1 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Chapter 1 Stats Starts Here

2 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Chapter 1 Objectives 1. Determine the context for the data values. 2. Identify the cases and variables in any data set. 3. Classify a variable as categorical or quantitative. 4. Identify the population from which a sample was chosen.

3 Copyright © 2014, 2012, 2009 Pearson Education, Inc. 1.1 What is Statistics?

4 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide 1- 4 Why study statistics? What are statistics used for? What was life like BEFORE statistics? Resource – The Lady Tasting Tea by David Salsburg

5 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide 1- 5 What Is (Are?) Statistics? Statistics (as a discipline) is a way of reasoning, a collection of tools and methods, designed to help us understand the world. In other words: Statistics is the art of distilling meaning from data. Statistics also refers to particular calculations made from data. Data are values with a context.

6 Copyright © 2014, 2012, 2009 Pearson Education, Inc. How to Make Sense of Information Data Any collection of numbers, characters, images, or other items that provide information about something Data vary: Surveys and experiments produce a variety of outcomes. Statistics helps us make sense of the data and how the data vary.

7 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide 1- 7 Example – class survey On a piece of paper write your initials, gender, your height (in inches), how many siblings you have (0 means only child), your major (or undecided), how many semesters of college you have completed, and a random number between 1 and 10. Lets look at our data set – In statistics variables are characteristics we measure or observe. What are the variables? Are there any patterns? Can we do any meaningful calculations on our data? These are statistics! Are there any issues with our variables? How well do you think our data generalizes to the student population of the college as a whole? To the population of the state? To the world?

8 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide 1- 8 What is Statistics Really About? 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.

9 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Example of Data Uses: Facebook Facebook collects data about you. Personal information: age, gender, education, etc. Interests: based on what you “like” Statistics is used to determine which ads you see. If you follow an ad Facebook now has even more data. Your information on Facebook is a goldmine for the company.

10 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Example: Texting While Driving Is texting while driving dangerous? Texting has grown dramatically in the last five years. Driving fatalities have gone down significantly in the last five years. Is texting while driving safe? How might you decide?

11 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Texting While Driving: University of Utah Study Measured reaction times of sober, drunk, and texting drivers in simulated driving emergencies Result: Those texting had the slowest reactions. Is texting while driving safe?

12 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Learning Outcomes Interpret data and communicate your results. Spot deficiencies in conclusions given in articles. Become a more informed citizen.

13 Copyright © 2014, 2012, 2009 Pearson Education, Inc. 1.2 Data

14 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Organizing Data Difficult to decipher the data above Presentation can make all the difference.

15 Copyright © 2014, 2012, 2009 Pearson Education, Inc. The six “W”s Who: Describe the individuals who were surveyed. What: Determine what is being measured. When: When was the research conducted? Where: Where was the research conducted? Why: What was the purpose of the survey or experiment? How: Describe how the survey or experiment was conducted.

16 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Who and What Respondents: Individuals who answer the survey Customers at Amazon Subjects or Participants: People who are experimented on Patients who receive the new medication Experimental Units: The object of the experiment when it is not a person Rats that run through a maze Records: Rows in a database Each person’s purchase record at Amazon

17 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Sample and Population The goal is to describe the population. This is usually impractical or impossible. A sample is used to make inferences about the population. The sample should be representative of the population.

18 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Think, Show, and Tell Think about what information you want to know. Show your results by displaying the data in a professional and accurate manner. Tell your story by describing what can be concluded from the data that was collected.

19 Copyright © 2014, 2012, 2009 Pearson Education, Inc. 1.3 Variables

20 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Categorical Variables Categorical Variable: A variable that tells us what group or category an individual belongs to Synonyms: nominal and qualitative Examples: Favorite color, country of birth, area code Drawback of Categorical Variables: Challenging to analyze with computation

21 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Quantitative Variables Quantitative Variable: Contains measured numerical values with measurement units Typically records the amount or degree of something Unit Examples: ounces, dollars, degrees Fahrenheit

22 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Categorical or Quantitative? Amazon knows your age and will use it to present an age-appropriate image customized for you. Is Age categorical or quantitative? Perceived as Child, Teen, Young Adult, Middle Aged, Senior, age is categorical. Can also be perceived as quantitative if not categorized into a type.

23 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Identifiers Identifier Variable: A variable that is used to uniquely identify the individual. It does not describe the individual. Login ID Customer Number Transaction Number Social Security Number Identifier Variables are a special type of Categorical Variable.

24 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Example What is the Who and What from our class survey? Who – students in Math 138 What (these are our variables) – gender, height, number of siblings, major, number of semesters of college completed, number between 1 and 10 What types of variables did we examine (quantitative or categorical)? What (if specified) are the units?

25 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Example Cola preference: let 1 indicate Coke and 2 indicate Pepsi. Is this variable categorical or quantitative?

26 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide What and Why (cont.) The questions we ask a variable (the Why of our analysis) shape what we think about and how we treat the variable.

27 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide What and Why (cont.) Example: In a student evaluation of instruction at a large university, one question asks students to evaluate the statement “The instructor was generally interested in teaching” on the following scale: 1 = Disagree Strongly; 2 = Disagree; 3 = Neutral; 4 = Agree; 5 = Agree Strongly. Question: Is interest in teaching categorical or quantitative?

28 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide What and Why (cont.) Question: Is interest in teaching categorical or quantitative? We sense an order to these ratings, but there are no natural units for the variable interest in teaching. Variables like interest in teaching are called ordinal variables. With an ordinal variable, look at the Why of the study to decide whether to treat it as categorical or quantitative.

29 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Ordinal Variables Ordinal Variable: A variable that reports order without natural units Four-point Likert Scale: Strongly Disagree, Disagree, Agree, Strongly Agree Olympic Rank: Gold, Silver, Bronze Can be treated as quantitative by using the rank number 1 = Strongly Disagree, 2 = Disagree, 3 = Agree, 4 = Strongly Agree

30 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide 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 The first step of any data analysis should be to examine the W’s—this is a key part of the Think step of any analysis. And, make sure that you know the Why, Who, and What before you proceed with your analysis.

31 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide What Can Go Wrong? Don’t label a variable as categorical or quantitative without thinking about the question you want it to answer. Just because your variable’s values are numbers, don’t assume that it’s quantitative. Always be skeptical—don’t take data for granted.

32 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Don’t confuse counts for quantitative data… 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 (shipping method) are the What, and the individuals counted (cases) are the Who.

33 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Summary Data are information in a context. The W’s help with context. We must know the Who (cases), What (variables), and Why to be able to say anything useful about the data.

34 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Summary (cont.) We treat variables as categorical or quantitative. Categorical variables identify a category for each case. Quantitative variables record measurements or amounts of something and must have units. Some variables can be treated as categorical or quantitative depending on what we want to learn from them.

35 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Practice A study was conducted to compare the abilities of men and women to perform the strenuous tasks required of a shipboard firefighter (Human Factors, 24 [1982]). The study reports the pulling force (in newtons) that a firefighter was able to exert in pulling the starting cord of a P-250 water pump. The study also gives the weight and, of course, sex of the firefighters. Identify the Who, What, and Why? Also Where, When, and How (if given)? Name the variables Which variables are categorical and which are quantitative? What are the units of the quantitative variables (or note that they aren’t provided)?

36 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Practice A study was conducted to compare the abilities of men and women to perform the strenuous tasks required of a shipboard firefighter (Human Factors, 24 [1982]). The study reports the pulling force (in newtons) that a firefighter was able to exert in pulling the starting cord of a P-250 water pump. The study also gives the weight and, of course, sex of the firefighters. Who – shipboard firefighters Cases – each firefighter as an individual What (Variables) – pulling force, weight, and gender When – reported in 1982 Where – not specified Why – The researchers wanted to compare the abilities of men and women How – not specified Variables: Pulling force WeightGender Type: quantitative quantitativecategorical Units: Newtons not specified, probably pounds

37 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Practice The EPA tracks fuel economy of automobiles. Among the data the agency collects are the manufacturer (Ford, Toyota, etc), vehicle type (car, SUV, etc), weight, horsepower, and gas mileage (mpg) for city and highway driving Identify the Who, What, and Why? Also Where, When, and How (if given)? Name the variables Which variables are categorical and which are quantitative? What are the units of the quantitative variables (or note that they aren’t provided)?

38 Copyright © 2014, 2012, 2009 Pearson Education, Inc. Slide Practice The EPA tracks fuel economy of automobiles. Among the data the agency collects are the manufacturer (Ford, Toyota, etc), vehicle type (car, SUV, etc), weight, horsepower, and gas mileage (mpg) for city and highway driving Who – Each model of automobile Cases – each vehicle model is a case What (Variables) – vehicle manufacturer, vehicle type, weight, horsepower, and gas mileage for city and highway driving When – current Where – United States Why – By the EPA to track fuel economy of vehicles How – The data are collected from the manufacturer of each model Variables: manufacturer: categorical, vehicle type: categorical, weight: quantitative - units not specified (pounds), horsepower: quantitative – units not specified (horsepower), gas mileage for city: quantitative – miles per gallon, gas mileage for highway: quantitative – miles per gallon Concerns – do manufacturers’ ratings of their own vehicles’ gas mileage reflect customer experience?