Chapter 2 Data

Learning Objectives 1.Define Data. 2.Identify populations and samples. 3.Identify the cases and variables in any data set. 4.Know the key features of a categorical versus a quantitative variable and classify a variable as categorical or quantitative. 5.Know the definition of a discrete versus a continuous quantitative variable. Rubric: Level 1 – Know the objectives. Level 2 – Fully understand the objectives. Level 3 – Use the objectives to solve simple problems. Level 4 – Use the objectives to solve more advanced problems. Level 5 – Adapts and applies the objectives to different and more complex problems. 2

Learning Objectives 6.Define statistic. 7.Identify the Who, What, When, Where, Why, and How of data, or recognize when some of this information has not been provided. 3

4 Learning Objective 1: Data Definition ‒Data: (latin for fact) Characteristics or numbers that are collected by observation or experimentation. Data are numbers with context. 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 without their context…

Learning Objective 1: Data Data is information we gather with experiments and with surveys. Example: Experiment on low carbohydrate diet – Data could be measurements on subjects before and after the experiment Example: Survey on effectiveness of a TV ad – Data could be percentage of people who went to Starbucks since the ad aired

Learning Objective 2: Population and Samples Population: All subjects of interest. Sample: Subset of the population for whom we have data. Population Sample

Learning Objective 2: Example: Population and Samples In California in 2003, a special election was held to consider whether Governor Gray Davis should be recalled from office. An exit poll sampled 3160 of the 8 million people who voted. Define the sample and the population for this exit poll. – The population was the 8 million people who voted in the election. – The sample was the 3160 voters who were interviewed in the exit poll.

Learning Objective 3: Case Case - an individual about whom or which we have data. – Individuals are the objects described by a set of data. Individuals may be people, but they may also be animals or things. – Example: Freshmen, 6-week-old babies, golden retrievers, fields of corn, cells – People are referred to as respondents, subjects, or participants, while objects are referred to as experimental units.

Learning Objective 3: Variable Variable - is any characteristic that is recorded for the individuals in a study. Called a variable because it varies between individuals. Examples: Marital status, Height, Weight, IQ Example: Data – Student data base (includes data on each student enrolled). Individuals – students Variables – DOB, Gender, GPA, etc.

Learning Objective 3: Variable A variable can be classified as either – Categorical, or – Quantitative (Discrete, Continuous)

11 Learning Objective 4: Categorical Variable A variable can be classified as categorical if each observation belongs to one of a set of categories. What can be counted is the count or proportion of individuals in each category. Numerical values are categorical when it makes no sense to find an average for them – zip codes, jersey numbers, etc. Examples: – Gender (Male or Female) – Religious Affiliation (Catholic, Jewish, …) – Type of residence (Apt, Condo, …) – Belief in Life After Death (Yes or No)

12 Learning Objective 4: Quantitative Variable A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable. Numerical values for which arithmetic operations such as adding and averaging make sense. Numerical values that have measurement units such as dollars, degrees, inches, etc. Examples: – Age – Number of siblings – Annual Income

Ask: What are the n individuals/units in the sample (of size “n”)? What is being recorded about those n individuals/units? Is that a number (  quantitative) or a statement (  categorical)? Individuals in sample DIAGNOSISAGE AT DEATH Patient AHeart disease56 Patient BStroke70 Patient CStroke75 Patient DLung cancer60 Patient EHeart disease80 Patient FAccident73 Patient GDiabetes69 Quantitative Each individual is attributed a numerical value Categorical Each individual is assigned to one of several categories Learning Objective 4: How to decide if a variable is categorical or quantitative?

14 Learning Objective 4: Main Features of Quantitative and Categorical Variables For Quantitative variables: key features are the center and spread (variability). For Categorical variables: a key feature is the percentage or proportion of observations in each of the categories.

15 Learning Objective 4: Class Problem Identify the variable type as either categorical or quantitative. 1.Number of siblings in a family 2.County of residence 3.Distance (in miles) of commute to school 4.Marital status quantitative categorical quantitative categorical

16 Learning Objective 5: Discrete Quantitative Variable A quantitative variable is discrete if its possible values form a set of separate numbers, such as 0,1,2,3,…. Discrete variables have a finite number of possible values Examples: – Number of pets in a household – Number of children in a family – Number of foreign languages spoken by an individual

17 Learning Objective 5: Continuous Quantitative Variable A quantitative variable is continuous if its possible values form an interval Continuous variables have an infinite number of possible values Examples: – Height/Weight – Age – Blood pressure

18 Learning Objective 5: Class Problem Identify each of the following variables as continuous or discrete. 1.Length of time to take a test 2.Number of people waiting in line 3.Number of speeding tickets received last year 4.Your dog’s weight continuous discrete continuous

Learning Objective 4 & 5: Summary Data Categorical Quantitative DiscreteContinuous Examples: Marital Status Are you registered to vote? Eye Color (Defined categories or groups) Examples: Number of Children Defects per hour (Counted items) Examples: Weight Voltage (Measured characteristics)

Learning Objective 6: Statistic A statistic is a numerical summary of data. – Examples: mean, median, standard deviation, range, etc.

Learning Objective 7: the W’s The Who, What, When, Where, Why, and How of data. Provides the context of the data.

22 Learning Objective 7: the W’s Who – Who are the individuals or cases? The Who tells us the individual cases for which (or whom) we have collected data. – People are referred to as respondents, subjects, or participants, while objects are referred to as experimental units. Sometimes people just refer to data values as observations and are not clear about the Who.

Learning Objective 7: the W’s What – What variables were recorded about each of the individuals? – Variables are characteristics recorded about each individual. – The variables should have a name that identify What has been measured or counted.

Learning Objective 7: the W’s When – When the data was collected. – Gives us some nice information about the context. – Example: Values recorded in 1930 may mean something different than similar values recorded in 2010.

Learning Objective 7: the W’s Where – Where the data was collected. – Gives us more 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.

Learning Objective 7: the W’s Why – Why the data was collected. This can determine whether a variable is treated as categorical or quantitative.

Learning Objective 7: the W’s How - How the data are collected can make the difference between insight and nonsense. – Examples: survey, observation, experimentation, etc. – Example: results from Internet surveys are often useless.

Learning Objective 7: the W’s The first step of any data analysis should be to examine the W’s—this is a key step of any data analysis. Knowing the context of the data.

Learning Objective 7: the W’s - Example For the following description of data, identify the W’s, name the variable, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured. The State Education Department requires local school districts to keep these records on all students: age, race, days absent, current grade level, standardized test scores in reading and math, and any disabilities. Solution:Who – Students What – Age (probably in years), Race, Number of absences, Grade Level, Reading score, Math score, Disabilities. When – Must be kept current. Where – Not specified. Why – State required. How – Information collected and stored as part of school records. Categorical Variables: Race, grade level, disablities Quantitative Variables: Number of absences, age, reading score, math score.

Learning Objective 7: the W’s – Your Turn For the following description of data, identify the W’s, name the variable, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured. The Gallup Poll conducted a representative telephone survey of 1180 American voters during the first quarter of Among the reported results were the voters region (Northeast, South, etc.), age, party affiliation, and whether or not the person had voted in the 2006 midterm congressional election. Solution:Who – 1180 Americans. What – Region, age (in years), political affiliation, and whether or not the person voted. When – First quarter Where – United States Why – Gallup public opinion poll. How – Telephone survey. Categorical Variables: Region, political affiliation, whether or not the person voted. Quantitative Variable: Age.

Finial Thought on Data

Assignment Chapter 2, pg. 16 – 18; #1, 3, 10, 11, 15, 22, 25 Read Chapter 3, pg