![Page 2: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/2.jpg)
The sampling question du joir: just how tall IS Iowa corn?
04/21/23 2Sampling Strategies
![Page 3: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/3.jpg)
Professional basketball players’ view of Iowa Corn
(In our dreams…but what about reality??)
04/21/23 3Sampling Strategies
![Page 4: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/4.jpg)
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.
04/21/23 4Sampling Strategies
![Page 5: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/5.jpg)
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.
04/21/23 5Sampling Strategies
![Page 6: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/6.jpg)
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.
04/21/23 6Sampling Strategies
![Page 7: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/7.jpg)
Iowa has 99 counties -- perfect for a random number table…
04/21/23 7Sampling Strategies
![Page 8: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/8.jpg)
Bubble, bubble, toil and trouble…
04/21/23 8Sampling Strategies
![Page 9: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/9.jpg)
(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)
04/21/23 9Sampling Strategies
![Page 10: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/10.jpg)
Oops?
04/21/23 10Sampling Strategies
![Page 11: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/11.jpg)
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.
04/21/23 11Sampling Strategies
![Page 12: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/12.jpg)
Possible pockets: Golden Gopher Droppings?
04/21/23 12Sampling Strategies
![Page 13: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/13.jpg)
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.
04/21/23 13Sampling Strategies
![Page 14: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/14.jpg)
To accomplish this representation, we could use a stratified random sample.
60 Pristine, 39 contaminated…
Pristine counties
Contaminated counties
04/21/23 14Sampling Strategies
![Page 15: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/15.jpg)
MathPrbrandInt(1, 60, 6) (6 random pristine counties)
MathPrbrandInt(1, 39, 4) (4 random contaminated counties)
04/21/23 15Sampling Strategies
![Page 16: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/16.jpg)
Bravo!
04/21/23 16Sampling Strategies
![Page 17: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/17.jpg)
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.
04/21/23 17Sampling Strategies
![Page 18: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/18.jpg)
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.)
04/21/23 18Sampling Strategies
![Page 19: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/19.jpg)
randInt(1, 9, 2)L1
04/21/23 19Sampling Strategies
![Page 20: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/20.jpg)
A special cluster sample: The transect.
04/21/23 20Sampling Strategies
![Page 21: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/21.jpg)
04/21/23 21Sampling Strategies
![Page 22: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/22.jpg)
04/21/23 22Sampling Strategies
![Page 23: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/23.jpg)
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
![Page 24: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/24.jpg)
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)
04/21/23 24Sampling Strategies
![Page 25: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/25.jpg)
Systematic – every 11
04/21/23 25Sampling Strategies
![Page 26: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/26.jpg)
Systematic – every 5
04/21/23 26Sampling Strategies
![Page 27: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/27.jpg)
Systematic – alphabetical, every 9
04/21/23 27Sampling Strategies
![Page 28: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/28.jpg)
Questions before practice?
04/21/23 28Sampling Strategies
![Page 29: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/29.jpg)
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
04/21/23 29Sampling Strategies
![Page 30: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/30.jpg)
Problem #1: The Cultured Crowd
04/21/23 30Sampling Strategies
![Page 31: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/31.jpg)
Problem #2: Some populations are elusive and/or difficult to sample:
04/21/23 31Sampling Strategies
![Page 32: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/32.jpg)
Problem #2: Pick your difficult population…
1.Homeless
2.Illegal aliens
3.Teen texters in school
04/21/23 32Sampling Strategies
![Page 33: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/33.jpg)
Problem #3:
The Case of the Fiddler Crab…(Uca pugilato)
04/21/23 33Sampling Strategies
![Page 34: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/34.jpg)
Path integration, eh?
04/21/23 34Sampling Strategies
![Page 35: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/35.jpg)
The Sex Ratio of Fiddler Crabs?
Just to be clear, the sex ratio we’re talking about is
• males / females, • NOT # events / time!!!
04/21/23 35Sampling Strategies
![Page 36: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/36.jpg)
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.
04/21/23 36Sampling Strategies
![Page 37: Selecting Sampling Strategy Chris Olsen COlsen@mchsi.com 12/14/20151Sampling Strategies](https://reader036.vdocuments.net/reader036/viewer/2022062305/5697bfa21a28abf838c965e9/html5/thumbnails/37.jpg)
The end!
04/21/23 37Sampling Strategies