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Economic Reasoning Using StatisticsPowerPoint Presentation

Economic Reasoning Using Statistics

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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)
- Due Sundays by 11:59pm

- Quizzes (5 out of 6)
- Exams
- Oct. 10th
- Nov. 28

- Cumulative Optional Final
- Data Project

Help for this Class

- READ THE BOOK
- Come to class prepared and awake
- READ THE BOOK
- Office Hours: T, H 9-11am and by Appointment
- READ THE BOOK
- Get a tutor at the Visor Center

Economic reasoning using statistics

- What is economics?
- The study of scarcity, incentives, and choices.
- The branch of knowledge concerned with the production, consumption, and transfer of wealth. (google)

- Wealth
- The health, happiness, and fortunes of a person or group. (google)

- 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.

Statistics Will the sun rise tomorrow?

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

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.

The language of Statistics

- For of literacy
- 4 cows in a field
- 7 cows by the road
- 4 cows in a field on the left
- 3 cows in a field on the right

- At a party
- Average age is 18
- Average age is 22
- Average age is 75

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

Questioning a Statistic

- 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)

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

- 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)

Chapter 2 - What Are Data?

- Information
- 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 without their context…

The “W’s”

- To provide context we need the W’s
- Who
- What (and in what units)
- When
- Where
- Why (if possible)
- and How
of the data.

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

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 subjectsor participants.
- Animals, plants, and inanimate subjects are called experimental units.

- 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.

Identify the Who in the following dataset?

- Are physically fit people less likely to die of cancer?
- Suppose an article in a sports medicine journal reported results of a study that followed 22,563 men aged 30 to 87 for 5 years.
- The physically fit men had a 57% lower risk of death from cancer than the least fit group.

Who are they studying?

- The cause of death for 22,563 men in the study
- The fitness level of the 22,563 men in the study
- The age of each of the 22,563 men in the study
- The 22,563 men in the study

What and Why

- Variables are characteristics recorded about each individual.
- The variables should have a name that identify What has been measured.
- A categorical (or qualitative) variable names categories and answers questions about how cases fall into those categories.
- Categorical examples: sex, race, ethnicity

What and Why (cont.)

- 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)

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?

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.

Are Fit People Less Likely to Die of Cancer? --------------Who is the population of interest?

- All people
- All men who exercise
- All men who die of cancer
- All men

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.

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.

Where, When, and How

- Whenand 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 – Washington State university
- When – during the fall and spring semesters

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 ‘Who will win Republican Primary?’
- Survey ISU students on campus
- Run a Facebook survey
- Rasmussen Reports national telephone survey

Why statistics is challenging?

- Word problems…
- Rules of statistics don’t change
- Data is information
- If you are struggling with a problem, always ask the W questions about the data collected.
- Who
- What
- When
- Where
- Why

Chapter 3

- Displaying and Describing
- Categorical Data

Methods of Displaying Data

- Frequency Table
- Relative Frequency table
- Bar Chart
- Relative Frequency bar chart
- Pie Chart
- Contingency table
- Contingency tables and Conditional Distributions
- Segmented Bar charts

Frequency Tables: Making Piles

- We can “pile” the data by counting the number of data values in each category of interest.
- We can organize these counts into a frequency table, which records the totals and the category names.

Frequency Tables: Making Piles (cont.)

- A relative frequency table is similar, but gives the percentages (instead of counts) for each category.

Bar Charts

- A bar chart displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison.
- A bar chart stays true to the area principle.
- Thus, a better display for the ship data is:

Bar Charts (cont.)

- A relative frequencybar chart displays the relative proportion of counts for each category.
- A relative frequency bar chart also stays true to the area principle.
- Replacing counts with percentages in the ship data:

What year in school are you?

- Freshman
- Sophomore
- Junior
- Senior

Pie Charts

- When you are interested in parts of the whole, a pie chart might be your display of choice.
- Pie charts show the whole group of cases as a circle.
- They slice the circle into pieces whose size is proportional to the fraction of the whole in each category.

Methods of Displaying Data

- Frequency Table (How much?)
- Relative Frequency table (What percentage?)
- Bar Chart (How much?)
- Relative Frequency bar chart (What percentage?)
- Pie Chart (How much?)
- Contingency table and Marginal Distributions
- Contingency tables and Conditional Distributions

Contingency Tables

- A contingency table allows us to look at two categorical variables together.
- It shows how individuals are distributed along each variable, contingent on the value of the other variable.
- Example: we can examine the class of ticket and whether a person survived the Titanic:

Contingency Table

The two variables in this contingency table is gender and class/section number.

Contingency Tables (cont.)

- The margins of the table, both on the right and on the bottom, give totals and the frequency distributions for each of the variables.
- Each frequency distribution is called a marginal distribution of its respective variable.

Conditional Distributions

- A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable.
- The following is the conditional distribution of ticket Class, conditional on having survived:

Conditional Distributions (cont.)

- The following is the conditional distribution of ticket Class, conditional on having perished:

What Can Go Wrong? (cont.)

- Don’t confuse similar-sounding percentages—pay particular attention to the wording of the context.
- The percentage of students that are female & in ECO 138 Section 1
- (cell distribution)

- The percentage of females that are in ECO 138 Section 1
- (conditioned upon females)

- The percentage of ECO 138 Section 1 students that are females
- (conditioned upon ECO 138 Section 1)

- The percentage of students that are female & in ECO 138 Section 1

Conditional Distributions (cont.)

- The conditional distributions tell us that there is a difference in class for those who survived and those who perished.
- This is better shown with pie charts of the two distributions:

Segmented Bar Charts

- A segmented bar chart displays the same information as a pie chart, but in the form of bars instead of circles.
- Here is the segmented bar chart for ticket Class by Survival status:

Conditional Distributions (cont.)

- We see that the distribution of Class/Section for the male is different from that of the female.
- This leads us to believe that Class/Section and Gender are associated, that they are not independent.
- The variables would be considered independent when the distribution of one variable in a contingency table is the same for all categories of the other variable.

Which of the comparisons do you consider most valid?

- Overall average, b/c it does not differentiate between the four programs.
- Individual program comparisons, b/c they take into account the different number of applicants and admission rates for each of the four programs.
- Overall average, b/c it takes into account the differences in number of applicants and admission rates for each of the four programs.

Next Time…

- Chapter 4 – Displaying Quantitative Data

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