11. Describe the relationship between the concept of “statistic” as function of known data as opposed as to concept of “state of nature” or “parameter” in the unknown population?
There are two meanings to the word “statistic”:
- Statistic as a function of known data
- Statistic as a science
More specifically, regarding the first meaning, statistic (singular) or *sample statistic is any quantity computed from values in a sample, often the mean. Technically speaking, a statistic can be calculated by applying any mathematical function to the values found in a sample of data. The function itself is independent of the unknown estimands; that is, the function is strictly a function of the data.
In statistics (as a science), there is an important distinction between a statistic and a parameter. “Parameter” refers to any characteristic of a population under study. When it is not possible or practical to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. Parameter is generally an unobservable quantity describing a property of a statistical population. A parameter can only be computed exactly if entire population can be observed without error; for instance, in a perfect census or for a population of standardized test takers. A parameter is to a population as a statistic is to a sample.