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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.
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]
Yield is usually stated as percentage per fission, so that the total yield percentages sum to 200%. Less often, it is stated as percentage of all fission products, so that the percentages sum to 100%. Ternary fission, about 0.2–0.4% of fissions, also produces a third light nucleus such as helium-4 (90%) or tritium (7%).
The test statistic is approximately F-distributed with and degrees of freedom, and hence is the significance of the outcome of tested against (;,) where is a quantile of the F-distribution, with and degrees of freedom, and is the chosen level of significance (usually 0.05 or 0.01).
The F-test in ANOVA is an example of an omnibus test, which tests the overall significance of the model. A significant F test means that among the tested means, at least two of the means are significantly different, but this result doesn't specify exactly which means are different one from the other.
Example: To find 0.69, one would look down the rows to find 0.6 and then across the columns to 0.09 which would yield a probability of 0.25490 for a cumulative from mean table or 0.75490 from a cumulative table. To find a negative value such as –0.83, one could use a cumulative table for negative z-values [3] which yield a probability of 0.20327.
The p-value for the permutation test is the proportion of the r values generated in step (2) that are larger than the Pearson correlation coefficient that was calculated from the original data. Here "larger" can mean either that the value is larger in magnitude, or larger in signed value, depending on whether a two-sided or one-sided test is ...
Developed in 1940 by John W. Mauchly, [3] Mauchly's test of sphericity is a popular test to evaluate whether the sphericity assumption has been violated. The null hypothesis of sphericity and alternative hypothesis of non-sphericity in the above example can be mathematically written in terms of difference scores.