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Statistical significance dates to the 18th century, in the work of John Arbuthnot and Pierre-Simon Laplace, who computed the p-value for the human sex ratio at birth, assuming a null hypothesis of equal probability of male and female births; see p-value § History for details.
Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure ...
The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complex studies ...
Exact tests that are based on discrete test statistics may be conservative, indicating that the actual rejection rate lies below the nominal significance level . As an example, this is the case for Fisher's exact test and its more powerful alternative, Boschloo's test. If the test statistic is continuous, it will reach the significance level ...
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 ...
With large samples, a chi-squared test (or better yet, a G-test) can be used in this situation. However, the significance value it provides is only an approximation, because the sampling distribution of the test statistic that is calculated is only approximately equal to the theoretical chi-squared distribution. The approximation is poor when ...
This is not necessarily the case – the key restriction, as per Fisher (1966), is that "the null hypothesis must be exact, that is free from vagueness and ambiguity, because it must supply the basis of the 'problem of distribution', of which the test of significance is the solution."
The difference between the two sample means, each denoted by X i, which appears in the numerator for all the two-sample testing approaches discussed above, is ¯ ¯ = The sample standard deviations for the two samples are approximately 0.05 and 0.11, respectively. For such small samples, a test of equality between the two population variances ...