Sampling Probability Random Selection Essentials Study Types Terminology

Sampling Probability & Random Selection • • • Essentials Study Types Terminology Sampling Error Probability and Sampling Probability and Non-Probability Sampling Approaches • Examples & Problems

Essentials: Sampling (stuff I should know) General types of data collection Importance of randomization in obtaining samples Sampling Error Difference between non-probability sampling and probability sampling Different types of random samples and how each is obtained via probability sampling Ability to obtain samples using probability sampling approaches

Methods of Data Collection • Observation – observe and measure; can identify association, not causation. • Visual Observation • Surveying • Experimentation – impose treatment and observe characteristics; can help establish causation. • Clinical Trials fall within this research approach. • Simulation – used in situations where other approaches are impractical; mathematical or physical reproductions of situations (e. g. car safety testing)

SAMPLING • Census vs. Sample • Sampling and Experimentation • Representative Sample • Probability Sampling

Randomness • Random sampling from a population enables generalization to the population. • Random assignment in an experiment permits causal conclusions to be drawn.

Sampling is the process by which we gain information about the whole population of interest, by examining only a part of (a sample of) that population. A sample is a “piece” of a population. . . . Population. . . . . Sample. . .

Sampling Terms • Unit: a single member of a population (element) • Sampling Frame: a list of units from which the sample is drawn • Response Rate: the percent of individuals from whom we actually obtain data. A high response rate is desirable. • Objective Variable: the variable(s) that is/are directly related to the objective of the study. • Explanatory Variable: variable(s) that may explain or contribute to the measurement obtained on the objective variable(s)

Sampling Error: Problems that can occur when we sample • Sampling Error (Also called Sampling Variability) - error that occurs simply because we are using a sample from the population, as opposed to the entire population. We will get variation from sample to sample. This error can never be eliminated, however in the long run, this error is quite small. • Non-sampling Error - error not attributed to chance sampling fluctuations. These errors could occur even if the entire population were being used. Errors associated with data collection, recording, and analysis are examples.

Sampling: Many Approaches – Some Good, Some Not So Good Probability based Sampling Simple Random Sampling Systematic Random Sampling Cluster Sampling Stratified Sampling Multi-stage Sampling Non-probability based sampling approaches Convenience Sampling Quota Sampling

Probability Sampling • Probability sampling gives each member of the population a known chance (greater than zero) of being selected. • NOTES: This is a basic and important definition. Be aware of the difference between this definition and that of a Simple Random Sample (SRS), a form of probability sampling.

Simple Random Sample (SRS) • Simple Random Sample: A process by which each possible sample of a given size N has an equally likely chance of being drawn from the population. • A probability sampling technique is used to obtain the sample, e. g. table of random numbers, coin flip, draw from a hat, random number generator.

Simple Random Sample Every possible sample of the same size has the same chance of being selected. x xxxxx x x x xx xx x x x x xx x x xx x x xxxx x x x x x x xx x Source: Larson/Farber 4 th ed.

Systematic Sample • Systematic Random Sample is similar to a SRS (simple random sample), but it incorporates a formula to assure data are collected from throughout the population. • Advantage: Easy to obtain. • Disadvantage: susceptible to problems where there are repetitive or cyclical data

Systematic Sampling: The process • • 1) Determine the size of the desired sample (n). 2) Divide the population size (N) by the sample size (n): N/n = m. 3) Divide the population into “m” sections 4) Randomly pick a number within the first “m” group; a value between 1 and m. This would be “k, ” the random seed. • 5) k is the first value in the sample. Proceed by adding “m” to “k” to obtain the second value. Continue this process by adding m until the sample has been selected. Example: 1) Sample size n =5 2) N/n = m; Below 16/5 = 3. 2, which is rounded DOWN to 3 (always round down) 3) Where m = 3 it will divide this population into 6 groups. 4) Randomly pick a number between 1 and m (here 1 and 3); picked 2 = k, the random seed. 5) Start the sample with the second house in the first group. Continue by adding m to the preceding number (e. g. k = 2; k + m => 2 + 3 = 5; 5 + m => 5 + 3 = 8, etc. ) 6) Sample equals the houses 2, 5, 8, 11, 14. m divides population every 3 units 2 k 5 k+m 8 k+2 m 11 k+3 m 14 k+4 m

Stratified Sampling • Stratified Sampling with proportional allocation: Divide the population into Strata (groupings); draw a SRS from each Strata (singular stratum) in proportion to its occurrence in the population (Proportional Allocation). • Advantage: Assures inclusion of sub-groups with few members • Disadvantages: Time, Cost, Complexity

Stratified Sample: The process • Divide a population into groups (strata) • Select a random sample from each group. • Use proportional allocation to obtain a sample reflecting the sub-group proportions within the population. • (A non-proportional stratified sample would have the same number of sample units selected from each strata. ) Example using Proportional Allocation 1) Population, N, consists of 50 Democrats (50%); 25 Republicans (25%); 10 Independents (10%); 10 Conservatives (10%); and 5 Liberals (5%). N = 100. 2) Desired sample size, n = 20. 3) Convert the population percentages to a proportion by dividing by 100 (so 50% becomes. 50, etc. ) 4) Multiply the desired sample size, n, by each of the proportions to obtain your sample. Generally round up any sample strata containing a fraction

Cluster Sampling • Cluster Sampling: Divide the population into areas; randomly select areas; include all members in selected areas. • Advanatges: Time, Cost and Distances • Disadvantages: Homogeneity within clusters

Cluster Sample • Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters. • Example: In West Ridge County you could divide the households into clusters according to zip codes, then select all the households in one or more, but not all, zip codes. Source: Larson/Farber 4 th ed.

Convenience Sampling • Convenience Sampling: Collect data from readily available sources. • Advantage: Quick and dirty (Cheap too) • Disadvantage: Quick and dirty; may be severely biased

Identify the Sampling Technique Example: You are doing a study to determine the number of years of education each teacher at your college has. Identify the sampling technique used if you select the samples listed. 1. ) You randomly select two different departments and survey each teacher in those departments. 2. ) You select only the teachers you currently have this semester. 3. ) You divide the teachers up according to their department and then choose and survey some teachers in each department.

Example: Identifying Sampling Techniques You are doing a study to determine the opinion of students at your school regarding stem cell research. Identify the sampling technique used. 1. You divide the student population with respect to majors and randomly select and question some students in each major. 2. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected. Source: Larson/Farber 4 th ed.

Examples of obtaining various sampling approaches

Simple Random Sampling (SRS): Starbucks here we come! A statistics class has 36 members. Obtain a SRS of 8 class members who will be invited to Starbucks for a free beverage of their choice. Select the sample from the following class members. Alex Dana Tatiana Ashley D. Edosa Victoria F. Matt Caitlin Hannah Kayla Elyise Danielle H 1 Danielle H 2 Jenna Chris Jason Sabrinna Nathaniel Tiffini Kyle Stephanie N. Alicia Adam Teddi-Jo Corey Stephanie S. Ashley S. Victoria S. Deanna Molly Stefan Mike Keri Karin Jenna Mary

Systematic Sampling: Coopers MINI builds Coopers in its Oxford England plant. Five-hundred Coopers are made per day. The management wants to select 25 Coopers daily to go through a quality control inspection consisting of 144 items. Demonstrate how you would use systematic sampling to identify the 25 Coopers.

Systematic Sampling: CD Production Quality Control researchers at the manufacturing plant which presses Windham Hill Records’ compact discs periodically inspect CD’s from the plant’s production line. If on a given day 1, 500 of the album “Deep Breakfast” are pressed and the researchers wish to insure their quality by testing 15 CD’s (1% of the production) via a systematic random sample. Show you would determine the sample and then identify it based upon your randomly selected starting point.

Stratified Sampling: Accounting Practices (Using Equal Allocation (non-proportional) vs. Proportional Allocation by Account Size) Accountants often use stratified random sampling during audits to verify a company’s records of such things as accounts receivable. One company reports 5000 accounts receivable of which 200 are in accounts over $100, 000, 1000 accounts are between $10, 000 and $100, 000 and 3800 accounts are under $10, 000. The auditor decides to review 200 accounts using a stratified sample with proportional allocation. Determine the number of accounts that will be audited within each stratum.

Cluster Sampling: Airline Satisfaction As part of an advertising campaign Alaska Air has hired you assess the level of customer satisfaction with its new in-flight services from Seattle to Anchorage. You elect to conduct a survey of 1, 540 passengers and plan to collect data for each day of the week. The company indicates that there are 10 flights per day into Anchorage, each with an average 110 passengers. Use a cluster sampling approach to obtain the sample. Why might you select this approach?