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The correct answer is E E. For stratified random sampling, we get to choose the sample size for each stratum. By picking larger/smaller numbers for one group, we're changing their probability of being selected without changing anyone else's. That means that (unless by coincidence) the chance of different samples being selected is not the same.
How do you conduct disproportionate stratified random sampling? Home Office Total Men 100 250 350 Women 120 30 150 Total 220 280 500 An overall sampling fraction of 10% has been decided on. Su...
Procedure for sample mean: We calculate the proportions of stratums: wi =Ni/N w i = N i / N. Do simple random sampling for each stratum and calculate stratum sample mean Xi¯ X i ¯. Sample mean is: X¯ = ∑wiXi¯ X ¯ = ∑ w i X i ¯. Equation for population variance inside stratum 1 (symetrical for others): N1−n1 (N1−1)n1 ∑N1 k=1(Xk ...
1. One of the first steps when one use stratified sampling is to define the strata. Strata should be define such that the elements in a stratum are as homogeneous as possible. In addition, the elements of different strata must be heterogeneous. One way of getting strata like that is using machine learning techniques.
Since we are doing simple random sampling without replacement (with a large population assumption K ≫ N), each xi has the same statistical properties. In particular, the same expected value, E(xi) = μX. Therefore, 1 N ∑ i=1N E(xi) = 1 N ∑ i=1N μX = NμX N =μX. However, simple random sampling also implies that P(xi ∈Gj) = nj K (again ...
Then a simple random sample is chosen from each strata separately. These simple random samples are combined to form the overall sample. Examples of characteristics on which strata might be based include: gender, state, school district, county, age. Reasons to use a stratified rather than simple random sample include:
It can be shown that stratified sampling reduces the overall variance of our estimator, but I don't see intuitively why this is true. In classical Monte Carlo, we sample points from the function, and then take the average. In stratified sampling, we partition the interval into strata, collect samples from each stratum, and then combine our results.
My Understanding. I know that for a stratified simple random sample, the variance of t^y,st t ^ y, s t is. Vp(t^y,st) =∑h=1L N2 h(1 − nh Nh)S2 h nh V p (t ^ y, s t) = ∑ h = 1 L N h 2 (1 − n h N h) S h 2 n h. where S2h S h 2 is the true variance, Nh N h the Total number of units and nh n h the Number of units in sample.
By contrast, if you had a random sample from a large population of school districts with one dependent variable measuring 'performance' and one explanatory variable 'student-teacher' ratio, then you might see if there is a significantly positive Pearson correlation, and if so do a regression analysis to explore the linear relationship.
Stratified sampling is done when there is a heterogenous population with identifiable co-variates (in this case, college major). So you randomly sample from each strata, but the sample size is proportional to fraction of the total population a particular strata represents.