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================================================================================

R version: R version 3.6.1 (2019-07-05)
RJafroc version: 1.2.0
Run date: Jul 29 2019 Mon 09:19:48 EDT
 FOM selected         :     Wilcoxon
 Input  Data          :     dataset
 Output Data Filename :     ./goodValues361/OutputReport/dataset02WilcoxonDBMH.txt

================================================================================

 Significance testing method:  DBM-MRMC-HILLIS SIGNIFICANCE TESTING: MyDataDescription: 
 Number of Readers          :  5
 Number of Treatments       :  2
 Number of Normal Cases     :  69
 Number of Abnormal Cases   :  45
 Fraction of Normal Cases   :  0.605263

================================================================================

 Modality IDs in the input file are:  0, 1

 Modality IDs in the output file are: 0, 1

 Reader IDs in the input file are:    0, 1, 2, 3, 4

 Reader IDs in the output file are:   0, 1, 2, 3, 4

================================================================================

 ====================================================================
 *****                        Overview                          *****
 ====================================================================
 Three analyses are presented: 
 (1) Analysis 1 treats both readers and cases as random samples
     --results apply to the reader and case populations;
 (2) Analysis 2 treats only cases as a random sample
     --results apply to the population of cases but only for the
     readers used in this study; and
 (3) Analysis 3 treats only readers as a random sample
     --results apply to the population of readers but only for the
     cases used in this study.

 For all three analyses, the null hypothesis of equal treatments is
 tested in part (a), treatment difference 95% confidence intervals
 are given in part (b), and treatment 95% confidence intervals are
 given in part (c).  Parts (a) and (b) are based on the treatment x
 reader x case ANOVA while part (c) is based on the reader x case
 ANOVA for the specified treatment; these ANOVA tables are displayed
 before the analyses.  Different error terms are used as indicated
 for parts (a), (b), and (c) according to whether readers and cases
 are treated as fixed or random factors.  Note that the treatment
 confidence intervals in part (c) are based only on the data for the
 specified treatment, rather than the pooled data.  Treatment
 difference 95% confidence intervals for each reader are presented
 in part (d) of Analysis 2; each interval is based on the treatment
 x case ANOVA table (not included) for the specified reader.

 ===========================================================================
 *****                            Estimates                            *****
 ===========================================================================

                        TREATMENT
              -----------------------
  READER      0            1         
----------    ----------   ----------
0             0.91964573   0.94782609
1             0.85877617   0.90531401
2             0.90386473   0.92173913
3             0.97310789   0.99935588
4             0.82979066   0.92995169


 TREATMENT MEANS (averaged across readers)
----------    -----------------------------
0             0.89703704
1             0.94083736



 TREATMENT MEAN DIFFERENCES
----------   ----------    -----------
0          - 1             -0.04380032




 ===========================================================================
 *****                          ANOVA Tables                           *****
 ===========================================================================

 TREATMENT X READER X CASE ANOVA

Source            SS               DF             MS        
------   --------------------    ------   ------------------
     T             0.54676344         1           0.54676344
     R             1.74930720         4           0.43732680
     C            44.84629692       113           0.39686988
    TR             0.25126996         4           0.06281749
    TC            11.28283352       113           0.09984808
    RC            29.15447929       452           0.06450106
   TRC            18.06716464       452           0.03997160
 Total           105.89811497      1139



 TREATMENT X READER X CASE ANOVA



                        Mean Squares
 Source     df   0            1         
 ------    ---   ----------   ----------   
      R      4   0.35141967   0.14872462
      C    113   0.33629430   0.16042367
     RC    452   0.06043607   0.04403659
 ===========================================================================
 *****                  Variance Components Estimates                  *****
 ===========================================================================

 DBM variance component and covariance estimates

     DBM Component             Estimate    
 -----------------------  ----------------
 Var(R)                        0.00153500
 Var(C)                        0.02724923
 Var(T*R)                      0.00020040
 Var(T*C)                      0.01197530
 Var(R*C)                      0.01226473
 Var(Error)                    0.03997160


 ===========================================================================
 *****           Analysis 1: Random Readers and Random Cases           *****
 ===========================================================================


 (Results apply to the population of readers and cases)


    a) Test for H0: Treatments have the same Wilcoxon figure of merit.


 Source        DF    Mean Square      F value  Pr > F 
 ----------  ------  ---------------  -------  -------
 Treatment        1       0.54676344     4.46   0.0517
 Error        15.26       0.12269397
 Error term: MS(TR) + max[MS(TC) - MS(TRC), 0]

 Conclusion: The Wilcoxon FOMs of treatments are not significantly different,
             F(1,15.26) = 4.46, p = 0.0517.


    b) 95% confidence intervals for treatment differences

       Treatment         Estimate   StdErr      DF      t     Pr > t          95% CI      
----------   ----------  --------  --------  -------  ------  -------  -------------------
0          - 1           -0.04380   0.02075    15.26   -2.11   0.0517  -0.08796 ,  0.00036



 H0: the two treatments are equal.
 Error term: MS(TR) + max[MS(TC) - MS(TRC), 0]


    c) 95% treatment confidence intervals based on reader x case ANOVAs
       for each treatment (each analysis is based only on data for the
       specified treatment

  Treatment     Area      Std Error     DF     95% Confidence Interval 
  ----------  ----------  ----------  -------  -------------------------
  0           0.89703704  0.03317360    12.74  (0.82522360 , 0.96885048)
  1           0.94083736  0.02156637    12.71  (0.89413783 , 0.98753689)
 Error term: MS(R) + max[MS(C) - MS(RC), 0]



 ===========================================================================
 *****           Analysis 2: Fixed Readers and Random Cases            *****
 ===========================================================================


 (Results apply to the population of cases but only for the readers
 used in this study)


    a) Test for H0: Treatments have the same Wilcoxon figure of merit.


 Source        DF    Mean Square      F value  Pr > F 
 ----------  ------  ---------------  -------  -------
 Treatment        1       0.54676344     5.48   0.0210
 Error       113.00       0.09984808
  Error term: MS(TC)

 Conclusion: The Wilcoxon FOMs of treatments are not equal,
             F(1,113.00) = 5.48, p = 0.0210.


    b) 95% confidence intervals for treatment differences

       Treatment         Estimate   StdErr      DF      t     Pr > t          95% CI      
----------   ----------  --------  --------  -------  ------  -------  -------------------
0          - 1           -0.04380   0.01872   113.00   -2.34   0.0210  -0.08088 , -0.00672



 H0: the two treatments are equal.
 Error term: MS(TC) 


    c) 95% treatment confidence intervals based on reader x case ANOVAs
       for each treatment (each analysis is based only on data for the
       specified treatment

  Treatment     Area      Std Error     DF     95% Confidence Interval 
  ----------  ----------  ----------  -------  -------------------------
  0           0.89703704  0.02428971   113.00  (0.84891474 , 0.94515933)
  1           0.94083736  0.01677632   113.00  (0.90760044 , 0.97407428)
 Error term: MS(C) 



 TREATMENT X CASE ANOVAs for each reader


                        Sum of Squares
 Source     df   0             1             2             3             4             
 ------    ---   -----------   -----------   -----------   -----------   -----------   
      T      1     0.0452655     0.1234489     0.0182112     0.0392705     0.5718372   
      C    113    13.8142273    24.0405509    15.4283316     1.9536987    18.7639677   
     TC    113     4.1922466     4.4557943     6.2738049     1.9257860    12.5023663   



                        Mean Squares
 Source     df   0             1             2             3             4             
 ------    ---   -----------   -----------   -----------   -----------   -----------   
      T      1     0.0452655     0.1234489     0.0182112     0.0392705     0.5718372   
      C    113     0.1222498     0.2127482     0.1365339     0.0172894     0.1660528   
     TC    113     0.0370995     0.0394318     0.0555204     0.0170424     0.1106404   





    d) Treatment-by-case ANOVA CIs for each reader 
       (each analysis is based only on data for the specified reader)

  Reader         Treatment        Estimate  StdErr       DF      t     Pr > t          95% CI      
---------- ---------- ----------  --------  --------  -------  ------  -------  -------------------
0          0         -1           -0.02818   0.02551   113.00   -1.10   0.2717  -0.07872 ,  0.02236
1          0         -1           -0.04654   0.02630   113.00   -1.77   0.0795  -0.09865 ,  0.00557
2          0         -1           -0.01787   0.03121   113.00   -0.57   0.5680  -0.07971 ,  0.04396
3          0         -1           -0.02625   0.01729   113.00   -1.52   0.1318  -0.06051 ,  0.00801
4          0         -1           -0.10016   0.04406   113.00   -2.27   0.0249  -0.18745 , -0.01288



 ===========================================================================
 *****           Analysis 3: Random Readers and Fixed Cases            *****
 ===========================================================================
 (Results apply to the population of readers but only for the cases used in this study)


    a) Test for H0: Treatments have the same Wilcoxon figure of merit.


 Source        DF    Mean Square      F value  Pr > F 
 ----------  ------  ---------------  -------  -------
 Treatment        1       0.54676344     8.70   0.0420
 Error         4.00       0.06281749
 Error term: MS(TR)

 Conclusion: The Wilcoxon FOMs of treatments are not equal,
             F(1,4.00) = 8.70, p = 0.0420.


    b) 95% confidence intervals for treatment differences

       Treatment         Estimate   StdErr      DF      t     Pr > t          95% CI      
----------   ----------  --------  --------  -------  ------  -------  -------------------
0          - 1           -0.04380   0.01485     4.00   -2.95   0.0420  -0.08502 , -0.00258



 H0: the two treatments are equal.



    c) Reader-by-case ANOVAs for each treatment (each analysis is based only on data for the
       specified treatment

  Treatment     Area      Std Error     DF     95% Confidence Interval 
  ----------  ----------  ----------  -------  -------------------------
  0           0.89703704  0.02482994     4.00  (0.82809808 , 0.96597599)
  1           0.94083736  0.01615303     4.00  (0.89598936 , 0.98568536)
