ECON 310STATISTICSECON 310: STATISTICS: MEASUREMENT IN ECONOMICS•Professor: Andres Aradillas-Lopez ([email protected])•Office Hours: Wednesday 2:00-3:30PM (6458 Soc. Sci)•Teaching Assistants:•Shenjie Hong ([email protected])•Irina Merkurieva ([email protected])•Office Hours: TBAGrading•Homework (20%) There will be 10 problem sets Lowest•Homework (20%). There will be 10 problem sets. Lowest problem set grade will be dropped from final grade. No late homework accepted•One midterm exam (35%) will take place on October 28th. No make-up datesmake-up dates.Final exam (45%) scheduled for December22nd•Final exam (45%) scheduled for December 22nd.TextbookTextbook•“Introduction to the Practice of Statistics”, by David Moore, George McCabe and Bruce Craig sixth edition (Freeman)McCabe and Bruce Craig, sixth edition (Freeman).•Note: Textbook problems assigned for homework refer to sixtheditionedition.Computational ProblemsComputational Problems•The course has a strong applied component. A number of homework problems involve the use of computerhomework problems involve the use of computer. • Excel is sufficient. You can use this or any other statistical kf f Eliilldill lbpackage of your preference. Excel is installed in all computer labs in UW.Notes and Homeworks Lecture slides will be posted on the web (link will be available through My UW website).gy ) Problem sets and solutions will also be posted.  If you have to be absent from lecture, you will have access to the y,ymaterial covered, the problem sets and their solutions.ANNOUNCEMENT: There will be no sections on the first week of classes. Sections will start meeting regularly from the second week onwards.will start meeting regularly from the second week onwards.Looking at DataDistributionsLooking at Data -DistributionsDisplaying Distributions with GraphsChapter 1.1Chapter 1.1 ObjectivesDisplaying distributions with graphsIntroduce the concept of variables and distributionsIntroduce the concept of variables and distributions.  Types of variables Graphs for categorical variablespg Bar graphs  Pie charts Graphs for quantitative variables Histograms StemplotsStemplots  Stemplots versus histograms Interpreting histograms Time series plotsVariablesIn a study, we collect information—data—from individuals or units.Individuals can be people animals plants or any object of interestIndividuals can be people, animals, plants, or any object of interest.A variable is any characteristic of an individual. A variable variesamong individuals.Example: age, height, blood pressure, ethnicity, leaf length, first languageExample: age, height, blood pressure, ethnicity, leaf length, first languageThe distribution of a variable tells us what values the variable takes and how often it takes these values.More formally, the distribution of a variable is a function that describes the frequency (probability) with which the variable takes each one of its possible values.Two types of variables Quantitative variablesSthithttk illfhihithti tiSomething that takes numerical values for which arithmetic operations, such as adding and averaging, make sense. Example: How tall you are, your age, your blood cholesterol level, the number of credit cards you own.CategoricalvariablesCategorical variables Something that falls into one of several categories. What can be counted is the count or proportion of individuals in each categoryis the count or proportion of individuals in each category. Example: Your blood type (A, B, AB, O), your hair color, your ethnicity, whether you paid income tax last tax year or not. Categorical variables refer to qualitative attributes.Distinguishing Categorical and Quantitative variablesAkAsk:  What are the individuals/units in the sample? What is being recorded about those individuals/units? If it is a number ( quantitative) If it is a statement or attribute ( categorical)QuantitativeCategoricalEach individual is attributed a numerical value.Each individual is assigned to one of several categories.Individualsin sampleDIAGNOSIS AGE AT DEATHPatient A Heart disease 56Patient B Stroke 70Patient C Stroke 75Patient D Lung cancer 60Patient EHeart disease80Patient EHeart disease80Patient F Accident 73Patient G Diabetes 69Ways to chart categorical dataBecause the variable is categorical, there is no obvious way to order the data (alphabetical, by increasing value, by year, by personal preference etc )preference, etc.)  Bar graphsEach category isEach category isrepresented by a bar.Pi h tPie chartsThe slices must represent the parts of one whole.Example: Top 10 causes of death in the United States 2001%of top%oftotalRank Causes of death Counts%of top 10s% oftotal deaths1 Heart disease 700,142 37% 29%2Cancer553,76829%23%2Cancer553,76829%23%3 Cerebrovascular 163,538 9% 7%4 Chronic respiratory 123,013 6% 5%Aid101 3%4%5Accidents101,5375%4%6 Diabetes mellitus 71,372 4% 3%7 Flu and pneumonia 62,034 3% 3%8 Alzheimer’s disease 53,852 3% 2%9 Kidney disorders 39,480 2% 2%10Septicemia32 2382%1%10Septicemia32,2382%1%All other causes 629,967 26%For each individual who died in the United States in 2001, we record what was the cause of death. The table above is a summary of that information.Bar graphsEh t i tdb b Thb’hihth th t(Each category is represented by one bar. The bar’s height shows the count (or sometimes the percentage) for that particular category.6007008000)Top 10 causes of deaths in the United States 2001300400500600unts (x1000The number of individuals who died of an accident in 2001 is approximately 0100200esrslarrytsusiasersiaCou100,000.Heart diseasesCancersCerebrovasculahronic respiratoryAccidentsDiabetes mellitusFlu & pneumoniaheimer's diseaseKidney disordersSepticemiaCChrDiFAlzheK500600700800000)Top 10 causes of deaths in the United States 2001100200300400500Counts (x10Bar graph sorted by rank Easy to analyze0100tdiseasesCancersbrovascularrespiratoryAccidentses mellituspneumoniar's diseasedisordersSepticemiaHeart dCerebroChronic reADiabetesFlu & pnAlzheimer'sKidney dSep800300400500600700800ts (x1000)Sorted alphabetically Much less useful0100200300ntsasecersculartoryitusoniasesdersmiaCountAccidentAlzheimer's diseasCanceCerebrovascuChronic respiratoDiabetes mellituFlu & pneumonHeart diseaseKidney disordeSepticemPie chartsEach slice represents a piece of one whole. The size of a slice depends on what Percent of