Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 1 of 28 Chapter 1 Section 3 Other Effective Sampling Methods

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 2 of 28 Chapter 1 – Section 3 ●Learning objectives  Obtain a stratified sample  Obtain a systematic sample  Obtain a cluster sample 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 3 of 28 Chapter 1 – Section 3 ●Learning objectives  Obtain a stratified sample  Obtain a systematic sample  Obtain a cluster sample 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 4 of 28 Chapter 1 – Section 3 ●There are other effective ways to collect data  Stratified sampling  Systematic sampling  Cluster sampling ●Each of these is particularly appropriate in certain specific circumstances

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 5 of 28 Chapter 1 – Section 3 ●A stratified sample is obtained when we choose a simple random sample from subgroups of a population  This is appropriate when the population is made up of nonoverlapping (distinct) groups called strata ●A stratified sample is obtained when we choose a simple random sample from subgroups of a population  This is appropriate when the population is made up of nonoverlapping (distinct) groups called strata  Within each strata, the individuals are likely to have a common attribute ●A stratified sample is obtained when we choose a simple random sample from subgroups of a population  This is appropriate when the population is made up of nonoverlapping (distinct) groups called strata  Within each strata, the individuals are likely to have a common attribute  Between the stratas, the individuals are likely to have different common attributes

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 6 of 28 Chapter 1 – Section 3 ●Example – polling a population about a political issue  It is reasonable to divide up the population into Democrats, Republicans, and Independents  It is reasonable to believe that the opinions of individuals within each party are the same  It is reasonable to believe that the opinions differ from group to group ●Therefore it makes sense to consider each strata separately

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 7 of 28 Chapter 1 – Section 3 ●Example – a poll about safety within a university ●Three identified strata  Resident students  Commuter students  Faculty and staff ●Example – a poll about safety within a university ●Three identified strata  Resident students  Commuter students  Faculty and staff ●It is reasonable to assume that the opinions within each group are similar ●It is reasonable to assume that the opinions between each group are different

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 8 of 28 Chapter 1 – Section 3 ●Assume that the sizes of the strata are  Resident students – 5,000  Commuter students – 4,000  Faculty and staff – 1,000 ●If we wish to obtain a sample of size n = 100 that reflects the same relative proportions, we would want to choose  50 resident students  40 commuter students  10 faculty and staff

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 9 of 28 Chapter 1 – Section 3 ●For each strata  Choose 50 out of 5,000 resident students with a simple random sample  Choose 40 out of 4,000 commuter students with a simple random sample  Choose 10 out of 1,000 faculty and staff with a simple random sample ●This provides us with a stratified sample that reflects the actual proportions of our strata within the population

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 10 of 28 Chapter 1 – Section 3 ●Learning objectives  Obtain a stratified sample  Obtain a systematic sample  Obtain a cluster sample 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 11 of 28 Chapter 1 – Section 3 ●A systematic sample is obtained when we choose every k th individual in a population ●The first individual selected corresponds to a random number between 1 and k ●Systematic sampling is appropriate  When we do not have a frame  When we do not have a list of all the individuals in a population

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 12 of 28 Chapter 1 – Section 3 ●Example – polling customers about satisfaction with service ●We do not have a list of customers arriving that day ●We do not even know how many customers will arrive that day ●Simple random sampling (and stratified sampling) cannot be implemented

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 13 of 28 Chapter 1 – Section 3 ●Assume that  We want to choose a sample of 40 customers  We believe that there will be about 350 customers ●Assume that  We want to choose a sample of 40 customers  We believe that there will be about 350 customers ●Values of k  k = 7 is reasonable because it is likely that enough customers will arrive to reach the 40 target  k = 2 is not reasonable because we will only interview the very early customers  k = 20 is not reasonable because it is unlikely that enough customers will arrive to reach the 40 target

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 14 of 28 Chapter 1 – Section 3 ●Using the value k = 7  We choose a random number between 1 and 7, assume that it is 4  We interview the 4 th customer that day ●Using the value k = 7  We choose a random number between 1 and 7, assume that it is 4  We interview the 4 th customer that day  We interview the 11 th customer that day (11 = 4 + 7) ●Using the value k = 7  We choose a random number between 1 and 7, assume that it is 4  We interview the 4 th customer that day  We interview the 11 th customer that day (11 = 4 + 7)  We interview the 18 th customer that day (18 = ) ●Using the value k = 7  We choose a random number between 1 and 7, assume that it is 4  We interview the 4 th customer that day  We interview the 11 th customer that day (11 = 4 + 7)  We interview the 18 th customer that day (18 = )  We interview the 25 th customer that day (25 = ) ●Using the value k = 7  We choose a random number between 1 and 7, assume that it is 4  We interview the 4 th customer that day  We interview the 11 th customer that day (11 = 4 + 7)  We interview the 18 th customer that day (18 = )  We interview the 25 th customer that day (25 = ) ●We continue to interview customers until we reach our target of 40 in the sample

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 15 of 28 Chapter 1 – Section 3 ●This requires approximately 280 customers  280 is small enough so that we will have enough customers arriving (we expect around 350)  280 is large enough to cover the majority of the expected 350 customers ●The choice of k is difficult if have no idea of the total number of customers ●Sometimes some values of k are not appropriate (for example k = 10 when the individuals arrive as male, female, male, female, male, …)

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 16 of 28 Chapter 1 – Section 3 ●Learning objectives  Obtain a stratified sample  Obtain a systematic sample  Obtain a cluster sample 1 2 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 17 of 28 Chapter 1 – Section 3 ●A cluster sample is obtained when we choose a random set of groups and then select all individuals within those groups ●We can obtain a sample of size 50 by choosing 10 groups of 5 ●Cluster sampling is appropriate when it is very time consuming or expensive to choose the individuals one at a time

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 18 of 28 Chapter 1 – Section 3 ●Example – testing the fill of bottles  It is time consuming to pull individual bottles  It is expensive to waste an entire cartons of 12 bottles to just test one bottle ●If we would like to test 240 bottles, we could  Randomly select 20 cartons  Test all 12 bottles within each carton ●This reduces the time and expense required

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 19 of 28 Chapter 1 – Section 3 ●A convenience sample is obtained when we choose individuals in an easy, or convenient way ●Self-selecting samples are examples of convenience sampling  Individuals who respond to television or radio announcements ●A convenience sample is obtained when we choose individuals in an easy, or convenient way ●Self-selecting samples are examples of convenience sampling  Individuals who respond to television or radio announcements ●“Just asking around” is an example of convenience sampling  Individuals who are known to the pollster

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 20 of 28 Chapter 1 – Section 3 ●Convenience sampling has little statistical validity  The design is poor  The results are suspect ●However, there are times when convenience sampling could be useful as a rough guess  If none of your co-workers are concerned about a particular issue, then it is possible that the set of all employees would not be concerned about that issue

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 21 of 28 Chapter 1 – Section 3 ●A multistage sample is obtained using a combination of  Simple random sampling  Stratified sampling  Systematic sampling  Cluster sampling ●Many large scale samples (the US census in noncensus years) use multistage sampling

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 22 of 28 Chapter 1 – Section 3 ●Example – choosing 3 rd grade students ●The following method combines cluster sampling with simple random sampling ●We want a sample of rd grade students  We randomly select 20 elementary schools  We perform a simple random sample within each school to choose 12 students

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 23 of 28 Chapter 1 – Section 3 ●The sample size is very important in statistical analysis ●Certain sample sizes are required to reach certain conclusions ●This will be covered in later chapters

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 24 of 28 Summary: Chapter 1 – Section 3 ●There are other sampling methods that are particularly useful in certain situations  Stratified sampling to cover the different strata  Systematic sampling when the frame is unknown  Cluster sampling to reduce the time and expense required  Multistage sampling for effective large scale samples ●The choice of sampling methods depends on the structure of the population and the goals of the analyst

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 25 of 28 Summary: Chapter 1 – Section 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 26 of 28 Summary: Chapter 1 – Section 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 27 of 28 Summary: Chapter 1 – Section 3

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 1 Section 3 – Slide 28 of 28 Summary: Chapter 1 – Section 3