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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.
To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true. [5] [12] The null hypothesis is rejected if the p-value is less than (or equal to) a predetermined level, .
[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 qualitatively different. [3] [6]
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 ...
A statistical significance test starts with a random sample from a population. If the sample data are consistent with the null hypothesis, then you do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then you reject the null hypothesis and conclude that the alternative hypothesis is true. [3]
Once the t value and degrees of freedom are determined, a p-value can be found using a table of values from Student's t-distribution. If the calculated p-value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.
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.
"The value for which P = .05, or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation is to be considered significant or not." [11] In Table 1 of the same work, he gave the more precise value 1.959964. [12] In 1970, the value truncated to 20 decimal places was calculated to be