 Levels of Measurement Mutually exclusive: An individual, object, or measurement is included in only one category. “Male” and “female” are two categories that are mutually exclusive. Heights of “100 up to 150” and “150 up to 200” are two classes that are mutually exclusive. The marital status (single, married, divorced, separated, windowed) are mutually exclusive. Heights of “100 up to 150” and “140 up to 200” are two classes that are not mutually exclusive.

Ka-fu Wong © 2003 Chap 1-30 Levels of Measurement Exhaustive: Each individual, object, or measurement must appear in one of the categories. The two categories “Male” and “female” exhaust all possibility of gender. The two categories “Christian” and “Muslim” do not exhaust all possibilities of religion. The employment status (employed, unemployment, not in labor force) exhaust all possibilities.

Ka-fu Wong © 2003 Chap END - Chapter One What is Statistics?