Data = collections of observations, measurements, gender, survey responses etc. Sample = collection of some members (a subset) of the population

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1 Chapter 1: Basic Ideas 1.1 Sampling Statistics = the Science of Data By collecting a limited amount of data, we want to say something about the whole group that we want to study, i.e. we want to say something about the population. Data = collections of observations, measurements, gender, survey responses etc. Population = complete collection of all individuals to be studied Census = collection of data from every member of the population Sample = collection of some members (a subset) of the population Ex) The magazine, The Book Literary Digest, correctly predicted the presidential elections in 1916, 20, 24, 28, and 32. In 1936, the magazine sent out 10 million ballots. Of the 2,221,566 ballots that were returned: 1,293,669 ballots were for Landon (57%) 927,897 ballots were for Roosevelt (43%) The actual results were: Landon 37%, Roosevelt 63% During the same election, George Gallup used a much smaller poll of 50,000 subjecs. He correctly prediced the win. A SAMPLE NEEDS TO REPRESENT THE POPULATION AS A WHOLE!!! The sampling method is very important. Types of Samples 1. Simple Random Sampling of size n: Each sample of size n is equally likely to be picked. Number each individual of the population, then randomly select n of these numbers. A simple random sample is like a lottery. 2. Sample of Convenience: A sample not drawn by a well-defined random method. 3. Stratified Sampling: The population is divided into groups called strata. A simple random sample is drawn from each strata. 4. Cluster Sampling: Divide the population into groups, then randomly sample (pick) some of those clusters.

2 Ex) Exit polls during elections: randomly pick a certain number of precincts, then poll every voter in those precincts. 5. Systematic Sampling: Population individuals are numbered. Randomly pick a starting point. The sample every kth item after that. 6. Voluntary Response Sampling: Tweets as feedback to a TV program, calls into a radio station to say what listeners think about a topic etc. Exercises 1.1: : 21 Simple random sample: Draw a simple random sample of eight animals from the list of 40 animals in the table 1.1: 22 Draw a sample of eight animals by drawing a simple random sample of two animals from each group. What kind of sample is this?

3 1.1: 23 Draw a simple random sample of two groups of animals from the four groups, and construct a sample of 20 animals by including all the animals in the sampled groups. What kind of sample is this? 1.1: 24 Choose a random number between 1 and 5. Include the animal with that number in your sample, along with every fifth animal thereafter, to construct a sample of eight animals. What kind of sample is this? 1.2 Types of Data Data Set = The information collected during sampling. Individuals = Single members of a population from which data is collected Ex) A single student, if the population is all students Variables = The different types of data or characteristics collected from an individual Ex) Age, Height, weight, eyecolor, number of years in college etc Data = Values of the variables collected Qualitative versus Quantitative Variables A. Qualitative Variables = Classify individuals into categories (data is non-numerical) Ex) Eye color, hair color, political party affiliation, number on soccer jersey, letter grade 1. Ordinal variables: have a natural numbering Ex) letter grade received, placement, size of a drink (small, medium, large) 2. Nominal variables: Qualitative variables that do not have a natural numbering Ex) eye color, hair color, party affiliation

4 B. Quantitative Variables = numerical variables (counts or measures) Ex) Age, Height, weight, GPA, distance to work etc. 1. Discrete variables: Quantitative variables whose possible values can be listed Ex) Number of automobiles in a family, Number of kids, age 2. Continuous variables: Quantitative variables that can take on any value in some interval Ex) Height, weight, distance to work, amount of water used by a family 1.2: Determine whether the data described are qualitative or quantitative. 16. Your best friend s age 18. The title of your statistics book 20. The waist size of a pair of jeans 22. Your school colors 24. The number of cars sold by a car dealer last month 1.2: Determine whether the data described are nominal or ordinal. 26. The names of the counties in a state 30. I ordered a pizza with pepperoni, mushrooms, olives, and onions. 32. I finished first in the high jump and third in the pole vault. 1.2: Determine whether the data described are discrete or continuous. 34. The distance from a student s home to his school 36. The number of students enrolled at a college 38. The number of patients who reported that a new drug had relieved their pain 1.3 Design of Experiments Outcome = What is measured on each experimental unit Treatments = Procedures applied to each experimental unit. Randomized Experiment = A study in which the investigator assigns the treatments to the experimental units at random. Observational Study = The assignment to treatment groups is not made by the investigator. Double-Blind Experiments = Neither the investigators nor the subjects know who has been assigned to which treatment

5 Confounding = A confounder is a variable that is related to both the treatment and the outcome. They are common in observational studies as the researcher does not have much control of the experimental units. When a confounder is present, it is difficult to determine whether differences in the outcome are due to the treatment or to the confounder (= some other factor that might affect the outcome). 1.3: Determine whether the data described are qualitative or quantitative. 18. A medical researcher wants to determine whether exercising can lower blood pressure. At a health fair, he measures the blood pressure of 100 individuals, and interviews them about their exercise habits. He divides the individuals into two categories: those whose typical level of exercise is low, and those whose level of exercise is high. a. Is this a randomized experiment or an observational study? b. The subjects in the low-exercise group had considerably higher blood pressure, on the average, than subjects in the high-exercise group. The researcher concluded that exercise decreases blood pressure. Is this conclusion well justified? Explain. 20. An agricultural scientist wants to determine the effect of fertilizer type on the yield of tomatoes. There are four types of fertilizer under consideration. She plants tomatoes on four plots of land. Each plot is treated identically except for receiving a different type of fertilizer. a. What are the treatments? b. Is this a randomized experiment or an observational study? c. The yields differ substantially among the four plots. Can you conclude that the differences in yield are due to the differences in fertilizer? Explain. 22. Cold medications: A scientist wants to determine whether a new cold medicine relieves symptoms more effectively than a currently used medicine. Do you think it is possible to design a randomized experiment to study this question, or will an observational study be necessary? Explain. 1.4 Bias in Studes Unbiased study: Produces the correct result on the average. Biased study: Over- or underestimates the true value Types of Bias Voluntary Response Bias Self-interest bias Social acceptability bias Leading question bias Nonresponse bias

6 Sampling bias A BIG SAMPLE DOES NOT MAKE UP FOR BIAS!! 1.4: Specify the type of bias involved. 10. To determine his constituents feelings about election reform, a politician sends a survey to people who have subscribed to his newsletter. More than 1000 responses are received. 12. A sign in a restaurant claims that 95% of their customers believe them to have the best food in the world. 14. A police department conducted a survey in which police officers interviewed members of their community to ask their opinions on the effectiveness of the police department. The police chief reported that 90% of the people interviewed said that they were satisfied with the performance of the police department. 16. To estimate the prevalence of illegal drug use in a certain high school, the principal interviewed a simple random sample of 100 students and asked them about their drug use. Five percent of the students acknowledged using illegal drugs.

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