ANOVA is a test use to measure the significance of the difference in the means of various groups. The F distribution is a significant test in ANOVA. The significance of the F distribution is brought about by the basic assumption made by an analyst when performing ANOVA. The principle assumption is that the populations have equal variances. The F distribution helps the analyst test the assumption (Goos & Meintrup, 2016).
This is because during the calculation of the F ratio, the computation process also gives the result of the estimate of variance. One of the estimates of variance yielded through the computation of the F ratio is the variance between the samples (Goos & Meintrup, 2016). The variance between the samples entails the variance between the means of various group means. The other estimate of the variance that is the product of the computation of the F ratio is the variance within the sample. This value is the mean of the variance of the samples (Goos & Meintrup, 2016).
The F distribution is a significant test in the analysis of variance because it considers the variance within and between the samples. This action means that two sums of squares are generated through scaled chi-square distributions (Goos & Meintrup, 2016). The effect is that there is an increase in the testing power for variance compared to other tests for the analysis of variance. The F distribution achieves a minimized of the number of false negative errors when the rate of occurrence of false positive errors is kept at a constant (Goos & Meintrup, 2016).
This means that the test of the hypotheses for the significance of variance between different samples is robust when the F-test for the analysis of variance is employed (Goos & Meintrup, 2016). The maximum test power highlighted above ensure that against many alternative hypotheses, the F-test, through the close approximation of the permutations of the p-values of the F-test of the samples gives the analyst the best possible outcome considering all the possible hypotheses (Goos & Meintrup, 2016).
Conducting a linear regression takes into account several assumptions that are critical to developing a correct outcome. One of the assumptions that a basic to a linear regression are that for every value or X, all the values of Y are distributed normally (Montgomery, 2011). The precise meaning of this assumption is that for every value of X, all the values of Y are found on the line of regression, that there is not scatter in the values of Y away from the line of linear regression. The assumption that the dependent and independent variables in a linear regression have a linear relationship highlights the effect of outliers on the outcome and accuracy of the linear regression (Montgomery, 2011).
The second assumption that the normal distributions of the values of Y for every value of X have equal standard deviations. This means that there is almost not multicollinearity of the independent variable. This is a situation that occurs when the independent variables in the selection of a sample are dependent on the previous value of X (Montgomery, 2011).The assumption of a multivariate normality is checked using histograms, or goodness of fit tests. If the testing of this assumption is not done and fixed, the issued causes multicollinearity and its issues which then affects the outcome and accuracy of the linear regression (Montgomery, 2011).
Another assumption that is basic to linear regressions is that the values of Y in the sample are statistically independent of each other (Montgomery, 2011). The meaning of this assumption is that when selecting a sample of subjects, the values of Y that are chosen for a given value of X are not dependent on the values of Y for other values of X in the selection. This implies that the values of X and the corresponding values of Y are not influenced by the selection of other values (Montgomery, 2011).
References
Goos, P., & Meintrup, D. (2016). Statistics with JMP: Hypothesis tests, ANOVA, and regression. Chichester, West Sussex. John Wiley & Sons.
Montgomery, D. C. (2011). Introduction to linear regression analysis. Oxford: Wiley-Blackwell.
