Statistical Population
Definition
A statistical population is a set of similar items or events which is of interest for some question or experiment. It is a complete set of items that share at least one property in common that is the subject of a statistical analysis. For example, the population of all people living in a particular town, the population of bacteria in a petri dish, or the population of all atoms making up a crystal.
Characteristics
A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about the population.
In statistics, a population is assumed to be large enough to accurately describe characteristics of a population, such as the mean or standard deviation. When dealing with a finite population, it is possible to measure every member of the population, but in most cases this is not feasible, so a sample is taken from the population.
Types of Populations
There are different types of statistical populations:
1. Finite Population: This refers to the population of a statistical study where the number of observations or data points is finite. For example, the population of students in a school.
2. Infinite Population: This refers to the population of a statistical study where the number of observations or data points is infinite. For example, the population of all possible tosses of a coin.
3. Hypothetical Population: This refers to a statistical population that does not exist in reality but is considered for the purpose of statistical inference. For example, the population of all possible outcomes of a future event.
Population Parameters
In statistics, a parameter is a characteristic of a population. Unlike statistics, which are calculated from sample data, the parameters are usually unknown and are often estimated based on data collected from a sample. Commonly used parameters include the population mean (μ), population standard deviation (σ), population proportion (p), and population variance (σ²).
Sampling
Sampling is a method that allows us to get information about the population based on the statistics of a sample. Sampling methods may be either random (random sampling, stratified sampling, systematic sampling) or non-random/ nonprobability (convenience sampling, quota sampling, purposive sampling). Each method has its own advantages and disadvantages.
Population Size and Power Analysis
The size of a population can greatly affect the results of a study. In general, larger populations allow for more accurate predictions and stronger statistical power. Power analysis can be used to determine the minimum sample size required so that one can be reasonably likely to detect an effect of a given size.
Population Models
Population models are mathematical descriptions of populations that allow scientists to predict how those populations will change over time. They are often used in population ecology and in epidemiology.