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Homework Check Homework check now... Please take out your homework so we can check it.

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Homework Answers 1.2 1.Nominal and ordinal 2.Ordinal, interval, and ratio 3.True 4.False 5.False 6.False 7.qualitative

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Answers to 1.2 8. quantitative 9. quantitative 10. qualitative 11. ordinal 12. nominal 13. ratio 14. nominal

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Answers to 1.2 15. interval 16. ratio 17. ordinal 18. ordinal 19. nominal 20. ordinal 21. Interval data can be ordered and difference between entries can be calculated. Ratio data has all the properties of interval data with the addition that a ratio of two data values can be formed so one data value can be expressed as a multiple of another. 22. An inherent zero is a zero that implies, “none.”

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1.3 Experimental Design Statistics Mrs. Spitz Fall 2008

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Objectives How to design a statistical study. How to collect data by performing an experiment, using a simulation, taking a census, or using a sampling. How to create a sample using random sampling, stratified sampling, systematic sampling, and convenience sampling.

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Assignment Pgs 20-21 #1-20 all Technology – pg. 23 #1-8 As far as I have planned, I am planning to take 2 days for notes, so 1.3 won’t be due until Wednesday. Wednesday/Thursday, we will go to computer lab to work on pg. 23. -- Just in case, make sure you can log into a machine. If you need a password reset, we need to do that before Wednesday. Friday – I am planning a Review – pages. 25 & 26, and you should look at the chapter quiz and ALL of your vocabulary from this chapter for a test next Monday!

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Experimental Design The goal of every statistical study is to collect data and then use the data to make a decision. Any decision you make using the results of a statistical study is only as good as the process used to obtain the data. If the process is flawed, then the resulting decision is questionable.

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Experimental Design You may never have to develop a statistical study, but it is likely you will have to interpret the results of one. Before you interpret the results, you should make sure the results are valid or not. So... You should be familiar with how to design a statistical study.

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Guidelines: Designing a Statistical Study 1.Identify the variable(s) of interest (the focus) and the population of the study. 2.Develop a detailed plan for collecting the data. Make sure the data are representative of the population. 3.Collect the data. 4.Describe the data with descriptive statistics techniques. 5.Make decisions about using inferential statistics. Identify any possible errors.

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Data Collection There are several ways to collect the data. Often, the focus of the study will dictate the best way to collect it. The following slides give a brief summary of the four methods of data collection.

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Perform an Experiment When performing an experiment, a treatment is applied to part of a population and responses are observed. A second part of the population is often used as a control group. This group receives no treatment or is given a placebo.

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Use a Simulation A simulation is the use of a mathematical or physical model to reproduce the conditions of a situation or process. Collecting data often involves the use of computers. Simulations allow you to study situations which are impractical or dangerous to create in real life and often save time and money. i.e. Crash test dummies used by auto companies

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Take a Census A census is a count or measure of an ENTIRE population. Taking a census provides complete information, but it is often costly and difficult to perform.

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Use Sampling A sampling is a count or measure of part of a population. The statistics calculated from a sample are used to predict various population parameters. For instance... US Census Bureau sampling the US population to update the most recent census data. Using sampling is often more practical than taking a census.

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Surveys Once you determine which method you will use to collect data, you might decide that a survey can help you. Surveys can be used to take a census or sampling. A survey is an investigation of one or more characteristics of a population. Most often, surveys are carried out on people by asking them questions. A disadvantage of using a survey to collect data is the wording of questions can lead to biased results.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 1. A study of the effect of an asteroid colliding with Earth.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 1. Because it is impractical to create this situation, you would want to use a simulation.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 2. A study of the effect of aspirin on preventing heart attacks.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 2. In this study, you want to measure the effect a treatment (taking aspirin) has on patients. So, you would want to perform and experiment.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 3. A study of the weights of all linemen in the National Football League.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 3. Because National Football League teams keep accurate physical records of all players, you could take a census.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 4. A study of Americans’ approval rating of the U.S. President.

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Ex. 1: Deciding upon a method of Data Collection Consider the following statistical studies. Which method would you use to collect data for each study? Explain your reasoning. 4. It would be nearly impossible to ask every American whether or not he/she approves of the President’s job performance. So, you should use a sampling to collect these data.

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Try it yourself... Some more Consider the following statistical studies. Which method of data collection would you use to collect data for each study? 1. A study on the effect of exercise on senior citizens. Identify the focus and population of the study and choose an appropriate method of data collection.

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Try it yourself... Some more Consider the following statistical studies. Which method of data collection would you use to collect data for each study? 1. A study on the effect of exercise on senior citizens. Identify the focus and population of the study and choose an appropriate method of data collection. Focus: the effect of exercise on senior citizens. Population: Collection of all senior citizens. Method of data collection: experiment.

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Try it yourself... Some more Consider the following statistical studies. Which method of data collection would you use to collect data for each study? 2. A study of the effect of radiation fallout on senior citizens. Identify the focus and population of the study and choose an appropriate method of data collection.

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Try it yourself... Some more Consider the following statistical studies. Which method of data collection would you use to collect data for each study? 2. A study of the effect of radiation fallout on senior citizens. Focus: the effect of radiation fallout on senior citizens. Population: Collection of all senior citizens. Method of data collection: sampling

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End of slides for presentation 1 Too much information for just one presentation.

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Sampling Techniques To collect data that is unbiased, it is important that you use correct sampling techniques. Remember that when a study is done with faulty data, the results are questionable. A simple random sample is one in which every member of the population has an equal chance of being selected. One way to do this is to assign every member of the population a number and use a random number table like the one in Appendix B.

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Ex. 2 Using a simple random sample There are 731 students currently enrolled in English in your school. You wish to form a sample of eight students to answer some survey questions. Select the students who will belong to the simple random sample.

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Ex. 2 Using a simple random sample Assign numbers 1 through 731. to each student in the course. On the table of random numbers, choose a starting place at random and read the digits in its first column in groups of three (because 731 is a three-digit number). Use the appendix B – Table 1 – Random numbers.

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Solution 92630 79445 59654 31524 06348 28703 68108 99938 Assign number 1 – 731 to each student in the course. On the table of random numbers, choose a starting place at random and read the digits in the first column in groups of three (because 731 is a 3-digit number)

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Solution 92630 79445 59654 31524 06348 28703 68108 99938 926|307|944|559|654|315| 240|634|828|703|681 Ignoring the numbers that are greater than 731, the first eight numbers are: 307|559|654|315| 240|634|703|681 Students who are assigned these numbers will make up the sample.

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Try it yourself... Simple random sample A company employs 79 people. Choose a random sample of five to participate in a health habits study. A. On the table, randomly choose a starting place. B. Read the digits in groups of two. C. Write the five random numbers.

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Solution 92630 79445 59654 31524 06348 28703 68108 99938 Assign number 1 – 79 to each person in the study. On the table of random numbers, choose a starting place at random and read the digits in the first column in groups of 2 (because 79 is a 2-digit number)

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Solution 92|63|07|82|40|19|26| Ignoring the numbers that are greater than 79, the first five numbers are: 63|07|40|19|26 People who are assigned these numbers will make up the sample. 926307824019267

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Stratified Sample Sometimes it is important that your sample contain members from each part (strata) of your population. Using a stratified sample, member of the population are separated into groups with similar characteristics such as age, gender, or ethnicity. Then a random sample is selected from each of the strata. For example if you wanted to ensure that your sample had students under 21 years of age, between 21 and 30, and some 30 or more; separate them into three strata according to their age. Choose a sample from each age group.

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Cluster Sample In a cluster sample, the unit for sampling is a naturally occurring sub-group. One or more of the subgroups is selected and each member from that group is used in the sample. Clusters could be the different sections of the course.

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Systematic Sample In a systematic sample, each member of the population is assigned a number. A starting number is randomly selected and then every k-th (example every 3 rd, 5 th, 100 th, or 1000 th )is selected. K=integer

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Convenience Sample A convenience sample consists only of the available people. For example, survey the students who come to class early. This often leads to biased studies and is not recommended as a result.

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Ex. 3 Identify sampling Techniques You are doing a study to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. 1. You select a class at random and question each student in the class. 2. You divide the student population with respect to majors and randomly select and question some students in each major. 3. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

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Ex. 3 Identify sampling Techniques You are doing a study to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. 1. You select a class at random and question each student in the class. Answer: Because each class is a naturally occurring subgroup (cluster), this is a cluster sample.

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Ex. 3 Identify sampling Techniques You are doing a study to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. 2. You divide the student population with respect to majors and randomly select and question some students in each major. Answer: Because students are divided into strata (majors), and a sample is selected from each major, this is a stratified sample.

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Ex. 3 Identify sampling Techniques You are doing a study to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. 3. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected. Answer: Each student has an equal chance of being selected, so this is a simple random sample.

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Try it yourself #3 You want to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. A. Determine how the sample is selected and B. Identify the corresponding sampling technique. 1. You select students who are in your statistics class.

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Try it yourself #3 You want to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. A. Determine how the sample is selected and B. Identify the corresponding sampling technique. 1. You select students who are in your statistics class. Answer: The sample is selected out of convenience, so it is convenience sampling.

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Try it yourself #3 You want to determine the opinion of students at your school regarding gun control. Identify the sampling technique you are using if you select the samples listed. A. Determine how the sample is selected and B. Identify the corresponding sampling technique. 2. You assign each student a number, and after choosing a starting number, you question every 25 th student. Answer: The sample is selected after you ordered the sample by numbering and then selected at a regular basis (every 25 th student).

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