Who do I ask, what do I ask them, what does that tell me? Sampling and Surveys Who do I ask, what do I ask them, what does that tell me?

The Cycle of Statistics Population Sample Parameter Statistic

Types of Sampling Simple Random Sample Every member of the population has an equal chance of being chosen for the sample Method Create a sample frame Assign a number to each individual in the sampling frame Select only those whose numbers satisfy some rule

SRS Example There are 80 students enrolled in an introductory Statistics course; you are to select a sample of 5 Sampling frame The roster of all students enrolled in the course Label each student 01 - 80 Use a random number generator and choose the first 5 students from the list that match the random numbers. Ignore numbers not on the list and repeats.

Stratified Random Sampling strata Homogenous groups within the population Method Divide the population into strata Take a SRS within each strata Compare the results

Stratified random sampling Example What is the freshman opinion of the cafeteria food on campus? Strata: Men, Women Sampling Frame: A list of all enrolled students Create two lists, one with males and one with females, label all of the individuals SRS Using random numbers choose 50 males, repeat for females. Determine the male opinion and the female opinion

Cluster Sampling Cluster A representative group of the population Method Select one or multiple clusters at random and perform a census within each of them Example What is the freshman opinion of the cafeteria food on campus? (gender not an issue) Problem: It can be difficult to track down the members chosen for the stratified sample All Freshmen live in dorms which can serve as a cluster (assuming that there is no all male/female dorm) Randomly choose 1 or 2 dorms at random and ask everyone in the dorm their opinion.

Multistage sampling Sampling schemes that combine several methods Example What is the freshman opinion of the cafeteria food on campus? Gender matters. Perform a cluster sample as mentioned Many dorms house females and males on separate floors. Randomly choose a dorm (cluster) and then randomly choose a few floors with only men or women (strata) and then interview every member of that floor (cluster).

Systematic Sampling A sample that selects individuals systematically. Ex. Every 10th person Method Create a sampling frame Choose a random starting point Choose every nth individual from that starting point Benefits Cheap and easy Need to make sure the sampling frame has no associations. ie. Every 5th individual is not the same.

Bias and Problems with sampling Voluntary Response sampling Bad sampling frame Telephone book misses people with only cell phones, homeless, prisoners Undercoverage Telephone surveys If calling at dinner time will miss people that eat out often Convenience sampling Non respondents Those that don’t respond may differ significantly from those that do respond. Response Bias from poorly designed questions or poor interviewer