人大陈卫教授手把手教你统计LecSamplingDistribution

1、this lecture coverslpopulation parameterslsample statisticslsampling distributionintroductionlresearchers in the social sciences almost never have enough time or money to collect information about the entire population that interests them, for example, everyone in beijing, or even everyone in china.

2、lfortunately, we can learn a lot about a population if we carefully select a subset(子集) of it. this subset is called a sample. lthrough the process of samplingselecting a subset from the populationwe attempt to generalize to the characteristics of the population based on what we learn from the sampl

3、e. lparameter： measures used to describe the distribution of the population. lpopulation meanlpopulation proportionlpopulation standard deviation lwe use the term when referring to a corresponding characteristic calculated for the sample. lsample meanlsample proportionlsample standard deviation l we

4、 know the value of the parameter. lthe is to find the population parameter. researchers usually select a sample from the population and from the sample. is to provide estimates of unknown parameters from sample statistics that can be calculated.lmost important concepts in sampling theory and statist

5、ical inferencesampling distribution. lto helps and enables us to generalize from the sample to the population. the populationlconcept of the sampling distribution, lets consider as our population the 20 individuals listed in the right. our variable y is the income for the 20 individualsl the paramet

6、er we are trying to estimate is the mean income.population parameterslpopulation mean and standard deviation:the samplelpopulation mean is unknown lwe estimate its value by drawing a random sample of three individuals (n=3) lcalculate the mean income for this sample. sample statisticlmean for the sa

7、mple:lnotice that our sample mean differs from the population parameter.lthis discrepancy is due to sampling error.sampling errorlsampling error is the discrepancy between sample estimate of a population parameter and the real population parameter. lthe sample error for this sample is: 22766-20817=1

8、949another samplelanother random sample : lmean for this sample is: the dilemmalthe sampling error for this sample is 22766-21345=1421, somewhat less than the error for the first sample. ldilemma: if sample estimates vary and if most estimates result in some sort of sampling error, how much confiden

9、ce can we place in the estimate? on what basis can we infer from the sample to the population?the sampling distributionlthe answer to this dilemma is to use a device known as the sampling distribution. lthe sampling distribution is a theoretical probability distribution(抽样分布是理论上的概率分布) of all possibl

10、e sample values for the statistic in which we are interested. the sampling distributionlif we were to draw all possible random samples of the same size from our population of interestlcompute the each statistic lplot the frequency distribution for that statisticlwe would obtain an approximation of t

11、he sampling distribution. levery statisticfor example, a proportion, a mean, a standard deviationhas a sampling distribution. lbecause it includes all possible sample values, the sampling distribution enables us to compare our sample result with other sample values and determine the likelihood assoc

12、iated with that result.sampling distribution of the meanlsampling distributions are theoretical distributions, which means that they are never really observed (they are non empirical). lsampling distribution of the mean is a theoretical distribution of sample means that would obtained by drawing fro

13、m the population all possible samples of the same size.lin illustrating the relationship between the population, the sample, and the sampling distributions, i have generated an empirical sampling distribution of the mean age at first marriage. lconsider as the population of 5006 women in the 1997 su

14、rvey. we draw 500 samples of n=20 and calculate the mean age at first marriage of each sample.lmake a histogram of the 500 means. this is the sampling distribution of the meanlshowing the mean values and frequency (number of samples).the population distributionl=21.4801, =2.701500 samples of n=20l=2

15、1.4481, =0.68971lsampling distribution can be described in terms of its mean and standard deviation. lto obtained the mean of the sampling distribution, add all individual sample means and divide by the number of samples. thus, the mean of the sampling distribution of the mean is actually the mean o

16、f means.lthe mean of the sampling distribution of the mean（抽样分布均值的均值）standard error of the meanlthe standard deviation of the sampling distribution is called the standard error of the mean. lit is a measure to describe how much dispersion in the sampling distribution of the mean(均值的抽样分布的离散程度)lit is

17、equal to :lthe standard deviation of the population 6yldivided by the square root of the sample size: n1/2basic properties of sampling distribution of the meanl1 regardless of the shape of the population distribution, the sampling distribution of the mean is approximately normal.l2 only a few of the

18、 sample means coincide exactly with the population mean, l3 sampling distribution centers around the population mean.lvariability of the sampling distribution is smaller than the variability of the population distribution. lthese properties are even more striking as the sample size increases(每次抽样的数量

19、n). the mean of the sampling distribution getting closer to the population mean and standard error of the mean becoming smaller.500 samples of n=100l=21.4979, =0.29517500 samples of n=400l=21.4837, =0.13838central limit theorem las the sample size increases, the sampling distribution of the mean more and more closely resembles a normal distribution （usu.30 or more）. lthus even if a variable is not normally distributed in the population, the mean of all possible sample mea