Samples and Sampling

As described in Statistics Defined, a sample is a set of raw data values drawn from a much larger source, the population. Purpose is  …. Before drawing a sample, an investigator should clearly define the population from which it is to come. Outline of this essay …

In order for a sample to be effective in achieving its purpose, its selection must have the property of randomness ….

  1. Random sample
    1. Given random variable X with distribution F, a RS of size n is the set  random_sample   where n elementof N and all Xi‘s are independent and identically distributed (i.i.d.).

Simple (SRS) is one in which every possible sample of the desired size has an equal chance of being selected …

  1. Explain in simple terms why a given sampling method may be unsatisfactory
  2. A sample is biased if in some critical way it does not represent the population
  3. Sample statistics
    1. Location
      1. Mean
      2. Median, ;
    2. Spread
      1. Standard deviation
    3. Recognize that the sample mean, , can be regarded as a random variable
    4. In general, any statistic, Gs , computed from a random sample is a random variable and has an associated sampling distribution
    5. Sampling error
      1. Is not a mistake, but rather refers to the natural variability between samples
      2. Relates to confidence of statistical claims
  • Standard error,
  1. Sampling distribution
    1. The probability distribution showing how a sample statistic, Gs , varies
    2. Unbiased if its mean is equal to the associated population parameter

A sample is the result of n (chance) experiments in which the same quantity is measured ….

Sample size, n