CHAPTER 5: SAMPLING EXAMPLES Sequence Name Gender (female=1, male=0) School GPA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Adam Alexandra Beth Bryan Carol Cindy Deanna Donald Elizabeth Eric Francine Frank George Greg Holly Ileana Isabelle Jose Karyn Kyle Lamar Latrell Leslie Max Melissa Michael Molly Nancy Norman Otto Patricia Paul Ricardo Sally Simon Suzanne Tara Tim Todd Yanissa 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 Stanford Stanford Cornell FAU Stanford Stanford Duke Cornell FAU Duke Duke FAU Stanford Stanford Duke FAU Cornell Cornell Duke FAU Stanford Stanford FAU Stanford Cornell FAU Duke FAU Stanford Duke FAU FAU Cornell Duke Duke Stanford Stanford Cornell Cornell FAU 3.0 1.4 1.2 2.7 2.8 3.5 3.4 3.6 2.0 2.3 4.0 4.0 3.8 3.3 2.8 0.2 2.3 3.0 3.1 3.2 3.3 2.7 3.3 2.4 3.6 3.0 2.9 3.0 2.9 1.8 3.5 2.5 2.3 3.0 2.6 2.6 3.7 2.4 2.0 2.0 Table of random numbers: 0.82 0.78 0.66 0.88 0.67 0.55 0.42 0.75 Sequence for the male strata 1 Sequence for the female strata 1 2 2 3 4 5 3 6 4 7 5 6 7 8 9 10 8 11 9 10 11 12 12 13 13 14 15 14 15 16 16 17 17 18 18 19 19 20 0.22 Notice: each time we use a new random number from the random number table! 20 SIMPLE RANDOM: Pick a sample of 4 people from the list. [sequence # to pick] = [random #] [total #of subjects] 1st record to pick 2nd record to pick 3rd record to pick 4th record to pick = .82 40 = 32.80 33 = .78 40 = 31.20 31 = .66 40 = 26.40 26 = .88 40 = 35.20 35 Ricardo Patricia Michael Simon SYSTEMATIC: Pick a sample of 4 people from the list. [interval length] = [population] / [sample size] Interval length = 40/4 = 10 [initial record picked] = [interval length] [random #] Initial record picked = 10 .67 = 6.70 7 Deanna [next record to pick] = [previous pick] + [interval length] 2nd record to pick = 6.70 + 10 = 16.70 17 Isabelle 3rd record to pick = 16.70 + 10 = 26.70 27 Molly 4th record to pick = 26.70 + 10 = 36.70 37 Tara STRATIFIED RANDOM: Simple random sampling yielded 3 males & 1 female and systematic sampling yielded 4 females, but we'd like the proportion of each gender in our sample to resemble those in the target population. [number to select from strata] = [sample size] {[strata size]/[population]} # females needed = 4 {20/40} = 2 # males needed = 4 - 2 = 2 Next, divide the population into two strata: males versus females. Re-sort students by alphabetical order within each strata (see the last two columns in the table above). Finally, pick two from each group using simple random sampling. Males: 1st record to pick 2nd record to pick = .55 20 = 11.00 11 = .42 20 = 8.40 8 Latrell Jose Females: 1st record to pick 2nd record to pick = .75 20 = 15.00 15 = .22 20 = 4.40 4 Nancy Cindy