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Chapter 2

Data, Reality, and Problem Solving. Chapter 2. Data, Reality, and Problem Solving Sections 2.1-2.4 The Reality of Conducting a Study. HAWKES LEARNING SYSTEMS math courseware specialists. Objectives:. Learn the ethical concerns of conducting a study.

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Chapter 2

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  1. Data, Reality, and Problem Solving Chapter 2

  2. Data,Reality, and Problem Solving Sections 2.1-2.4The Reality of Conducting a Study HAWKES LEARNING SYSTEMS math courseware specialists Objectives: • Learn the ethical concerns of conducting a study. • Determine the practical concerns of conducting a study.

  3. Data,Reality, and Problem Solving Section 2.1 The Lords of Data HAWKES LEARNING SYSTEMS math courseware specialists Measurement: • To develop suitable measurements we will be concerned with the following: • What should be measured? • How should the concept be measured? • Now we need to know how good the measurements are. Ask yourself the following: • Is the concept under study adequately reflected by the proposed measurements? • Is the data measured accurately? • Is there a sufficient quantity of the data to draw a reasonable conclusion? • If you answered yes to all three of these questions, the data possesses good properties.

  4. Data,Reality, and Problem Solving Section 2.2 Science and Data HAWKES LEARNING SYSTEMS math courseware specialists The Scientific Method: • The scientific method is a collection of methods that have become standard for exploring research problems. • The Scientific Method: • Gather information about the phenomenon being studied. • On the basis of that data, formulate a preliminary generalization or hypothesis. • Collect the data to test the hypothesis. • If the data and other subsequent experiments support the hypothesis, it becomes a law.

  5. Data,Reality, and Problem Solving Section 2.3 Decision Making and Data HAWKES LEARNING SYSTEMS math courseware specialists Decision Making: • We make decisions every day and collecting data is a natural part of our lives. One decision we make every day is: • “What will I have for dinner?” • Although we may not apply the scientific method, most people perform experiments and collect data (by eating). This leads to generalizations such as “I like everything except liver, sweet peas, and beets.” • After sufficient experimentation, these generalizations become personal preference laws. • Do you have any personal preference laws?

  6. Data,Reality, and Problem Solving Section 2.3 Decision Making and Data HAWKES LEARNING SYSTEMS math courseware specialists Decision Making Method: • Clearly define the problem and any influential variables. • Decide upon objectives and decision criteria for choosing a solution. • Create alternative solutions. • Compare alternatives using the criteria established in the second step. • Implement the chosen alternative. • Check the results to make sure the desired results are achieved.

  7. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Ways to Collect Data: • The two ways to collect data are: • Controlled experiments • Observation • The data collection method is related to the nature of the problem to be solved and the ethical and practical constraints of collecting data in some particular environment.

  8. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Controlled Experiments: • The purpose of a controlled experiment is to reveal the response of one variable to the changes of another variable. • In a controlled experiment there are two groups: the control group and the experimental group. • During the experiment a treatment is applied to the experimentalgroup. • The exact treatment will depend on the particular experiment. • The treatment changes the level of the explanatory variable in the experiment. The effect of the treatment can be measured by comparing the response variable in the control and experimental groups.

  9. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Definitions: • The response variable measures the outcome of interest in a study. • An explanatory variable causes or explains changes in the response variable.

  10. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Calculus before Physics Experiment:

  11. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Flowchart for the Calculus before Physics Experiment: Treatment (Take Calculus before Physics) Treatment Group Observe Randomly Select Students Compare Performance Control Group Observe

  12. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Does an SAT Course Improve an SAT Score?

  13. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Flowchart for the SAT Experiment: Before The control group: Is high school students that have taken the SAT exactly one time. The value of the response variable is the students’ scores on their first SAT. Treatment The same high school students are given an SAT preparation course. After Now, the students are the treatment group and they take the SAT again. The value of the response variable is the score on the second SAT. Compare Compare students performance on the SAT before and after the course

  14. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Definitions: • Sometimes in clinical trials people are given placebos. Placebos are “fake” treatments. • Double blind studies are used to counteract the placebo effect. In these studies neither the subjects know if they are members of the control or experimental group, nor do the evaluators know whether their subjects are members of the control or experimental group.

  15. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Observational Data: • Observational data comes by measuring “what is.” • For example, observational data is: • What is happening in the marketplace at the time. • The measure of how things are in a specific geographic area at a given point in time. • Virtually all data we routinely encounter is observational.

  16. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Examples of Observational Data: • Stock, commodity, bond, option, and currency market data. • Almost all federal data, including census, economic, and educational data. • Sports data. • Can you think of an example of observational data?

  17. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Example: 8,442 men and 4,321 women applied to graduate school at Berkeley. Subsequently, 3,714 men and 1,512 women accepted. Thus 44% of the men and 35% of the women were accepted. Was the graduate school discriminating against women? To the left is the admissions data from Berkeley. Does this data show discrimination?

  18. Data,Reality, and Problem Solving Section 2.4 Collecting Data HAWKES LEARNING SYSTEMS math courseware specialists Solution: • In all but one of the majors, women were admitted more frequently than men. Not only were women not being discriminated against, but there appears to be potential discrimination against men in Major I. • The majors that had very low acceptance rates had relatively very few men and a large number of women applying. • The variable, major field of study, was confounding the variable gender in the original analysis and biasing the original conclusion.

  19. Data,Reality, and Problem Solving Section 2.4 Collecting Data Ch 2. Data, Reality, & Problem Solving 2.5 Data Classifications Example: • Determine whether each of the following studies is observational • or experimental. • A medical researcher wants to examine the effects of exercise on cardiovascular health. • Solution: Experimental • A recording company is interested in knowing the percentage of teenagers that download music off of the internet. • Solution:Observational • A chain of grocery stores wants to know how much the average family spends on produce each month. • Solution: Observational

  20. Data,Reality, and Problem Solving Sections 2.5-2.6 Levels of Measurement HAWKES LEARNING SYSTEMS math courseware specialists Objectives: • Classify data as discrete or continuous. • Determine if data are qualitative or quantitative. • Identify the level of measurement.

  21. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Data Classifications: • Data or variables can be categorized in several ways: • Discrete or continuous • Level of measurement • Quantitative or qualitative

  22. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Discrete Data: • Discrete data is a restricted set of values. • Examples of discrete data: • The number of people in a classroom • A variable that only has the values 1, 1.5, 2, 2.5 • A variable that contains integer values • Can you think of some data that is discrete?

  23. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Continuous Data: • Continuous data can take on any value in an interval. • Examples of continuous data: • Height • Age • A variable that has any value between 0 and 2 • Can you think of some data that is continuous?

  24. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Level of Measurement: • The quality of data is referred to as its level of measurement. • Terms used to describe the level of measurement: • Nominal • Ordinal • Interval • Ratio

  25. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Nominal Data: • Nominal measuresoffernames or labels for certain characteristics. • Examples of nominal measures: • Gender • Hair color • Jersey number of a basketball player • Can you think of a measure that is nominal?

  26. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Ordinal Data: • Ordinal data represents data in an associated order. • Examples of ordinal data: • Ranking of sports teams • Year in college • Letter grades • Can you think of data that is ordinal?

  27. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Interval Data: • If the data can be ordered and the arithmetic difference is meaningful, the data is interval. • Examples of interval data: • Temperature • Dates • Level of difficulty rated from 1 to 5 • Can you think of data that is interval?

  28. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Ratio Data: • Ratio datahas a meaningful zero point and the ratio of two data points is meaningful. • Examples of ratio data: • Money • Height • Age • Can you think of data that is ratio?

  29. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Example: • Determine the level of measurement. • Today’s high temperature (in Fahrenheit) for varying cities across the U.S. • Solution: Interval • The colors contained in a box of crayons. • Solution: Nominal • The boiling point (in Kelvin’s) for varying chemical compounds. • Solution: Ratio • The individual page numbers at the bottom of each page in the statistics book. • Solution: Ordinal

  30. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Qualitative and Quantitative Data: • Qualitative data is measured on a nominal or ordinal scale. • Quantitative data is measured on an interval or ratio scale. Qualitative Quantitative Descriptions and labels Counts and measurements

  31. Data,Reality, and Problem Solving Section 2.5 Data Classifications HAWKES LEARNING SYSTEMS math courseware specialists Example: • Classify each of the following as qualitative or quantitative data. • The weights of members of the football team. • Solution: Quantitative • The flavors of Ben and Jerry’s Ice Cream. • Solution: Qualitative • The jersey numbers of a women’s basketball team. • Solution: Qualitative • Student ID numbers. • Solution: Qualitative

  32. Data,Reality, and Problem Solving Section 2.5 Data Classifications Levels of Measurement: Ratio 0 means the absence of something Interval 0 is a placeholder Ordinal Order Nominal Names

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