Biometry and Statistics Notes
8/29/11
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Sample fixed values variable
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Values fixed sample random
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Valued round
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Some distance
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Population size = N<infinity
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Values are fixed
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Ex.) N=40
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300 class
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Y1,…,y40 are your ages in years
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They are fixed, we can line us up and calculate that
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18, 20, 21, 19, 20
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40 of these
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They don’t change for today
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Let’s say N=1,999 and y1,…,y1000
are the house prices in Tompkins Co. in 100k
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1.4, 20, 0.5, then there would be 1000 of these
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The point is what they ‘s stand for
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Ex.) N=175 M
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0,1,2,3,4,5,6
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A sample is just a subset of the y’s
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If we take a sample would be three guys in the class from the front because it is not
necessarily representative of the class.
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Technically: sample of n<IJ these would be really
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If he lifts us by numerically increasing cornell id numbers, that becomes the list of
population values.
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That is not y1, y2, y3
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A random sample is a sample selected at random from the collection of possible samples
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We are used to one, which is a simple random sample
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Take a crack at defining
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Question: What is a simple random sample?
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Def. Collection of possible samples, all possible subsets of a fixed size
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SRS (N,n) (always means sample size)
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n out of N
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We have a picture of the entire universe which is a big N
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And we have a small sample, little n
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The probability of each sample is equal
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This statement does not mean the same thing as each person has an equal probability
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However, the latter statement is implied by the first
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There = “N choose n”=
possible subsets of n out of N things
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Number of ways of choosing things out of N
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Unordered
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Therefore, in our example.
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=20*13*38=9880
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The probability of a given sample
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In our example
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1/9880 is the answer
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How do we implement this?
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Implementation:
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The initial statement would be to say 1) List all 9,880 samples of size 3 indices:
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1,2,3
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1,2,4
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1,2,5
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These are the samples where there are roughly 10000 of those
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Probably listed in excel
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Then you would select 1 sample at random meaning with equal probability, which of
course means 1/9880
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That would be the sample
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It is not obvious that sampling without repetition is this
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The proof isn’t that interesting about whether sampling at random without replacement is
obvious, it is just writing it down in sampling at random without replacement?
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This is a way of doing it, an operational method
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It leads to a critical notion
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If you take a 7.5 percent random sample, each person has a 7.5 percent chance of
selection
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Also turns out that the probability (given indir. Appearing in sample= for an indiv.)
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If we have a universe and we are a dot in the universe.
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There are possible samples
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Since we are fixing that one, there are N1 remaining places in the population and n1
places in the sample
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Therefore, there are
with you
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The probability of you getting in there is how many possible ways you can get in there
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 Spring '11
 Ooz
 Statistics, Simple random sample

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