F-test
The researcher conducts an F-test based on the F statistic. The F statistic is the ratio of two independent chi-square variates, each divided by its respective degrees of freedom. The F-test follows the Snedecor’s F- distribution.
The F-test has several applications in statistical theory. This document will detail the applications.
A researcher uses the F-test to test the equality of two population variances. A researcher generally employs the F-test to test whether two independent samples come from a normal population with the same variability.
The researcher also uses the F-test to determine whether two independent estimates of the population variances are homogeneous.
An example of applying it is when a researcher grows two sets of pumpkins under different experimental conditions to test if their population variances are equal. In this case, the researcher would select a random sample of size 9 and 11. The standard deviations of their weights are 0.6 and 0.8 respectively. After making an assumption that the distribution of their weights is normal, the researcher conducts it to test the hypothesis on whether or not the true variances are equal.
The researcher uses it to test the significance of an observed multiple correlation coefficient. The researcher also uses it to test the significance of an observed sample correlation ratio. The sample correlation ratio measures association by assessing the statistical dispersion within the categories of the sample as a whole. The researcher tests its significance.
The researcher should note that there is some association between the t and F distributions of the F-test. According to this association, if a statistic t follows a student’s t distribution with ‘n’ degrees of freedom, then the square of this statistic will follow Snedecor’s F distribution with 1 and n degrees of freedom.
The F-test also has some other associations, like the association between the it and chi square distribution.
Due to such relationships, it has many properties, like chi square. The F-values are all non negative. The F-distribution in the F-test is always non-symmetrical. The mean in F-distribution in the F-test is approximately one. There are two independent degrees of freedom in F distribution, one in the numerator and the other in the denominator. There are many different F distributions in the F-test, one for every pair of degree of freedom.
The F-test is a parametric test that helps the researcher make inferences about data drawn from a particular population. It is called a parametric test because of the presence of parameters in the F- test. These parameters in the F-test are the mean and variance. The mode of the F-test is the value that is most frequently in a data set and it is always less than unity. According to Karl Pearson’s coefficient of skewness, it is highly positively skewed. The probability distribution of F increases steadily before reaching the peak, and then it starts decreasing in order to become tangential at infinity. Thus, we can say that the axis of F is asymptote to the right tail.