Economic Reasoning Using Statistics

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Economic Reasoning Using Statistics. Econ 138 Dr. Adrienne Ohler. How you will learn. . Textbook: Stats : Data and Models 2 nd 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.

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### Economic Reasoning Using Statistics

Econ 138

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
• Come to class prepared and awake
• Office Hours: T, H 9-11am and by Appointment
• 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
• Statistics (the discipline) is a way of reasoning, a collection of tools and methods, designed to help us understand the world.
• Will the sun rise tomorrow?
• A statistic is a number that represents a characteristic of a population. (i.e. average, standard deviation, maximum, minimum, range)
• 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
• 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)
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