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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 09:19:51 EDT
 FOM selected         :     HrAuc
 Input  Data          :     dataset
 Output Data Filename :     ./goodValues361/OutputReport/dataset05HrAucORH.txt

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

 Significance testing method:  OBUCHOWSKI-ROCKETTE-HILLIS SIGNIFICANCE TESTING: MyDataDescription: 
 Number of Readers          :  9
 Number of Treatments       :  2
 Number of Normal Cases     :  45
 Number of Abnormal Cases   :  47
 Fraction of Normal Cases   :  0.489130
 Min number of lesions per diseased case   :  1
 Max number of lesions per diseased case   :  3
 Mean number of lesions per diseased case  :  1.255319
 Total number of lesions                   :  59
 Inc. Loc. Frac.          :  0.161348


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

 Avg. number of non-lesion localization marks per reader on non-diseased cases: 0.509877
 Avg. number of non-lesion localization marks per reader on diseased cases:  0.382979
 Avg. number of lesion localization marks per reader :  0.997636


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

 Modality IDs in the input file are:  1, 2

 Modality IDs in the output file are: 1, 2

 Reader IDs in the input file are:    1, 2, 3, 4, 5, 6, 7, 8, 9

 Reader IDs in the output file are:   1, 2, 3, 4, 5, 6, 7, 8, 9

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

 ====================================================================
 *****                        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      1            2         
----------    ----------   ----------
1             0.85886525   0.89148936
2             0.89314421   0.97612293
3             0.88226950   0.88274232
4             0.73026005   0.84822695
5             0.71418440   0.83995272
6             0.92907801   0.90898345
7             0.91891253   0.95248227
8             0.87919622   0.93380615
9             0.81442080   0.85697400


 TREATMENT MEANS (averaged across readers)
----------    -----------------------------
1             0.84670344
2             0.89897557



 TREATMENT MEAN DIFFERENCES
----------   ----------    -----------
1          - 2             -0.05227213




 ===========================================================================
 *****                  Variance Components Estimates                  *****
 ===========================================================================

 Obuchowski-Rockette variance component and covariance estimates

     OR Component             Estimate    
 -----------------------  ----------------
 Var(R)                        0.00221163
 Var(T*R)                     -0.00214704
 COV1                          0.00181425
 COV2                          0.00130213
 COV3                          0.00104824
 Var(Error)                    0.00542869


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


 (Results apply to the population of readers and cases)


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


 Source        DF    Mean Square      F value  Pr > F 
 ----------  ------  ---------------  -------  -------
 Treatment        1       0.01229569     3.51   0.0652
 Error        66.49       0.00121352
 Error term: MS(TR) + J * max[Cov2 - Cov3, 0]

 Conclusion: The HrAuc FOMs of treatments are not significantly different,
             F(1,66.49) = 3.51, p = 0.0652.


    b) 95% confidence intervals for treatment differences

       Treatment         Estimate   StdErr      DF      t     Pr > t          95% CI      
----------   ----------  --------  --------  -------  ------  -------  -------------------
1          - 2           -0.05227   0.02788    66.49   -1.87   0.0652  -0.10793 ,  0.00339



 H0: the two treatments are equal.
 Error term: MS(TR) + J * max[Cov2 - Cov3, 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 
  ----------  ----------  ----------  -------  -------------------------
  1           0.84670344  0.04271446    58.00  (0.76120119 , 0.93220569)
  2           0.89897557  0.04136549   363.74  (0.81763003 , 0.98032111)




 ===========================================================================
 *****           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 HrAuc figure of merit.


 Source        DF    Mean Square      F value  Pr > F 
 ----------  ------  ---------------  -------  -------
 Treatment        1       0.01229569     2.18   0.1400

 Error term: Var - Cov1 + (J - 1) * ( Cov2 - Cov3 )

 Conclusion: The HrAuc FOMs of treatments are not significantly different,
             F(1,Inf) = 2.18, p = 0.1400.


    b) 95% confidence intervals for treatment differences

       Treatment         Estimate   StdErr      DF      t     Pr > t          95% CI      
----------   ----------  --------  --------  -------  ------  -------  -------------------
1          - 2           -0.05227   0.03542      Inf   -1.48   0.1400  -0.12169 ,  0.01715



 H0: the two treatments are equal.
 Error term: Var - Cov1 + (J - 1) * ( Cov2 - Cov3 )

    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 
  ----------  ----------  ----------  -------  -------------------------
  1           0.84670344  0.04109073      Inf  (0.76616709 , 0.92723980)
  2           0.89897557  0.04281153      Inf  (0.81506652 , 0.98288462)
 Error term: Var - Cov1 + (J - 1) * ( Cov2 - Cov3 )

    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      
---------- ---------- ----------  --------  --------  -------  ------  -------  -------------------
1          1         -2           -0.03262   0.12205      Inf   -0.27   0.7892  -0.27184 ,  0.20659
2          1         -2           -0.08298   0.03347      Inf   -2.48   0.0132  -0.14858 , -0.01738
3          1         -2           -0.00047   0.09393      Inf   -0.01   0.9960  -0.18457 ,  0.18362
4          1         -2           -0.11797   0.13336      Inf   -0.88   0.3764  -0.37934 ,  0.14341
5          1         -2           -0.12577   0.08080      Inf   -1.56   0.1196  -0.28414 ,  0.03260
6          1         -2            0.02009   0.05639      Inf    0.36   0.7216  -0.09043 ,  0.13062
7          1         -2           -0.03357   0.03816      Inf   -0.88   0.3791  -0.10837 ,  0.04123
8          1         -2           -0.05461   0.05428      Inf   -1.01   0.3143  -0.16099 ,  0.05177
9          1         -2           -0.04255   0.09124      Inf   -0.47   0.6410  -0.22139 ,  0.13628

Reader  Var(Error)     Cov1   
------  ----------  ----------
1         0.011353    0.003905
2         0.000653    9.301827
3         0.006594    0.002182
4         0.010775    0.001883
5         0.010489    0.007225
6         0.001743    0.000153
7         0.000765    3.716165
8         0.002376    0.000903
9         0.004106    -5.62809



 ===========================================================================
 *****           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 HrAuc figure of merit.


 Source        DF    Mean Square      F value  Pr > F 
 ----------  ------  ---------------  -------  -------
 Treatment        1       0.01229569    10.13   0.0129
 Error         8.00       0.00121352
 Error term: MS(TR)

 Conclusion: The HrAuc FOMs of treatments are not equal,
             F(1,8.00) = 10.13, p = 0.0129.


    b) 95% confidence intervals for treatment differences

       Treatment         Estimate   StdErr      DF      t     Pr > t          95% CI      
----------   ----------  --------  --------  -------  ------  -------  -------------------
1          - 2           -0.05227   0.01642     8.00   -3.18   0.0129  -0.09014 , -0.01440



 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 
  ----------  ----------  ----------  -------  -------------------------
  1           0.84670344  0.02603087     8.00  (0.78667616 , 0.90673073)
  2           0.89897557  0.01592989     8.00  (0.86224118 , 0.93570997)
