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The term significance does not imply importance here, and the term statistical significance is not the same as research significance, theoretical significance, or practical significance. [ 1 ] [ 2 ] [ 18 ] [ 19 ] For example, the term clinical significance refers to the practical importance of a treatment effect.
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.
Suppose the data can be realized from an N(0,1) distribution. For example, with a chosen significance level α = 0.05, from the Z-table, a one-tailed critical value of approximately 1.645 can be obtained. The one-tailed critical value C α ≈ 1.645 corresponds to the chosen significance level.
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
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 ...
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 ...
For example, assume that one were to test 1,000 null hypotheses, all of which are true, and (as is conventional in single hypothesis testing) to reject null hypotheses with a significance level of 0.05; due to random chance, one would expect 5% of the results to appear significant (P < 0.05), yielding 50 false positives (rejections of the null ...
A significance level of 0.05 is often used as the cutoff between significant and non-significant results. The table below gives a number of p -values matching to χ 2 {\displaystyle \chi ^{2}} for the first 10 degrees of freedom.