Biostatistics
Sampling Distribution: n samples will be n a statistic, these n a statistic as a whole, that is, the overall distribution of the sampling distribution
The Khintchine law of large numbers, n from a main content of non-normal distribution of the sample population extracted, and when n is large enough, the sample mean asymptotically normal distribution. Therefore, the average number of sampling distribution is not very strict requirements for normality, but the variance of the sampling distribution, the requirements of normality overall is very strict.
The distribution of the sample mean:
Based on normal population ( both parameters are known ) sampling distribution :
EG ' : Overall n = 3,
Since n = 2 with replacement sample , there . 9 possibilities:
n = 4 with replacement sampling , there are 81 possibilities
Statistics and population parameter is not exactly the same, but satisfy the above relation, it is:
Standard error is the variance parameters
The overall non-normal distribution ( two parameters are known ) : According to the central limit theorem, based on a large sample with normal population
Therefore, as long as a large sample will satisfy z distribution, z is met N (0,1)
Unknown Variance: The overall standard deviation, and standard deviation obtained sample was replaced with t, and this was t satisfying degrees of freedom ( n--. 1 ) of the t distribution, the PDF apparent t distribution with only a degree of freedom, but not with others.
Because the n number to meet the mean, there must be a number value by the number of other impact, and because the degree of freedom is the number of independent observations, the degree of freedom is n. 1- :
When the degree of freedom, i.e. n when the normal distribution is large; T ---> U
Eigenvalues:
The relationship between population distribution and sampling distributions:
PS : For small sample population distribution is unknown there is no method
Distribution of the sample variance
When the normal population, the case of two parameters are aware, the sample variance to meet the chi-square distribution
Is a random variable S side, it is a chi-squared random variable, chi-square distribution associated with the degree of freedom only.
to sum up:
Two normally distributed population (all know that mean and variance), the distribution of the sum and difference of the two sample means: the use of normal Adding and Subtracting
Two normally distributed population (mean know, but unknown variance particular value, but know equal variance), and the distribution of the difference between two sample means: the use of his points subtraction Save Bucharest
Distribution Conditions: 1. mean if known? 2. whether the variance is known? 3. The sample size is large or small?
