10 Chapter Data Analysis/Statistics: An Introduction Copyright © 2016, 2013, and 2010, Pearson Education, Inc.

10-1 Designing Experiments/Collecting Data Students will be able to understand and explain: • Designing experiments to collect data; • Variability in data and how it relates to the study of statistics; • The difference between a survey population and a sample population; and • Simple data analysis methods and interpretation across grade levels.

Introduction and Variability Much of the study of statistics deals with variability of data, or the amount the pieces of data in a data set differ. It is important to understand different types of variability when designing experiments and examining data.

Variability Measurement variability Suppose you ask 20 students to measure the length of a board. In a perfect world, all the measurements would be the same. However, simple human fallibility will produce different results. Natural variability Any two individuals have differences; even genetically identical twins have differences in personality, aptitude, and so on.

Variability Induced variability Induced variability is frequently studied to see, for example, how individuals react to certain stimuli or how bean plants grow based on the amount of food, water, and sunlight they receive.

Variability Sampling variability If we choose, for example, a set of college students to see how they react to a question, we could do so in many ways. Some ways might elicit a reaction that could be judged as representative of the entire student population; other selection methods might produce a very biased result.

Underlying Issues in Designing Studies The following framework for statistical problem solving was suggested for the classroom: Formulate questions Collect data Analyze the data Interpret the results

Formulating Questions For any given problem where data are needed to determine either an answer or an approach to an answer, it is important that the problem is clarified to the extent that meaningful data can be collected. For example, if we wanted to collect data on the appearance of an average fifth grader, we must clarify what it means to consider “the appearance of an average” fifth grader.

Example The IM Reliable Polling Company plans to conduct a survey of college students to determine their favorite movies in 2014-2015. What are some survey methods that could be used to obtain the information from the students? Answers will vary. One possibility is to have randomly selected students list their favorite movies. A second possibility is to provide a list of movies from the time period and ask randomly selected students to rate them from most favored to least favored using a numerical scale.

Collecting Data The next step is to develop a plan for collecting the data needed to answer the questions. An immediate question is from whom or where the data have to be collected. The context is most important.

Analyze the Data In analyzing collected data, we must make a decision about how to display the data or whether to report numbers to summarize them. Often, decisions about how to analyze data will be made with the data in hand. However, a good plan for collecting data should include some consideration of how the data will be analyzed once it is collected.

Interpret the Results The results of data analysis must be interpreted. Some interpretations are clear-cut; others sometimes misuse data. The interpretation must be related to the original questions.