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The 0.05 significance level is merely a convention. [3] [5] The 0.05 significance level (alpha level) is often used as the boundary between a statistically significant and a statistically non-significant p-value. However, this does not imply that there is generally a scientific reason to consider results on opposite sides of any threshold as ...
In a significance test, the null hypothesis is rejected if the p-value is less than or equal to a predefined threshold value , which is referred to as the alpha level or significance level. α {\displaystyle \alpha } is not derived from the data, but rather is set by the researcher before examining the data.
More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; [4] and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. [5]
The false positive rate is = +. where is the number of false positives, is the number of true negatives and = + is the total number of ground truth negatives.. The significance level used to test each hypothesis is set based on the form of inference (simultaneous inference vs. selective inference) and its supporting criteria (for example FWER or FDR), that were pre-determined by the researcher.
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 ...
Approximate formula for median (from the Wilson–Hilferty transformation) compared with numerical quantile (top); and difference (blue) and relative difference (red) between numerical quantile and approximate formula (bottom). For the chi-squared distribution, only the positive integer numbers of degrees of freedom (circles) are meaningful.
The new multiple range test proposed by Duncan makes use of special protection levels based upon degrees of freedom.Let , = be the protection level for testing the significance of a difference between two means; that is, the probability that a significant difference between two means will not be found if the population means are equal.
Meaning that controlling the FDR can be very permissive (if the data justify it), or conservative (acting close to control of FWER for sparse problem) - all depending on the number of hypotheses tested and the level of significance.