Selecting Sampling Strategy

Chris OlsenCOlsen@mchsi.com

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The sampling question du joir: just how tall IS Iowa corn?

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Professional basketball players’ view of Iowa Corn

(In our dreams…but what about reality??)

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In order to measure the height of a stalk of corn we must chop it down.

Measuring all the corn stalks is not on the table; farmers being what they are, we have only one cornstalk per Iowa county that we can utilize.

The economy being what it is, we can only afford to chop down a small number of cornstalks.

Our problem: identify the counties.

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The generation of a subset of a population is known as “sampling” from the population.

We want our sample to be “representative” of the population – if it is, we can make credible statements about our population by generalizing from the sample.

We maximize the probability of getting a representative sample by generating the sample randomly.

The randomization scheme allows the calculation of probability distributions (“sampling” distributions) of statistics.

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A random (“probability”) sample is one such that each population member has a greater-than-zero probability of selection.

The basic random sampling strategy is the “simple” random sample.

A simple random sample of size n from a population of size N is a sample taken in such a way that each of the possible NCn samples is equally likely.

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Iowa has 99 counties -- perfect for a random number table…

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Bubble, bubble, toil and trouble…

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(All other states use calculators)

MathPrbrandInt(1, 99) (A random county)

MathPrbrandInt(1, 99, 10) (10 random counties)

MathPrbrandInt(1, 99, 15) (15 random counties, anticipating bad luck)

MathPrbrandInt(1, 99, 15)L1 (Put in List1)

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Oops?

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A possible improvement on the simple random sampling strategy is to take a stratified random sample.

Stratified random sampling capitalizes on known (or possibly suspected, but be careful) pockets of homogeneity in the population.

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Possible pockets: Golden Gopher Droppings?

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If certain areas of the state have been contaminated by a certain other state this might affect corn height, we would want to take note of this in our sampling – in advance!

We would not want to have each element of the sample from a non-contaminated county;

we would not want to have each element of the sample from a contaminated county;

we would want each part – contaminated and not – represented in our sample.

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To accomplish this representation, we could use a stratified random sample.

60 Pristine, 39 contaminated…

Pristine counties

Contaminated counties

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MathPrbrandInt(1, 60, 6) (6 random pristine counties)

MathPrbrandInt(1, 39, 4) (4 random contaminated counties)

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Bravo!

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In some circumstances we might have reason to believe that the variability in the state is captured in each region of the state.

As an example, consider the quadrennial blitz known as the presidential primary season. All the candidates don boots and overalls and milk the standard cow.

This event generally causes all the news channels to take a poll of Iowans on their opinions about the milking technique of the candidates.

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Newspersons would probably want to spend little time “down on the farm,” and simple random sampling could result in lots of drive time! So some sort of improvement on the simple random sample is desired.

If the variability and representativeness (?) in the state is captured in each region, why not just randomly pick a few regions in the state ?

Why not, that is, take a “cluster sample?” (a random sample of regions.)

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randInt(1, 9, 2)L1

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A special cluster sample: The transect.

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Some newspersons might be unable to follow complex directions. It is possible, however, they can at least count up to some relatively small number.

In this situation, systematic random sampling might be considered.

04/21/23 23Sampling Strategies

The Systematic Sample: Getting it done

1.Decide on the sampling fraction. (Judgment)

2.Decide on a starting point. (Random!)

3. Count off by n’s… (Arithmetic)

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Systematic – every 11

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Systematic – every 5

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Systematic – alphabetical, every 9

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Questions before practice?

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A Review of Sampling Strategies:

Simple Random Sample: The Basic Strategy, requires a list

Stratified Random Sample: Capitalizes on pockets of homogeneity

Cluster sample: Capitalizes on there being NO pockets of homogeneity

Systematic sample: (Alleged) Population arrives serially

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Problem #1: The Cultured Crowd

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Problem #2: Some populations are elusive and/or difficult to sample:

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Problem #2: Pick your difficult population…

1.Homeless

2.Illegal aliens

3.Teen texters in school

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Problem #3:

The Case of the Fiddler Crab…(Uca pugilato)

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Path integration, eh?

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The Sex Ratio of Fiddler Crabs?

Just to be clear, the sex ratio we’re talking about is

• males / females, • NOT # events / time!!!

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Just the facts, ma’am…

That big claw is for courtship & fighting, but is dysfunctional for foraging. (Males fight & forage more?)

Crabs outside burrows are susceptible to predation.

Males are territorial and promiscuous.

Females forage closer to water sources than males.

Breeding females may be smaller.

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The end!

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