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STAT-211 Principles of Statistics I Notes # 4: Sample Types Alexander Roitershtein August 30, 2022 Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 1 / 19
Types of sampling Key idea: A sample should have the same characteristics as the population it is representing. How do we get representative samples from the Most statisticians use various methods of random sampling in an attempt to achieve this goal, including: 1 Simple Random Sample (often abbreviated as SRS) 2 Systematic Sample 3 Stratified Sample 4 Cluster Sample Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 2 / 19
Types of sampling Key idea: A sample should have the same characteristics as the population it is representing. How do we get representative samples from the Most statisticians use various methods of random sampling in an attempt to achieve this goal, including: 1 Simple Random Sample (often abbreviated as SRS) 2 Systematic Sample 3 Stratified Sample 4 Cluster Sample Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 2 / 19
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Types of sampling Key idea: A sample should have the same characteristics as the population it is representing. How do we get representative samples from the Most statisticians use various methods of random sampling in an attempt to achieve this goal, including: 1 Simple Random Sample (often abbreviated as SRS) 2 Systematic Sample 3 Stratified Sample 4 Cluster Sample Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 2 / 19
Types of sampling Simple Random Sample (SRS) Every member of the population has an equal chance of being chosen. 1 Give each member of the population a number. 2 Use a random number generator to select a set of labels. 3 These randomly selected labels identify the members of your sample - use them to find out which members were sampled. Example Obtain an SRS of 5 students from the class: prepare 100 similarly looking tickets five of which are marked as "winning" with an invisible ink, put all the tickets in a hat, shuffle, let each student to choose one ticket from the hat at random. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 3 / 19
Types of sampling Simple Random Sample (SRS) Every member of the population has an equal chance of being chosen. 1 Give each member of the population a number. 2 Use a random number generator to select a set of labels. 3 These randomly selected labels identify the members of your sample - use them to find out which members were sampled. Example Obtain an SRS of 5 students from the class: prepare 100 similarly looking tickets five of which are marked as "winning" with an invisible ink, put all the tickets in a hat, shuffle, let each student to choose one ticket from the hat at random. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 3 / 19
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Types of sampling Simple Random Sample (SRS) Every member of the population has an equal chance of being chosen. 1 Give each member of the population a number. 2 Use a random number generator to select a set of labels. 3 These randomly selected labels identify the members of your sample - use them to find out which members were sampled. Example Obtain an SRS of 5 students from the class: prepare 100 similarly looking tickets five of which are marked as "winning" with an invisible ink, put all the tickets in a hat, shuffle, let each student to choose one ticket from the hat at random. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 3 / 19
Types of sampling Systematic sample Randomly select a starting point and then take every n th data piece after that. Example Suppose you have to do a phone survey. Your phone book contains 20,000 residence listings. You must choose 400 names for the sample. Number the population 1–20,000 and then use a simple random sample to pick a number between 1 and 50 that represents the first name in the sample. Then choose every fiftieth name thereafter until you have a total of 400 names (you might have to go back to the beginning of your phone list). Systematic sampling is frequently chosen because it is a simple method. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 4 / 19
Types of sampling Systematic sample Randomly select a starting point and then take every n th data piece after that. Example Suppose you have to do a phone survey. Your phone book contains 20,000 residence listings. You must choose 400 names for the sample. Number the population 1–20,000 and then use a simple random sample to pick a number between 1 and 50 that represents the first name in the sample. Then choose every fiftieth name thereafter until you have a total of 400 names (you might have to go back to the beginning of your phone list). Systematic sampling is frequently chosen because it is a simple method. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 4 / 19
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Types of sampling Stratified Sample We divide the population into groups called strata according to a criterion which is suitable to the specific study, and then take an SRS from each stratum. Example You could stratify (group) your college population by department and then choose a proportionate simple random sample from each stratum (each department) to get a stratified random sample. Suppose there are 5 departments, and you want to choose a sample of 50. You choose 10 from each department using SRS sampling. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 5 / 19
Types of sampling Stratified Sample We divide the population into groups called strata according to a criterion which is suitable to the specific study, and then take an SRS from each stratum. Example You could stratify (group) your college population by department and then choose a proportionate simple random sample from each stratum (each department) to get a stratified random sample. Suppose there are 5 departments, and you want to choose a sample of 50. You choose 10 from each department using SRS sampling. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 5 / 19
Types of sampling Cluster Sample We divide the population into similar clusters (groups) and then randomly select some of the clusters, often just one of them. All the members from these clusters are in the cluster sample. Example If you randomly sample four departments from your college population, the four departments make up the cluster sample. Divide your college faculty by department. The departments are the clusters. Number each department, and then choose four different numbers using simple random sampling. All members of the four departments with those numbers are the cluster sample. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 6 / 19
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Types of sampling Cluster Sample We divide the population into similar clusters (groups) and then randomly select some of the clusters, often just one of them. All the members from these clusters are in the cluster sample. Example If you randomly sample four departments from your college population, the four departments make up the cluster sample. Divide your college faculty by department. The departments are the clusters. Number each department, and then choose four different numbers using simple random sampling. All members of the four departments with those numbers are the cluster sample. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 6 / 19
Example of a biased sampling I Convenience Sample A type of sampling that is non-random is convenience sampling. Convenience sampling involves using subjects that are readily available. Example A computer software store conducts a marketing study by interviewing potential customers who happen to be in the store browsing through the available software. The results of convenience sampling may be very good in some cases and highly biased (favor certain outcomes or at best being an unsubstantiated "anecdotal evidence") in others. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 7 / 19
Example of a biased sampling I Convenience Sample A type of sampling that is non-random is convenience sampling. Convenience sampling involves using subjects that are readily available. Example A computer software store conducts a marketing study by interviewing potential customers who happen to be in the store browsing through the available software. The results of convenience sampling may be very good in some cases and highly biased (favor certain outcomes or at best being an unsubstantiated "anecdotal evidence") in others. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 7 / 19
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Example of a biased sampling II Volunteer Sample Let the individuals self-elect themselves. Example Medical trials. Volunteers can be further screened and approved, but in any case the subjects are selected among volunteers. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 8 / 19
Example of a biased sampling II Volunteer Sample Let the individuals self-elect themselves. Example Medical trials. Volunteers can be further screened and approved, but in any case the subjects are selected among volunteers. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 8 / 19
Comparative example Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 9 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ A sample of 100 undergraduate San Jose State students is taken by organizing the students’ names by classification (freshman, sophomore, junior, senior), and then selecting 25 from each. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ A sample of 100 undergraduate San Jose State students is taken by organizing the students’ names by classification (freshman, sophomore, junior, senior), and then selecting 25 from each. stratified Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ A random number generator is used to select from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student, every 50th student is chosen until 75 students are included in the sample. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ A random number generator is used to select from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student, every 50th student is chosen until 75 students are included in the sample. systematic Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process. SRS Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ The freshman, sophomore, junior, and senior years are numbers one, two, three, and four, respectively. A random number generator is used to pick two of those years. All students in those two years are in the sample. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ The freshman, sophomore, junior, and senior years are numbers one, two, three, and four, respectively. A random number generator is used to pick two of those years. All students in those two years are in the sample. cluster Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition the Fall semester. Those 100 students are the sample. Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Examples A study is done to determine the average tuition that San Jose State undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case? ▶ An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition the Fall semester. Those 100 students are the sample. convenience Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 10 / 19
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Sampling errors & non-sampling errors Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 11 / 19
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Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 12 / 19
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Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 13 / 19
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Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 14 / 19
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Last topic today Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 15 / 19
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Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 16 / 19
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Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 17 / 19
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Quiz Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 18 / 19
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Quiz Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 18 / 19
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Alexander Roitershtein STAT-211 Principles of Statistics I August 30, 2022 19 / 19
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