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Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters). [3]A tilde (~) denotes "has the probability distribution of". Placing a hat, or caret (also known as a circumflex), over a true parameter denotes an estimator of it, e.g., ^ is an estimator for .
A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean).
In general, the subscript 0 indicates a value taken from the null hypothesis, H 0, which should be used as much as possible in constructing its test statistic. ... Definitions of other symbols: Definitions of other symbols:
In statistics, a population is a set of similar items or events which is of interest for some question or experiment. [1] 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 ...
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the ...
The arithmetic mean of a population, or population mean, is often denoted μ. [2] The sample mean ¯ (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator).
A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics. However, a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily interpretable.
The z-test for comparing two proportions is a statistical method used to evaluate whether the proportion of a certain characteristic differs significantly between two independent samples. This test leverages the property that the sample proportions (which is the average of observations coming from a Bernoulli distribution ) are asymptotically ...