F Distribution, F Statistic, F Test

F table 3

An F-distribution is used to create a ratio of two process or sample variances.

  • The ratio between two sample variances
  • A measure of variances.
  • Used to test hypothesis about 2 population variances
  • Used to test hypotheses about the equality of population variances based on sample variances
  • Assumes both populations are normally distributed.
  • The larger sample variance always goes in the numerator.
  • Percent confident of less variation.
  • Does this process or machine have more or less variation than the other?

F Statistic

F-statistics are always positive. The F statistic is NEVER negative.

An F statistic is the ratio of the Mean Square for Treatment or Between Groups with the Mean Square for Error or Within Groups.

If the calculated F statistic is greater than the appropriate value of the critical F (found in a table or provided in software), then the null hypothesis is rejected. (helpful in ANOVA)

The calculated F-statistic for a known source of variation is found by dividing the mean square of the known source of variation by the mean square of the unknown source of variation.

I’m taking Unknown to be the variance between sets and known to be within the set.

F = MS Between / MS Within


F Test

F-test – compares the population variances using samples from each.

F test – testing significance in ANOVA


http://people.richland.edu/james/lecture/m170/ch13-f.html (F distribution)



F Test Sample Questions

At a manufacturing facility 2 Six Sigma Greenbelts are arguing over the variances of a critical characteristic measured on a part that is run on 2 different stamping presses they have been monitoring; each press runs the same progressive die. Student A says that he is 90% confident that the stamping presses have the same variance, while student B says at the 90% confidence level the variances are different. Which student is right? Press1: s = 0.035, n = 16 ; Press 2: s = 0.057, n = 10

F table 2 - 1 F table 2





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