统计学重点整理CH7 Distributions of the Sample Mean and Sample Proportion and Sampling Techniques

CH7
Nonrandom Sampling - Every unit of the population does not have the same probability of being included in the sample
Random sampling - Every unit of the population has the same probability of being included in the sample.
Random Sampling Techniques
Simple Random Sample – basis for other random sampling techniques Stratified Random Sample
Proportionate -- the percentage of the sample taken from each stratum is proportionate to the percentage that each stratum(層) is within the population
Disproportionate -- proportions of the strata within the sample are different than the proportions of the strata within the population
Population is divided into non-overlapping subpopulations called strata Researcher extracts a simple random sample from each subpopulation Stratified random sampling has the potential for reducing error Sampling error – a sample does not represent the population
Stratified random sampling has the potential to match the sample closely to the population Stratified sampling is more costly
Stratum should be relatively homogeneous, i.e. race, gender, religion Systematic Random Sample
Population elements are an ordered sequence.
With systematic sampling, every k th item is selected to produce a sample of size n from a population of size N
Systematic sampling is evenly distributed across the frame Sample elements are selected at a constant interval, k, from the ordered sequence frame.
Systematic sampling is based on the assumption that the source of the population is random Cluster (or Area) Sampling
Cluster sampling – involves dividing the population into non-overlapping areas Identifies the clusters that tend to be internally homogeneous Each cluster is a microcosm(縮圖) of the population
If the cluster is too large, a second set of clusters is taken from each original cluster This is two stage sampling
Advantages
More convenient for geographically dispersed populations Simplified administration of the survey
Unavailability of sampling frame prohibits using other random sampling methods
n =sample size N=population size k =size of selection interval
k =N n
Disadvantages
Statistically less efficient when the cluster elements are similar
Costs and problems of statistical analysis are greater than for simple random sampling
Non-Random sampling – sampling techniques used to select elements from the population by any mechanism that does not involve a random selection process
Errors:
Data from nonrandom samples are not appropriate for analysis by inferential statistical methods.
Sampling Error occurs when the sample is not representative of the population
Non-sampling Errors – all errors other than sampling errors
Missing Data, Recording, Data Entry, and Analysis Errors
Poorly conceived concepts , unclear definitions, and defective questionnaires
Response errors occur when people do not know, will not say, or overstate in their answers
Central Limit Theorem(中央極限定理)
Central limits theorem allows one to study populations with differently shaped distributions
Central limits theorem creates the potential for applying the normal distribution to many problems when sample size is sufficiently large
Advantage of Central Limits theorem is when sample data is drawn from populations not normally distributed or populations of unknown shape can also be analyzed because the sample means are normally distributed due to large sample sizes
As sample size increases, the distribution narrows
Due to the Std Dev of the mean
Std Dev of mean decreases as sample size increases
Z Formula for Sample Means
Sampling Distribution of P
Sample Proportion
Sampling Distribution
nQ > 5 (P is the population proportion and Q = 1 - P
.)
The mean of the distribution is P.
The standard deviation of the distribution is Z Formula for Sample Proportions
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