anchor.diff:  (**
   <a name = "FTest"></a>
   ##F-Test
  -The F-test is a method to determine if the variances of two samples are homogeneous. 
  -Also, ANOVA (analysis of variance) is based on the F-test and is used for the comparison of more than two samples.  
  -ANOVA can detect if there is a difference in variances between samples, without pre-specifying which samples should be compared. 
  -Knowing if your variances are equal (H<sub>0</sub> is true) helps to decide which test should be done next. 
  +The F-test is a method to determine if the variances of two samples are homogeneous.
  +Also, ANOVA (analysis of variance) is based on the F-test and is used for the comparison of more than two samples.
  +Knowing if your variances are equal (H<sub>0</sub> is true) helps to decide which test should be performed next.
   To determine if your variances are in fact equal you can perform a F-test. 
   
  -Prerequisite : 
  -
  -  -   samples are normally distributed 
  +Prerequisites: 
  +
  +  -   population distributions are normally distributed 
   
     -   samples are independent
   
  -Possible further tests :
  +Possible further tests:
   
     -   two sample t-test with equal variances
   
  
positive.code: // sample properties are given as (variance,degree of freedom) 
  let sampleF1 = (0.1, 15.)
  let sampleF2 = (0.05, 7.)
  // comparison of sample variances 
  let fTestFromParameters = FTest.testVariancesFromVarAndDof sampleF1 sampleF2
  (*
  
negative.code:   -   ...
  
  Note that there is no information about the direction of variance difference.
  In this implemented test the larger variance is always the numerator, therefore the comparison to F<sub>df1,df2,1-(alpha/2)</sub> is used for a two sided test. 
  
  _Important note: The effectiveness of a preliminary test of variances is discussed. 
  The F-test is extremely sensitive to normality-violations, and even if the samples follow a normal distribution, it often does not detect situations where a t-test should be avoided. 
  Conditions for the Effectiveness of a Preliminary Test of Variance , C. and E. Markowski, The American Statistician, Vol 44. No. 4, 11/1990_
  
  References:
  
    - Jürgen Bortz & Christof Schuster, Statistik für Human- und Sozialwissenschaftler (2010) Chapter 8.6
  
    - Ronald Ley, F curves have two tails but the F test is a one-tailed two-tailed test (1979)
    
  *F-Test from data*
  *)
  
  let sampleFA = vector [|5.0; 6.0; 5.8; 5.7|] 
  let sampleFB = vector [|3.5; 3.7; 4.0; 3.3; 3.6|]
  
  // comparison of sample variances 
  let fTestFromData = FTest.testVariances sampleFA sampleFB
  (* 
      { Statistic = 2.823383085
      DegreesOfFreedom1 = 3.0
      DegreesOfFreedom2 = 4.0
      PValue = 0.1708599931 }
      Using a significance level of 0.05 the sample variances do differ significantly.
  *)
  (** 
  *F-Test from given parameters*
  