Statistics Through Applications Chapter 1: How Do We Get “Good” Data? Copyright © 2004 by W. H. Freeman & Company

Individuals & Variables Individuals are the objects described by a set of data. –People, animals, or things A Variable is any characteristic of an individual. Variables can take different values for different individuals. –Categorical Variables: places an individual into one of several categories (Job type, gender, race) –Quantitative Variables: takes numerical values for which ordering and averaging make sense (age, weight, salary)

Example: A few lines from a teacher’s gradebook What individuals does this data describe? What variables does this data describe? Which of these are categorical? Which are quantitative? NameSexHomeroomGradeCalc No.Test 1 Hsu, DannyMBlair12B31981 Iris, FrancineFKingsley12B29892 Ruiz, RicardoMAlfonzo11B30487

Good Data is Valid, Unbiased & Reliable Valid – relevant and appropriate Unbiased – not consistently lower or higher than actuality Reliable – as little variation as possible

Good Data is Compared Fairly Often a rate expressed as a percent or fraction is a more valid measure than a simple count of occurrences –Two schools both had 1900 students pass TAKS. One school has 2000 students and the other has Did they perform equally as well?

Percent Change Percent change = From July 2008 to July 2009, the Dow Jones Industrial Average dropped from 11, to Find the percent change. What is another way to describe a 100% increase? What can be said about a 100% decrease? What can be said about a decrease higher than 100%?

Even Good Data needs to be Read Carefully Summertime is Burglary Time – or is it? –An advertisement for a home security system says, “When you go on vacation, burglars go to work. According to FBI statistics, over 26% of home burglaries take place between Memorial Day and Labor Day.”

Only one in two cameras is actually in operation, but this could soon increase to as many as one in three Watford Observer, 2 August 2002 Whereas five years ago the [professional conduct committee] panels sat for only 90 days a year, in 2000 the number of days was 242 and in 2001 it was 479. This year the number of days will be higher still... General Medical Council newsletter, 13 August 2002 Westchester County is a suburban area covering 438 square miles immediately north of New York City. The county is home to 800,000 deer. Fine Gardening, September/October 1989 Continental Airlines once advertised that it had “decreased lost baggae by 100% in the past six months.”

Even Good Data Varies How Long is a Minute? –How accurate are you and your classmates at knowing how long a minute is? –Get a partner and a stopwatch. You will take turns timing and guessing. Using the stopwatch, the timer tells the guesser when to start. When the guesser believes that a minute has passed, he says “Stop.” At that point, the timer stops the stopwatch and records the time that passed to the nearest tenth of a second. Do not tell your partner how much time actually passed! –Reset the stopwatch and switch roles. Continue timing and measuring until you each person has been timed three times.

Analyzing How Long is a Minute? Was your data valid? Was either partner’s data biased? Which partner was more reliable? How about the class as a whole? Add your data (all 6 measures) to the class list and graph.

Use Averages to Improve Reliability No measuring process is perfectly reliable. The average of several repeated measurements of the same individual is more reliable (and less variable) than a single measurement.

The Statistical Problem Solving Process - APAC A – Ask a question of interest P – Produce data A – Analyze and describe/graph the data C – Conclusion, answering the question

Using APAC Which element of APAC is shown here? What is a reasonable question of interest? How do you think the data were produced? –What are the individuals? –What is the variable? –Is it quantitative or categorical? What can be concluded?

First Homework Problem According to the National Institute on Media and the Family, a preschooler’s risk of obesity jumps 6% for every hour of television watched per day. The risk increases by 31% if the TV is in their bedroom. –1.What element of APAC is given here? –2. What is a reasonable question of interest in this case? –3. The actual study that produced these results involved 2761 low- income adults in New York with children aged 1 to 4 years. Who are the individuals in this study? –4. What variable(s) were measured?