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Statistical power may also be extended to the case where multiple hypotheses are being tested based on an experiment or survey. It is thus also common to refer to the power of a study, evaluating a scientific project in terms of its ability to answer the research questions they are seeking to answer.
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities.
Probability generating functions obey all the rules of power series with non-negative coefficients. In particular, () =, where () =, < (), x approaching 1 from below, since the probabilities must sum to one.
G*Power is a free-to use software used to calculate statistical power. The program offers the ability to calculate power for a wide variety of statistical tests including t-tests , F-tests , and chi-square-tests , among others.
PASS is a computer program for estimating sample size or determining the power of a statistical test or confidence interval. NCSS LLC is the company that produces PASS. NCSS LLC also produces NCSS (for statistical analysis). PASS includes over 920 documented sample size and power procedures.
In 2016, the American Statistical Association (ASA) made a formal statement that "p-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone" and that "a p-value, or statistical significance, does not measure the size of an effect or the importance of a ...
Power, sample size, and the detectable alternative hypothesis are interrelated. The user specifies any two of these three quantities and the program derives the third. A description of each calculation, written in English, is generated and may be copied into the user's documents.
The assumption of a particular form for the relation between Y and X is another source of uncertainty. A properly conducted regression analysis will include an assessment of how well the assumed form is matched by the observed data, but it can only do so within the range of values of the independent variables actually available.