Level of Significance of a Test: the F Test Statistic


INSTRUCTIONS

Once the applet has finished loading, a "Lab-value" buttonwill appear on the screen. This may take a minute or two depending on the speed of your internet connection and computer. Please be patient. If no begin button appears, it is probably because your browser does not support Java 1.1.




Introduction

For cases in which two population variances are to be compared, the F statistic is commonly used. For the null hypothesis Ho: sigma1 square/ sigma2 square = 1, the test of statistic given by

                          F = s1 square/s2 square

has an F(n1-1,n2-1) distribution. The assumptions that must be satisfied are that the distributions of the two independent populations belong to the normal family and the samples are chosen randomly and independently of one another.

There will be a table show the comparation from the percentiles of the theoretical normal distribution to the histogram. The first column of numbers (which includes 2.5, 5.0..., 97.5) are areas to the left of the numbers in the second column for the theoretical(standard F(n1-1,n2-1)) distribution. The third column of numbers are percentiles from the histogram. The numbers in the fourth column are the areas from the histogram to the left of the percentiles in the second column.