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Biostat Notes

# Biostat Notes - Biometry and Statistics Notes Sample fixed...

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Biometry and Statistics Notes 8/29/11 Sample fixed- values variable Values fixed- sample random Valued round Some distance Population size = N<infinity Values are fixed Ex.) N=40 o 300 class o Y1,…,y40 are your ages in years o They are fixed, we can line us up and calculate that o 18, 20, 21, 19, 20 o 40 of these o They don’t change for today Let’s say N=1,999 and y1,…,y1000 are the house prices in Tompkins Co. in 100k 1.4, 20, 0.5, then there would be 1000 of these The point is what they ‘s stand for Ex.) N=175 M o 0,1,2,3,4,5,6 A sample is just a subset of the y’s If we take a sample would be three guys in the class from the front because it is not necessarily representative of the class. Technically: sample of n<IJ these would be really If he lifts us by numerically increasing cornell id numbers, that becomes the list of population values. That is not y1, y2, y3 A random sample is a sample selected at random from the collection of possible samples We are used to one, which is a simple random sample Take a crack at defining Question: What is a simple random sample? Def. Collection of possible samples, all possible subsets of a fixed size SRS (N,n) (always means sample size) n out of N We have a picture of the entire universe which is a big N And we have a small sample, little n The probability of each sample is equal This statement does not mean the same thing as each person has an equal probability However, the latter statement is implied by the first There = “N choose n”= possible subsets of n out of N things Number of ways of choosing things out of N Unordered Therefore, in our example.

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=20*13*38=9880 The probability of a given sample In our example 1/9880 is the answer How do we implement this? Implementation: The initial statement would be to say 1) List all 9,880 samples of size 3 indices: 1,2,3 1,2,4 1,2,5 These are the samples where there are roughly 10000 of those Probably listed in excel Then you would select 1 sample at random meaning with equal probability, which of course means 1/9880 That would be the sample It is not obvious that sampling without repetition is this 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? This is a way of doing it, an operational method It leads to a critical notion If you take a 7.5 percent random sample, each person has a 7.5 percent chance of selection Also turns out that the probability (given indir. Appearing in sample= for an indiv.) If we have a universe and we are a dot in the universe. There are possible samples Since we are fixing that one, there are N-1 remaining places in the population and n-1 places in the sample Therefore, there are with you The probability of you getting in there is how many possible ways you can get in there
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Biostat Notes - Biometry and Statistics Notes Sample fixed...

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