1. Copyright © 2009 Pearson Education, Inc. Chapter 2 Data

2. Copyright © 2009Pearson Education, Inc. Slide 1- 2 Objectives: The student will be able to: Determine the context for the data values. Identify the cases and variables in any data set. Classify a variable as categorical or quantitative.

3. Copyright © 2009Pearson Education, Inc. Slide 2- 3 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…

4. Copyright © 2009Pearson Education, Inc. Slide 2- 4 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.

5. Copyright © 2009Pearson Education, Inc. Slide 2- 5 Data Tables The following data table of from Amazon clearly shows the context of the data presented: Who is the data referring to, What has been collected? Notice that this data table tells us the What (column titles) and Who (row titles) for these data.

6. Copyright © 2009Pearson Education, Inc. Slide 2- 6 Who The Who of the data tells us the individual cases about which (or whom) we have collected data. Cases are often a sample of a larger population. Context is important so that we know if there are conclusions that can be drawn about the larger population.

7. Copyright © 2009Pearson Education, Inc. Slide 2- 7 What and Why Variables are characteristics recorded about each individual. The variables should have a name that identify What has been measured. To understand variables, you must Think about what you want to know.

8. Copyright © 2009Pearson Education, Inc. Slide 2- 8 What and Why (cont.) Some variables have units that tell how each value has been measured and tell the scale of the measurement.

9. Copyright © 2009Pearson Education, Inc. Slide 2- 9 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, number of countries visited, number between 1 and 10 What (if specified) are the units?

10. Copyright © 2009Pearson Education, Inc. Slide 2- 10 What and Why (cont.) A categorical (or qualitative) variable names categories and answers questions about how cases fall into those categories. Categorical examples: sex, race, ethnicity 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) Examples” Which of our variables were categorical and which were quantitative? Cola preference: let 1 indicate Coke and 2 indicate Pepsi. Is this variable categorical or quantitative?

11. Copyright © 2009Pearson Education, Inc. Slide 2- 11 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.

12. Copyright © 2009Pearson Education, Inc. Slide 2- 12 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?

13. Copyright © 2009Pearson Education, Inc. Slide 2- 13 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 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.

14. Copyright © 2009Pearson Education, Inc. Slide 2- 14 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 (shipping method) are the What, and the individuals counted are the Who.

15. Copyright © 2009Pearson Education, Inc. Slide 2- 15 Counts Count (cont.) When we focus on the amount of something, we use counts differently. For example, Amazon might track the growth in the number of teenage customers each month to forecast CD sales (the Why). The What is teens, the Who is months, and the units are number of teenage customers.

16. Copyright © 2009Pearson Education, Inc. Slide 2- 16 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.

17. Copyright © 2009Pearson Education, Inc. Slide 2- 17 Where, When, and How We need the Who, What, and Why to analyze data. But, the more we know, the more we understand. When and 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.

18. Copyright © 2009Pearson Education, Inc. Slide 2- 18 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.

19. Copyright © 2009Pearson Education, Inc. Slide 2- 19 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.

20. Copyright © 2009Pearson Education, Inc. Slide 2- 20 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.

21. Copyright © 2009Pearson Education, Inc. Slide 2- 21 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.

22. Copyright © 2009Pearson Education, Inc. Slide 2- 22 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)?

23. Copyright © 2009Pearson Education, Inc. Slide 2- 23 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

24. Copyright © 2009Pearson Education, Inc. Slide 2- 24 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)?

25. Copyright © 2009Pearson Education, Inc. Slide 2- 25 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?

26. Copyright © 2009Pearson Education, Inc. Slide 2- 26 Ch 2 hand-in homework The State Education Department requires local school districts to keep these records on all students: age, race (or ethnicity), days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs the student may have. (0.5 point) What is the "who" for this study? (1 point) Name at least two quantitative variables is the study AND give their label. (1 point) Name at least two categorical variables in this study. (0.5 point) Write a "reasonable and logical" reason why the Education Department requires these data from local school districts. ("NA" or "not given" will not suffice as answers.)