Biostatistics and experimental design
Three types of evaluation criteria
No bias to qualitative ensure that the estimated amount of non-directional error. That is consistent with the estimated amount of the desired statistics and the population parameters.
For the population mean, moment estimation and maximum likelihood estimation estimates consistent with the desired overall mean parameters obtained by these two methods is unbiased. For the population variance, by moment estimation and maximum likelihood estimation method of estimation of these two parameters obtained inconsistent with the expected variance out of the population variance, it is biased, when using the denominator 1 n- time, i.e. using a sample with a desired mean the same population variance is unbiased.
The PS : when n is very large and is located in the denominator when calculating flexibility
Since a parameter can have different unbiased estimators, it is necessary to investigate the validity of the parameters, to take a quantitative way, the more effective the smaller the variance, the variance of the sample mean is also minimal, so the use of the sample mean estimate the population mean is the best .
Consistency refers to the sample becomes large so that the overall feature values eigenvalue approaches, this condition is not used in the actual process is not required.
The end result is an estimate of the point estimate a point, and interval estimation is demonstrated by estimating the true value of the drop zone gap between the true value and the estimated amount. FIG: the length of the interval is a random color bars, also known as the confidence l- [alpha] confidence interval.
The process of obtaining the confidence interval:
As n increases it will only have beneficial effects, so first determine the number of samples n . To find a function that is an equation, the right side is a common distribution (after learning can know the exact amount of sample graphics, all features known at this time), it does not depend on any parameters. Comprising a left unknown, using the method of undetermined coefficients is required here. When determining the confidence level, it is necessary to consider the precision L + confidence level [alpha], their relationship following formula.
- Determining a confidence level of the [alpha], then this will ensure that the area surrounded proportion, the value of the original upper and lower bounds are not unique, but to ensure the interval L minimum, preferably equally take [alpha] / 2 , so that the upper and lower bounds on the sole.
- BL shorter the higher the precision, but not too small α, it becomes untrustworthy.
Answer process:
Formula; variable; confidence + confidence interval
The mean and variance of the normal population interval estimation
- Known Population Variance reality does not exist, but as a transition from the population variance to the sample variance must exist.
- Unknown population variance: when the overall sample to, it is easy not to let color of the true range value falls, so the response is to relax the condition, i.e. an enlarged section, which explains the t distribution L value greater than Z distribution L value.
