Section 1.2 Random Samples 1 Larson/Farber 4th ed.

Section 1.2 Objectives Explain the importance of random samples Construct a simple random sample using random numbers Simulate a random process Describe stratified sampling, cluster sampling, systematic sampling, multi-stage and convenience sampling 2 Larson/Farber 4th ed.

Sampling Techniques Simple Random Sample Every possible sample of the same size has the same chance of being selected. Every individual of the population has an equal chance of being selected. xx x x x x x x x x x x x x x x x xx x x x x x xx x x x x x x xx x x x x x x xx x x x x x xx x x x x x x x x x x x x x x xx x x x x x xx x x x x x xx x x x x x x xx x x x x x xx x x x x x x xx x x x x x x x 3 Larson/Farber 4th ed.

Simple Random Sample Random numbers can be generated by a random number table, a software program or a calculator. Assign a number to each member of the population. Members of the population that correspond to these numbers become members of the sample. 4 Larson/Farber 4th ed.

Example: Simple Random Sample There are 731 students currently enrolled in statistics at your school. You wish to form a sample of eight students to answer some survey questions. Select the students who will belong to the simple random sample. Assign numbers 1 to 731 to each student taking statistics. On the table of random numbers, choose a starting place at random (suppose you start in the third row, second column.) 5 Larson/Farber 4th ed.

Solution: Simple Random Sample Read the digits in groups of three Ignore numbers greater than 731 The students assigned numbers 719, 662, 650, 4, 53, 589, 403, and 129 would make up the sample. 6 Larson/Farber 4th ed.

Other Sampling Techniques Stratified Sample Divide a population into groups (strata) and select a random sample from each group. To collect a stratified sample of the number of people who live in West Ridge County households, you could divide the households into socioeconomic levels and then randomly select households from each level. 7 Larson/Farber 4th ed.

Other Sampling Techniques Cluster Sample Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters. In the West Ridge County example 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. 8 Larson/Farber 4th ed.

Other Sampling Techniques Systematic Sample Choose a starting value at random. Then choose every k th member of the population. In the West Ridge County example you could assign a different number to each household, randomly choose a starting number, then select every 100 th household. 9 Larson/Farber 4th ed.

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. Solution: Stratified sampling (the students are divided into strata (majors) and a sample is selected from each major) 10 Larson/Farber 4th ed.

Sampling Terminology Sampling Frame: a list of individuals from which a sample is actually selected ideally, should match the population Example: When doing a phone survey, the sampling frame might be the phone book 11 Larson/Farber 4th ed.

Sampling Undercoverage Undercoverage: the condition resulting from omitting population members from the sample frame Example: The phone book might not be representative of all residents of a community 12 Larson/Farber 4th ed. Population Sampling Frame

Sampling Terminology Sampling Error is the mismatch between measurements taken from samples corresponding measurements taken from the respective population sampling errors do not represent mistakes! Nonsampling Error results from -poor sample design -sloppy data collection techniques -bias in questions -nonsampling errors are inadvertent errors 13 Larson/Farber 4th ed.

Multi-Stage Sampling Multi-stage sampling involves selecting a sample in at least two stages. Successively smaller groups are created at each stage Final sample consists of clusters 14 Larson/Farber 4th ed.

Example: Three-Stage Sampling 15 Larson/Farber 4th ed. The following is an example of the stages of selection that may be used in a three-stage household survey. STAGE 1: Electoral Subdivisions Electoral subdivisions (clusters) are sampled from a city or state STAGE 2: Blocks Blocks of houses are selected from within the electoral subdivisions. STAGE 3: Houses Houses are selected from within the selected blocks.

Convenience Sampling 16 Larson/Farber 4th ed. Create a sample by using data from population members that are readily available Example 1: Survey people in a shopping mall Select the mall entrance closest to where you parked your car Stand in a location next to the coffee bar and interview people as they are waiting on line Example 2: Survey people attending an opera concert Gather data regarding their musical preferences Potential Drawback: Your results might be severely biased!

Section 1.2 Summary Describe simple random samples Construct a simple random sample using random numbers Simulate a random process Describe stratified sampling, cluster sampling, systematic sampling, multi-stage and convenience sampling 17 Larson/Farber 4th ed.