# mrcImageVarianceAnalysis

## Usage

    Usage: mrcImageVarianceAnalysis
    Options:
        [-i[nput]            In                  (NULL      )] :Optional  :In: InputList
        [-r[ef]              Ref                 (NULL      )] :Optional  :Ref: InputList
        [-o[utput]           Out                 (NULL      )] :Optional  :Output: Variance Probability
        [-v[arianceAnalysis] OutV                (NULL      )] :Optional  :Output: Variance Analysis
        [-c[onfig]           configFile          (NULL      )] :Optional  :ConfigurationFile
        [-m[ode]             mode                (0         )] :Optional  :Mode
    ----- Additional Usage -----
    -i inFileList
    >>>>> Within inFileList
    In1
    In2
    ...
    >>>>> Within In1 etc. A + B*density
    filename1-1 A B
    .....
    ---- Variance Analysis-----
    -- Algorithm
       VarianceRatio := VarinceBetweenClasses/(SumOfVarianceWithinEachClass)
                      VarinceBetweenClasses: variance between classes
                      VarinceWithClasses:    variance within each class

       ---- General Information -----
       Kai-distribution: Kai^2 = SumOf (Xi - AvgOfXi)^2/sigma^2
                               = s^2*(n-1)/sigma^2  : degree of freedom n-1
                                 when variables Xi are due to N(u, sigma^2)
       Kai-distribution: Kai^2 = Kai1^2 + Kai2^2 : degree of freedom m1 + m2
       F-distribution: F = (Kai1^2/k1)/(Kai2^2/k2)           : degree of freedom : (k1, k2)
                           (s1^2/sigma1^2)/(s2^2/sigma2^2)   : degree of freedom : (k1-1, k2-1)
       If sigma1 == sigma2, then
                           s1^2/s2^2  (Variance Ratio)       : degree of freedom : (k1-1, k2-1)