Sampling Design

But First a Sampling Experiment

Each group of students should:1. Pull 5 candies out of the bag2. Weigh the candies3. Write down the weight4. Put the candies back in the bag!!5. Pass the scale and bag to your neighbors6. Silently multiply the weight of the 5 candies by 20.

No ScaleCandy Sample

Type Weight (g)3 Musketeers 60Carmels 8Tootsie Rolls 7Junior mints 18Peppermint Patties 17

Discussion

Definitions

• Sampling – procedure involving parts of the whole population

• Sample– a subset of the pop.

• Population– finite group of elements

• Universe– infinite group of elements

Why Sample?

• Pragmatic reasons– Cheaper– Easier– Faster

• Accurate and reliable results

• Census?

Sampling

• Define the target population• A sampling frame– Mailing lists

• Reverse directories• lists streets and the people that live on them

• Sampling frame error when the entire population is not represented in the sampling frame

• Sampling unit- Single

Random Sampling Error vs. Nonsampling (Systematic) Error

• Random Sampling Error– The difference between the sample results and

the results of a census using the same methods

• Systematic error– errors that are not due to chance fluctuations.

Sampling frame error is a systematic error.

Probability vs. Non-probability sampling

• Nonprobability- the probability of any particular member of the population being chosen is unknown.

• Therefore there are no appropriate statistical techniques for measuring random sampling error from a nonprobability sample. Thus making inference is inappropriate.

Non-probability Sampling

• Convenience Sampling – do you have a pulse?

Non-probability Sampling

• Judgment sampling – using your judgment to select the characteristics

of interest

Non-probability Sampling

• Quota sampling– a min number of individuals with a certain

characteristic.

Non-probability Sampling

• Snowball sampling – initial respondents selected with probability

methods, and they refer others

Probability Sampling

• Simple random sampling – – everyone in pop has an equal probability of being

selected

Probability Sampling

• Systematic Sampling- – using every 50th name in a phone book after a

random starting point is selected.• Sampling interval- in this case 50• Periodicity- when the names are not ordered randomly

Probability Sampling

• Stratified sampling (increase homogeniety within strata, increase heterogeniety between strata)– Proportional vs. disproportional strata– Optimal allocation

Probability Sampling

• Cluster sampling– Area sample– Multistage area sampling

Statistics

• When sampling is not simple random sampling the statistics get much harder, ie more complex.

• Observations need to be weighted based upon their probability of appearing in the sample.

What is the appropriate sample design?

But First a Sampling Experiment

Each group of students should:1. Pull 5 candies out of the bag2. Weigh the candies3. Write down the weight4. Put the candies back in the bag!!5. Pass the scale and bag to your neighbors6. Silently multiply the weight of the 5 candies by 20.

No ScaleCandy Sample

Type Weight (g)Nestle Crunch 43.93 Musketeers 60.43 Musketeers Mint 35.2Salted Nut Roll 51Twizzlers 14Starburst 5Tootsie Rolls 6.66Milk Duds 12Peppermint Patties 17

No ScaleCandy Sample

Type Weight (g)Twix 56.7Reese’s “Big Cup” 39Gum 5.6Milky Way 17Rolo 6

No ScaleCandy Sample

Type Weight (g)Crunch 43.9Heath 14Milk Duds 123 Muskateers 60Hot Tamales 14