Biostat Final Test Notes - Population size means Sample is...

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Population size means Sample is a subset of y-values means sample size possible subsets Probability of a given sample is If you have one value fixed and they ask what the probability is that you are in the sample you calculate For is which is for All SRS is when everyone has an equal chance of being in the sample. Second order inclusion probabilities: (Doing second order is what gives you standard errors) Total: Sum of all values in the population; Total: ; Mean: Second order inclusion probability is the probability that appears with Classical Infinite population sampling- fixed samples with random values that are random vs. finite population sampling- fixed values with random samples Every type of sampling has to give everyone a chance to be in the sample When estimating a population total, you can use the Horvitz-Thompson Estimator: SRS: HTE is always unbiased is the probability that i is in the sample is the probability that I and j are in the sample To get the standard error, you need a , so you can get Stratified mean: with as the sample mean is the finite population correction (the error) (fpc) meaning the closer n is to N, the less of an error there is HTE is good because it lets us think about statistical abnormality criteria and we need information about normality Frame: a list of identifiers that allow us to draw the sample ; PPSWR= probability proportional to size with replacement PPSWOR= probability proportional to size without replacement Find probabilities of possible samples being in it There is a different probability of getting AD and DA can occur as AB or BA so Therefore, For a sample of then the HTE of , meaning can be both quantitative and qualitative but it needs to be binary for qualitative and is an estimate of and is an estimate of The Harvis Thompson estimate of is is the weight of SRS: is the inflation factor for estimator: 1. Theoretically calculate the variance of what you are estimating 2. Find empirical estimate 3. Take square root: Reasons for stratification: practicality, guaranteed representation, increases precision and reduces variance Principle of stratifying- you could get the perfect answer if you could stratify into homogenous groups Two Stage Cluster Sampling: N= total number of PSUs n= amount being tested of PSUs is how many are being sampled of each unit number of SSUs in ith PSU i.e. k= total number of PSU’s To get you calculate for each M and y and then you add them up and multiply by N/n seen below HTE of multiply by 1/n-1 to get is the sample mean within the PSU Variance: Standard Error: Where and and is the sample variance within the sample PSU. Standard Error is the square root of variance. The optimal allocation of one is mean per PSU: and mean per SSU: z is the assumption of asymptotic normality 95% Confidence Intervals SRS Estimate for mean: The confidence interval of 95% does not mean that we are 95% sure that this is the mean but that we are 95% sure the mean is in the interval. More confidence comes with large sample sizes
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This note was uploaded on 01/28/2012 for the course STATISTICS 3010 taught by Professor Ooz during the Spring '11 term at Cornell University (Engineering School).

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Biostat Final Test Notes - Population size means Sample is...

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