Collecting Data Lesson 3 1 Introduction to Data

Collecting Data Lesson 3. 1 Introduction to Data Collection Statistics and Probability with Applications, 3 rd Edition Starnes & Tabor Bedford Freeman Worth Publishers

Introduction to Data Collection Learning Targets After this lesson, you should be able to: ü Distinguish statistical questions from other types of questions. ü Identify the population and sample in a statistical study. ü Distinguish between an observational study and an experiment. Statistics and Probability with Applications, 3 rd Edition 2

Introduction to Data Collection Suppose we want to find out what percent of young drivers in the United States text while driving. A statistics problem starts with a statistical question. Not just any question will do. A valid statistical question is based on data that vary. That is, the answer to the question won’t be the same each time an observation is recorded. How to Complete the Statistical Problem-Solving Process • Ask questions: Clarify the research problem and ask one or more valid statistical questions. • Collect data: Design and carry out an appropriate plan to collect the data. • Analyze data: Use appropriate graphical and numerical methods to analyze the data. • Interpret results: Draw conclusions based on the data analysis. Statistics and Probability with Applications, 3 rd Edition 3

Asking valid statistical questions PROBLEM: Determine if each of the following is a valid statistical question. Justify your answer. (a) How many days did students at your school play video games last week? (b) Which gender is more likely to choose vanilla over chocolate ice cream? (c) How many people in the United States were convicted of violent crimes last year? Statistics and Probability with Applications, 3 rd Edition 4

Introduction to Data Collection Back to the question of what percent of young drivers in the United States text while driving. To answer the question, we will survey 16 - to 20 -year-olds who live in the United States and drive. Ideally, we would ask them all (take a census). But contacting every driver in this age group wouldn’t be practical. It would take too much time and cost too much money. Instead, we put the question to a sample chosen to represent the entire population of young drivers. Population, Census, and Sample • The population in a statistical study is the entire group of individuals we want information about. • A census collects data from every individual in the population. • A sample is a subset of individuals in the population from which we collect data. Statistics and Probability with Applications, 3 rd Edition 5

Introduction to Data Collection Statistics and Probability with Applications, 3 rd Edition 6

Populations and samples PROBLEM: Identify the population and sample in each of the following settings. (a) A wildlife biologist in Alaska tranquilizes 42 grizzly bears in the state, records their weights, and then releases them. (b) A teenager selects 15 Beyoncé songs and counts the number of words in each song. Statistics and Probability with Applications, 3 rd Edition 7

Introduction to Data Collection A sample survey usually aims to gather information about a population without disturbing the population in the process. Sample surveys are one kind of observational study. In contrast to observational studies, experiments don’t just observe individuals or ask them questions. They actively impose some treatment to measure the response. Observational Study, Experiment • An observational study observes individuals and measures variables of interest, but does not attempt to influence the responses. • An experiment deliberately imposes some treatment on individuals to measure their responses. Statistics and Probability with Applications, 3 rd Edition 8

Introduction to Data Collection The distinction between observational study and experiment is one of the most important ideas in statistics. • The goal of an observational study can be to describe some group or situation, to compare groups, or to examine relationships between variables. • The purpose of an experiment is to determine if the treatment causes a change in the response. • An observational study, even one based on a random sample, is a poor way to gauge the effect that changes in one variable have on another variable. • When the goal is to understand cause and effect, experiments are the only source of fully convincing data. Statistics and Probability with Applications, 3 rd Edition 9

Observational studies and experiments Do fast-paced cartoons affect our behavior? PROBLEM: Determine whether each of the following settings describes an observational study or an experiment. Explain your reasoning. (a) Sixty 4 -year-old children were randomly divided into three groups. One group was shown a fast-paced cartoon, one group was shown an educational cartoon, and one group was given art supplies and instructed to draw pictures. Afterward, the 4 -year-olds who watched the fast-paced cartoon scored significantly worse than the other two groups on tests that measured the ability to make decisions. (b) One hundred teenagers between the ages of 16 -18 were surveyed. The teens were asked whether, as young children, they watched fast-paced cartoons more often than, less often than, or about equally as often as educational cartoons. They were also asked to reveal their GPA. The teens who watched fast-paced cartoons more often than educational cartoons had lower GPAs than teens from the other two groups, on average. Statistics and Probability with Applications, 3 rd Edition 10

LESSON APP 3. 1 Do you have dinner plans? Researchers at Columbia University randomly selected 1000 teenagers in the United States for a survey. According to an ABC News article about the research, “Teenagers who eat with their families at least five times a week are more likely to get better grades in school. ” 1. What is the statistical question that the researchers were trying to answer? 1. Identify the population and sample. 1. Is this an observational study or an experiment? Explain. Statistics and Probability with Applications, 3 rd Edition 11

Introduction to Data Collection Learning Targets After this lesson, you should be able to: ü Distinguish statistical questions from other types of questions. ü Identify the population and sample in a statistical study. ü Distinguish between an observational study and an experiment. Statistics and Probability with Applications, 3 rd Edition 12