Sampling HMS 320 Spring 2008

Why sample? Why not survey or collect data from the whole population?

Population Group of individuals defined along some characteristic or set of characteristics –Superintendents –Music teachers in Quincy public schools –4 th grade students 4 th grade students in Quincy –4 th grade students in Quincy parochial schools »4 th grade students in Quincy St. Peter’s school »4 th grade student in Ms. Jones’ class at St. Peter’s

Population Target population – desired population Accessible population – feasible/practical population Target population: All 4 th graders Accessible population : 4 th graders at St Peter’s

Simple Random Sample What is it? What is the advantage? equal chance generalizabilty What is the disadvantage? bias in sample sampling error Precision – reducing sampling error Systematic sampling primary Bias in sampling

Choosing the sample Random –Every person in the population has an equal chance of being selected –Best way to achieve “representative sample” –Difficulty is truly achieving a random sample

Sample Subset of a Population Individuals in the Sample are the participants in the study Population (in the green) A person Sample (in the small circle)

Simple Random Sample Sampling or selection is done by simply randomly selecting one member of the population, then another, then another, etc… Until the desired sample size is achieved Simple example: 100 people in the population, put their names in hat, and draw 20.

Simple Random Sample More likely methods: –Use computers –Use table of random numbers and a list

Stratified sampling advantages improves generalizability improves precision disadvantages sample size must be larger

Stratified Random Sampling Every person still has an equal chance of being selected Select the sample based upon one or more characteristics – strata Determine the stratum or strata Determine their proportions Select persons from the strata to create a sample that is consistent with the strata proportions

Stratified Random Sampling Strata are gender and race –In Population, 60% women, 70% white –Thus you have four groups White women – 42% Minority Women - 18% White men – 28% Minority men – 12% –Want 200 sample size. Select: 84 White women from all the white women in the population 36 Minority women from all the minority women in the pop 56 White men from all the white men in the pop 24 Minority men from all the minority men in the pop Another example next slide:

Middle school students 7th, 8th, 9th –Population th graders 1500/3700 = 41% th graders 1200/3700 = 32% th graders 1000/3700 = 27% 100 students –41 are 7 th graders –32 are 8 th graders –27 are 9 th graders Helps creates representation, but is more work Stratified Random Sampling

Other sampling techniques volunteers – ads and disads convienence – ads and disads purposive – ads and disads snowball – ads and disads cluster – ads and disads

Sample size “Larger is better” Sample size is related to precision (Use formula as exhibit of determining random sample size and precision and the relationship between population size and sample size)

Factors affecting sample size Results of a pilot study Resources Nature of the phenomena in question Homogeneity of the population Expected differences between groups large or small expected?

Sampling and Demographics Collect demographics race, gender, age, income, education Identifies differences exist between the sample and the population

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