Economic Reasoning Using Statistics

Econ 138 Dr. Adrienne Ohler

How you will learn.

• Textbook: Stats: Data and Models 2nd Ed., by Richard D. DeVeaux, Paul E. Velleman, and David E. Bock

• Homework: MyStatLab brought to by www.coursecompass.com

The rest of this class

• Attendance Policy• Cellphone Policy• Homeworks (10 out of 12)• Quizzes (5 out of 6)• Exams (March 3 and April 21)• Cummulative Optional Final• Data Project

Help for this Class

• READ THE BOOK• Come to class prepared and awake• READ THE BOOK• Office Hours: 1-3 M, 1-3 W, and by

Appointment• READ THE BOOK• Get a tutor at the Visor Center

How much sleep did you get last night?

Slide 1- 51 2 3 4 5 6

11% 11%

6%

11%

39%

22%

1. <62. 63. 74. 85. 96. >9

Why is this economic reasoning?

• Economics is the study of scarcity, incentives, and decision making.

• Your time is scarce.• You want to get the best grade in this class

possible.• You also want to do well in other classes.• Decision: What is the best use your time?

Class Objective

• The course objectives are to learn the basic ideas and tools behind statistics and probability theory, develop an understanding of statistical thinking, apply the basic statistical techniques, and accurately interpret results.

Slide 1- 8

Class ObjectiveInformation from

the Real World

Relevant and Meaningful Numbers

Calculate a Statistic that tell us about

the Real World

Examine probability of events in the Real

World

Slide 1- 9

Chapter 1 – The path to a statisticInformation, Information, Information

Numbers (Data)

Statistic

Slide 1- 11

Chapter 1 – The path to a statistic

Students, GPA, Hair Color, Eye color, weight, major, study habits,

health, number of children, hobbies, hope & dreams, current

facebook status

4.00, 3.23, 3.24, 2.15, 0, 1.25, 2.45, 3.15, 2.15, 2.45, 1.41, 3.54, 4.00, 3.23, 3.24, 2.15, 0, 1.25, 2.45, 3.15, 2.15, 2.45, 1.41,

3.54,4.00, 3.23, 3.24, 2.15, 0, 1.25, 2.45, 3.15, 2.15, 2.45, 1.41, 3.54,4.00, 3.23, 3.24, 2.15, 0, 1.25, 2.45, 3.15, 2.15, 2.45, 1.41,

3.54

3.45

Information, Information, Information

Numbers (Data)

Statistic

Slide 1- 12

What Is (Are?) Statistics?

• Statistics (the discipline) is a way of reasoning, a collection of tools and methods, designed to help us understand the world.

• Statistics (plural) are particular calculations made from data.

• Data are values with a context.

Questioning a Statistic

• How did they collect the data?

• How did they calculate it?

• Is their interpretation of the statistic correct?

StatisticsA. ½ of all American children will witness the breakup

of a parent’s marriage. Of these, close to 1/2 will also see the breakup of a parent’s second marriage. – (Furstenberg et al, American Sociological Review 1983)�

B. 66% of the total adult population in this country is currently overweight or obese. – (http://win.niddk.nih.gov/statistics/)

C. 28% of American adults have left the faith in which they were raised in favor of another religion - or no religion at all. – (http://religions.pewforum.org/reports)

Slide 1- 15

What is Statistics Really About?

• A statistic is a number that represents a characteristic of a population. (i.e. average, standard deviation, maximum, minimum, range)

• Statistics is about variation.• All measurements are imperfect, since there is

variation that we cannot see.• Statistics helps us to understand the real, imperfect

world in which we live and it helps us to get closer to the unveiled truth.

In this class• Observe the real world• Create a hypothesis• Collect data• Understand and classify our data• Graph our data• Standardize our data• Apply probability rules to our data• Test our hypothesis• Interpret our results

Slide 2- 17

Chapter 2 - What Are Data?

• Data can be numbers, record names, or other labels.

• Not all data represented by numbers are numerical data (e.g., 1=male, 2=female).

• Data are useless (but funny) without their context…

Slide 2- 18

The “W’s”• To provide context we need the W’s– Who– What (and in what units)– When– Where– Why (if possible)– and Howof the data.

• Note: the answers to “who” and “what” are essential.

Slide 2- 20

Who

• The Who of the data tells us the individual cases about which (or whom) we have collected data.– Individuals who answer a survey are called

respondents.– People on whom we experiment are called

subjects or participants.– Animals, plants, and inanimate subjects are called

experimental units.

Slide 2- 21

Who (cont.)

• Sometimes people just refer to data values as observations and are not clear about the Who.– But we need to know the Who of the data so we

can learn what the data say.

Who are they studying?

25%

25%

25%

25% 1. The cause of death for 22,563 men in the study

2. The fitness level of the 22,563 men in the study

3. The age of each of the 22,563 men in the study

4. The 22,563 men in the study

Slide 2- 24

What and Why

• Variables are characteristics recorded about each individual.

• The variables should have a name that identify What has been measured.

• To understand variables, you must Think about what you want to know.

Slide 2- 25

What and Why (cont.)

• Some variables have units that tell how each value has been measured and tell the scale of the measurement.

Slide 2- 26

What and Why (cont.)

• A categorical (or qualitative) variable names categories and answers questions about how cases fall into those categories.– Categorical examples: sex, race, ethnicity

• A quantitative variable is a measured variable (with units) that answers questions about the quantity of what is being measured.– Quantitative examples: income ($), height

(inches), weight (pounds)

Slide 2- 27

What and Why (cont.)

• Example: In a fitness evaluation, one question asked to evaluate the statement “I consider myself physically fit” on the following scale: – 1 = Disagree Strongly; – 2 = Disagree; – 3 = Neutral; – 4 = Agree; – 5 = Agree Strongly.

• Question: Is fitness categorical or quantitative?

Slide 2- 28

What and Why (cont.)

• We sense an order to these ratings, but there are no natural units for the variable fitness.

• Variables fitness are often called ordinal variables. – With an ordinal variable, look at the Why of the

study to decide whether to treat it as categorical or quantitative.

Who is the population of interest?

1 2 3 4

25% 25%25%25%1. All people2. All men who exercise3. All men who die of

cancer4. All men

Slide 2- 33

Counts Count• When we count the cases in each category of

a categorical variable, the counts are not the data, but something we summarize about the data.– The category labels are the What, and– the individuals counted are the Who.

Slide 2- 34

Counts Count (cont.)

• When we focus on the amount of something, we use counts differently. For example, Amazon might track the growth in the number of teenage customers each month to forecast CD sales (the Why). – The What is teens, the

Who is months, and the units are number of teenage customers.

Oregon Pts.• 72 (New Mexico) • 48 (Tennessee)• 69 (Portland State)• 42 (Arizona State) - Conference• 52 (Stanford) - Conference• 43 (Wash. State) - Conference• 60 (UCLA) - Conference• 53 (USC) - Conference• 53 (Wash.) - Conference• 15 (Cal) - Conference• 48 (Arizona) - Conference• 37 (Oregon State) - Conference• 19 (Auburn) –BCS Championship Game

Slide 2- 36

Identifying Identifiers

• Identifier variables are categorical variables with exactly one individual in each category.– Examples: Social Security Number, ISBN, FedEx

Tracking Number• Don’t be tempted to analyze identifier variables.• Be careful not to consider all variables with one

case per category, like year, as identifier variables.– The Why will help you decide how to treat identifier

variables.

Slide 2- 37

Where, When, and How

• We need the Who, What, and Why to analyze data. But, the more we know, the more we understand.

• When and Where give us some nice information about the context. – Example: Values recorded at a large public

university may mean something different than similar values recorded at a small private college.

Where, When, and How

• GPA of Econ 101 classes.• Class 1 – 2.56• Class 2 – 3.34

Where, When, and How

• GPA of Econ 101 classes.• Class 1 – 2.56• Class 2 – 3.34

• Where – Washington State university• When – during the fall and spring semesters

Slide 2- 40

Where, When, and How (cont.)

• How the data are collected can make the difference between insight and nonsense. – Example: results from voluntary Internet surveys

are often useless

– Example: Data collection of student evaluations• Course Evaluations• Ask students during office hours• Rate My Professors

Slide 2- 41

Data Tables

• The following data table clearly shows the context of the data presented:

• Notice that this data table tells us the What (column titles) and Who (row titles) for these data.

Next time…

• Chapter 3 – Describing and displaying categorical data