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In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
Just as extreme values of the normal distribution have low probability (and give small p-values), extreme values of the chi-squared distribution have low probability. An additional reason that the chi-squared distribution is widely used is that it turns up as the large sample distribution of generalized likelihood ratio tests (LRT). [8]
In 2016, the American Statistical Association (ASA) published a statement on p-values, saying that "the widespread use of 'statistical significance' (generally interpreted as 'p ≤ 0.05') as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process". [57]
The p-value does not indicate the size or importance of the observed effect. [2] A small p -value can be observed for an effect that is not meaningful or important. In fact, the larger the sample size, the smaller the minimum effect needed to produce a statistically significant p -value (see effect size ).
The weighted harmonic mean of p-values , …, is defined as = = = /, where , …, are weights that must sum to one, i.e. = =.Equal weights may be chosen, in which case = /.. In general, interpreting the HMP directly as a p-value is anti-conservative, meaning that the false positive rate is higher than expected.
A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio ...
If the resulting p-value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with equal variances. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference ...
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of one parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size ...