Quantitative Results

Statistical Analysis

An F-test is conducted by the researcher on the basis of the F statistic. The F statistic is defined as the ratio between the two independent chi square variates that are divided by their respective degree of freedom. The F-test follows the Snedecor’s F- distribution.

The F-test contains some applications that are used in statistical theory. This document will detail the applications.

The F-test is used by a researcher in order to carry out the test for the equality of the two population variances. If a researcher wants to test whether or not two independent samples have been drawn from a normal population with the same variability, then he generally employs the F-test.

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The F-test is also used by the researcher to determine whether or not the two independent estimates of the population variances are homogeneous in nature.

An example depicting the above case in which the F-test is applied is, for example, if two sets of pumpkins are grown under two different experimental conditions. 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 an F-test to test the hypothesis on whether or not the true variances are equal.

The researcher uses the F-test to test the significance of an observed multiple correlation coefficient. It is also used by the researcher to test the significance of an observed sample correlation ratio. The sample correlation ratio is defined as a measure of association as the statistical dispersion in the categories within the sample as a whole. Its significance is tested by the researcher.

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, the F-test has many properties, like chi square. The F-values are all non negative. The F-distribution in the F-test is always non-symmetrically distributed. 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 draw out an inference about the data that is drawn from a particular population. The F-test 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, the F-test 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.