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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 1 of 22 Chapter 1 Section 2 Observational Studies, Experiments, and Simple Random Sampling

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 2 of 22 Chapter 1 – Section 2 ●Learning objectives Distinguish between an observational study and an experiment Obtain a simple random sample 2 1

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 3 of 22 Chapter 1 – Section 2 ●Learning objectives Distinguish between an observational study and an experiment Obtain a simple random sample 2 1

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 4 of 22 Chapter 1 – Section 2 ●There are different ways to collect data Census Existing sources Survey sampling Designed experiments ●These are good methods of data collection, if done correctly

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 5 of 22 Chapter 1 – Section 2 ●A census is a list Of all the individuals in a population That records the characteristics of the individuals An example is the US Census held every 10 years (this is only an example though) ●A census is a list Of all the individuals in a population That records the characteristics of the individuals An example is the US Census held every 10 years (this is only an example though) ●Advantages Answers have 100% certainty ●A census is a list Of all the individuals in a population That records the characteristics of the individuals An example is the US Census held every 10 years (this is only an example though) ●Advantages Answers have 100% certainty ●Disadvantages May be difficult or impossible to obtain Costs may be prohibitive

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 6 of 22 Chapter 1 – Section 2 ●An existing source is An appropriate data set has already been collected That can be used for this study ●An existing source is An appropriate data set has already been collected That can be used for this study ●Advantages Saves time and money ●An existing source is An appropriate data set has already been collected That can be used for this study ●Advantages Saves time and money ●Disadvantages There may not be an applicable data set

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 7 of 22 Chapter 1 – Section 2 ●A survey sample is A study when only a subset of the population is considered A study where there is no attempt to influence the value of the variable of interest ●A survey sample is A study when only a subset of the population is considered A study where there is no attempt to influence the value of the variable of interest ●Advantages Saves time and money ●A survey sample is A study when only a subset of the population is considered A study where there is no attempt to influence the value of the variable of interest ●Advantages Saves time and money ●Disadvantages Choosing an appropriate sample could be difficult

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 8 of 22 Chapter 1 – Section 2 ●A survey sample is an example of an observational study An observational study is one where there is no attempt to influence the value of the variable An observational study is also called an ex post facto (after the fact) study ●A survey sample is an example of an observational study An observational study is one where there is no attempt to influence the value of the variable An observational study is also called an ex post facto (after the fact) study ●Advantages It can detect associations between variables ●A survey sample is an example of an observational study An observational study is one where there is no attempt to influence the value of the variable An observational study is also called an ex post facto (after the fact) study ●Advantages It can detect associations between variables ●Disadvantages It cannot isolate causes to determine causation

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 9 of 22 Chapter 1 – Section 2 ●A designed experiment is an experiment That applies a treatment to individuals Often compares the treated group to a control (untreated) group Where the variables can be controlled ●A designed experiment is an experiment That applies a treatment to individuals Often compares the treated group to a control (untreated) group Where the variables can be controlled ●Advantages Can analyze individual factors ●A designed experiment is an experiment That applies a treatment to individuals Often compares the treated group to a control (untreated) group Where the variables can be controlled ●Advantages Can analyze individual factors ●Disadvantages Cannot be done when the variables cannot be controlled Cannot apply in cases for moral / ethical reasons

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 10 of 22 Chapter 1 – Section 2 ●Observational studies and designed experiments have some fundamental differences Observational studies do not control the variable under analysis while designed experiments do ●Observational studies and designed experiments have some fundamental differences Observational studies do not control the variable under analysis while designed experiments do Because variables are uncontrolled in an observational study, the results can only be associations ●Observational studies and designed experiments have some fundamental differences Observational studies do not control the variable under analysis while designed experiments do Because variables are uncontrolled in an observational study, the results can only be associations Because variables are controlled in a designed experiment, the results can be conclusions of causation

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 11 of 22 Chapter 1 – Section 2 ●A danger in observational studies are lurking variables ●In an observational study, two variables can be determined to be associated ●Associated does not mean that one causes the other ●A simple observational study may find that smoking and cancer are associated Cannot conclude that smoking causes cancer Cannot conclude that cancer causes people to smoke

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 12 of 22 Chapter 1 – Section 2 ●Usually only a part of the population can be analyzed ●How do you choose your sample? ●The process is called sampling ●We will discuss Simple random sampling Stratified sampling Systematic sampling Cluster sampling Convenience sampling

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 13 of 22 Chapter 1 – Section 2 ●Learning objectives Distinguish between an observational study and an experiment Obtain a simple random sample 2 1

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 14 of 22 Chapter 1 – Section 2 ●A simple random sample is when every possible sample of size n out of a population of N has an equally likely chance of occurring ●Examples For a simple random sample of size n = 1 from a population size of N = 5, each of the 5 possible samples has an equally likely chance of occurring For a simple random sample of size n = 2 from a population size of N = 4, each of the 6 possible samples has an equally likely chance of occurring

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 15 of 22 Chapter 1 – Section 2 ●Simple random sampling requires that we have a list of all the individuals within a population ●This list is called a frame ●If we do not have a frame, then a different sampling method must be used

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 16 of 22 Chapter 1 – Section 2 ●A simple (but not foolproof) method Write each individual’s name on a separate piece of paper Put all the papers into a hat Draw a random paper from the hat ●A simple (but not foolproof) method Write each individual’s name on a separate piece of paper Put all the papers into a hat Draw a random paper from the hat ●Physical methods have some issues Are the papers sufficiently mixed? Are some of the papers folded?

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 17 of 22 Chapter 1 – Section 2 ●A method using a table of random numbers List and number the individuals Decide on a way to pick the random numbers (how to choose the starting point and what rule to use to select which digits to choose after that) Select the random numbers Match the numbers to the individuals ●With the technology available today, this method is outdated

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 18 of 22 Chapter 1 – Section 2 ●A method using technology List and number the individuals Use software (a calculator, software such as MINITAB or Excel) to generate random numbers Match the random numbers to the individuals ●The method must be decided in advance … it is not statistically correct to choose a series of samples until a “good” one comes up

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 19 of 22 Chapter 1 – Section 2 ●Simple random sampling example ●We wish to select a random sample of 3 out of a group of 30 students ●Simple random sampling example ●We wish to select a random sample of 3 out of a group of 30 students ●We generate a two digit random number to choose the first student ●Simple random sampling example ●We wish to select a random sample of 3 out of a group of 30 students ●We generate a two digit random number to choose the first student ●Examples If the number is “63”, we disregard this random number and choose another one ●Simple random sampling example ●We wish to select a random sample of 3 out of a group of 30 students ●We generate a two digit random number to choose the first student ●Examples If the number is “63”, we disregard this random number and choose another one If the number is “17”, we pick student number 17

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 20 of 22 Chapter 1 – Section 2 ●We generate another two digit random number to choose the second student Assume that the first student was number 17 ●We generate another two digit random number to choose the second student Assume that the first student was number 17 ●Examples If the second number is “17”, we disregard this random number and choose another one (we want 2 different people) ●We generate another two digit random number to choose the second student Assume that the first student was number 17 ●Examples If the second number is “17”, we disregard this random number and choose another one (we want 2 different people) If the number is “65”, we disregard this random number and choose another one ●We generate another two digit random number to choose the second student Assume that the first student was number 17 ●Examples If the second number is “17”, we disregard this random number and choose another one (we want 2 different people) If the number is “65”, we disregard this random number and choose another one If the number is “8”, we choose student 8 as our second student

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 21 of 22 Chapter 1 – Section 2 ●We generate another two digit random number to choose the third student Assume that the first student was number 17 and the second was number 8 ●We generate another two digit random number to choose the third student Assume that the first student was number 17 and the second was number 8 ●Examples If the third number is “17”, or “8”, or anything “31” and higher, we disregard this random number and choose another one (we want 3 different people) If the number is “2”, we choose student 2 as our third and final student ●We generate another two digit random number to choose the third student Assume that the first student was number 17 and the second was number 8 ●Examples If the third number is “17”, or “8”, or anything “31” and higher, we disregard this random number and choose another one (we want 3 different people) If the number is “2”, we choose student 2 as our third and final student ●Our sample is {student 17, student 8, student 2}

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Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 2 – Slide 22 of 22 Summary: Chapter 1 – Section 2 ●There are different ways of collecting data A census uses the entire population An existing source use an existing data set An observational study measures the characteristics of a sample without influencing the variable of interest A designed experiment applies a treatment to a sample to isolate the effects of a variable ●The method of simple random sampling can be used to select the sample

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