Other types of samples… 5.3: SAMPLING Other types of samples…

Review: Three sample designs covered so far: Simple Random Sample (SRS) Voluntary Response Sample Convenience Sample

Other ways to take samples Example: At a university, there are 1500 professors. However, 1000 are male and 500 are female. To take an accurate sample of the university faculty’s opinions, we decide to take a sample of 100 male professors and 50 female. Their total sample is these 150 professors. Why is this not an SRS? What was their process? Why is this sampling method better than just an SRS?

This is not an SRS because they do not put all people into one group and randomly select from that. They break them up into two groups and select some from each group. An SRS does not take into account a variable like Gender. Also, an SRS gives each person an equal chance of being selected. This does not. In this sample, the males have a 1/1000 chance but each female has a 1/500 chance. This is better because its more representative of the population. The population has more males in it, and this sampling method allows the sample to have the same percent of males as the population.

Stratified Random Sample: (NOT SRS) Divide population into groups with something in common (called STRATA) Example: gender, age, etc. 2) Take separate SRS in each strata and combine these to make the full sample - can sometimes be a % of each strata

Try p. 246 #62 BASKETBALL Instructions: Assign 01-19 to each player Use a TRD and read off 2 digits at a time Ignore 00, 20-99, and repeats First 7 numbers are our sample 01 Arenas 06 Duncan 11 Leslie 16 Robinson 02 Billups 07 Farmar 12 McGrady 17 Stoudamire 03 Brand 08 Fowles 13 Miller 18 Taurasi 04 Bryant 09 Gasol 14 Nowitzki 19 Wade 05 Carter 10 Iverson 15 Parker Line 101: 19223 95034 05756 28713 96409 1251 42544 82853 73676 47150 99400 01927 27754 42648 82425 36290 19, 05, 13, 14, 15, 09, 01 = Wade, Carter, Miller, Nowitski, Parker, Gasol, Arenas

Try p. 246 #62 GOLF (Use line 103) Instructions: Label each golfer with number 1 – 9 Use TRD, line 103, read every 1 digit Ignore 0 and repeats First 3 numbers are our sample 1 Cramer 4 Kim 7 Singh 2 Els 5 Mickelson 8 Wie 3 Gulbis 6 Prammanasudh 9 Woods Line 103: 45467 71709 77558 00095 32863 29485 82226 90056 4, 5, 6 = Kim, Mickelson, Prammanasudh

Try p. 247 #68 (a) Use Line 122 for females Use line 105 for males

Try p. 247 #68 (a) First separate the faculty into the 2000 males and 500 females MALES Assign the males #0001 – 2000 Use TRD, read across every 4 digits is a male Ignore 0000, 2001-9999 and repeats First 200 numbers are our sample (line 105) #0769, 1481, 1315, 0094, 0720

FEMALES Label the females #001 – 500 Use TRD, read across, every 3 digits is a female Ignore 000, 501-999 and repeats First 200 numbers are our sample (line 122) #138, 159, 052, 087, 359 The total 400 faculty selected are our sample

Systematic Sample: Randomly picking a first individual, and then selecting every ____ person after that. Good for situations where you do not know your population ahead of time * Example: Interview every 5th person that walks thru the back door of CB South in the morning. * Example: Write down the type of car in every 3rd spot in the CB South parking lot.

Cluster Sample Pick a certain area/part of the population. Try to get every individual in that selection Example: select one lunch period, and talk to everyone at that lunch Census Gather info from everyone in the entire population.

EXAMPLE: We need to survey a random sample of 30 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below: Pick every 10th passenger that boards From the boarding list, randomly choose 5 people flying first class, and 25 of the other passengers Randomly generate 30 seat numbers and survey the passengers who sit there Randomly select a seat position (right window, left window, right aisle, etc.) and survey all people in those seats

SYSTEMATIC STRATIFIED SRS CLUSTER EXAMPLE: We need to survey a random sample of 30 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below: SYSTEMATIC Pick every 10th passenger that boards From the boarding list, randomly choose 5 people flying first class, and 25 of the other passengers STRATIFIED Randomly generate 30 seat numbers and survey the passengers who sit there SRS Randomly select a seat position (right window, left window, right aisle, etc.) and survey all people in those seats CLUSTER

Random Rectangles Activity!