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The F table serves as a reference guide containing critical F values for the distribution of the F-statistic under the assumption of a true null hypothesis. It is designed to help determine the threshold beyond which the F statistic is expected to exceed a controlled percentage of the time (e.g., 5%) when the null hypothesis is accurate.
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
The p-value was first formally introduced by Karl Pearson, in his Pearson's chi-squared test, [39] using the chi-squared distribution and notated as capital P. [39] The p-values for the chi-squared distribution (for various values of χ 2 and degrees of freedom), now notated as P, were calculated in (Elderton 1902), collected in (Pearson 1914 ...
After computing the F-statistic, we compare the value at the intersection of each degrees of freedom, also known as the critical value. If one's F-statistic is greater in magnitude than their critical value, we can say there is statistical significance at the 0.05 alpha level. The F-test is used for comparing the factors of the total deviation ...
The critical value is the number that the test statistic must exceed to reject the test. In this case, F crit (2,15) = 3.68 at α = 0.05. Since F=9.3 > 3.68, the results are significant at the 5% significance level. One would not accept the null hypothesis, concluding that there is strong evidence that the expected values in the three groups ...
Thus an approximate p-value can be obtained from a normal probability table. For example, if z = 2.2 is observed and a two-sided p-value is desired to test the null hypothesis that =, the p-value is 2 Φ(−2.2) = 0.028, where Φ is the standard normal cumulative distribution function.
In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests.
The p-value is the probability that a test statistic which is at least as extreme as the one obtained would occur under the null hypothesis. At a significance level of 0.05, a fair coin would be expected to (incorrectly) reject the null hypothesis (that it is fair) in 1 out of 20 tests on average.