Case Study for a Credit Scorecard Analysis

Open Live Script

This example shows how to create a creditscorecard object, bin data, display, and plot binned data information. This example also shows how to fit a logistic regression model, obtain a score for the scorecard model, and determine the probabilities of default and validate the credit scorecard model using three different metrics.

Step 1. Create a creditscorecard object.

Use the CreditCardData.mat file to load the data (using a dataset from Refaat 2011). If your data contains many predictors, you can first use screenpredictors (Risk Management Toolbox) from Risk Management Toolbox™ to pare down a potentially large set of predictors to a subset that is most predictive of the credit scorecard response variable. You can then use this subset of predictors when creating the creditscorecard object.

When creating a creditscorecard object, by default, 'ResponseVar' is set to the last column in the data ('status' in this example) and the 'GoodLabel' to the response value with the highest count (0 in this example). The syntax for creditscorecard indicates that 'CustID' is the 'IDVar' to remove from the list of predictors. Also, while not demonstrated in this example, when creating a creditscorecard object using creditscorecard, you can use the optional name-value pair argument 'WeightsVar' to specify observation (sample) weights or 'BinMissingData' to bin missing data.

load CreditCardData
head(data)

ans=8×11 table
    CustID    CustAge    TmAtAddress    ResStatus     EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance    UtilRate    status
    ______    _______    ___________    __________    _________    __________    _______    _______    _________    ________    ______

      1         53           62         Tenant        Unknown        50000         55         Yes       1055.9        0.22        0   
      2         61           22         Home Owner    Employed       52000         25         Yes       1161.6        0.24        0   
      3         47           30         Tenant        Employed       37000         61         No        877.23        0.29        0   
      4         50           75         Home Owner    Employed       53000         20         Yes       157.37        0.08        0   
      5         68           56         Home Owner    Employed       53000         14         Yes       561.84        0.11        0   
      6         65           13         Home Owner    Employed       48000         59         Yes       968.18        0.15        0   
      7         34           32         Home Owner    Unknown        32000         26         Yes       717.82        0.02        1   
      8         50           57         Other         Employed       51000         33         No        3041.2        0.13        0

The variables in CreditCardData are customer ID, customer age, time at current address, residential status, employment status, customer income, time with bank, other credit card, average monthly balance, utilization rate, and the default status (response).

sc = creditscorecard(data,'IDVar','CustID')

sc = 
  creditscorecard with properties:

                GoodLabel: 0
              ResponseVar: 'status'
               WeightsVar: ''
                 VarNames: {1x11 cell}
        NumericPredictors: {1x6 cell}
    CategoricalPredictors: {'ResStatus'  'EmpStatus'  'OtherCC'}
           BinMissingData: 0
                    IDVar: 'CustID'
            PredictorVars: {1x9 cell}
                     Data: [1200x11 table]

Perform some initial data exploration. Inquire about predictor statistics for the categorical variable 'ResStatus' and plot the bin information for 'ResStatus'.

bininfo(sc,'ResStatus')

ans=4×6 table
         Bin          Good    Bad     Odds        WOE       InfoValue
    ______________    ____    ___    ______    _________    _________

    {'Home Owner'}    365     177    2.0621     0.019329    0.0001682
    {'Tenant'    }    307     167    1.8383    -0.095564    0.0036638
    {'Other'     }    131      53    2.4717      0.20049    0.0059418
    {'Totals'    }    803     397    2.0227          NaN    0.0097738

plotbins(sc,'ResStatus')

Figure contains an axes. The axes with title ResStatus contains 3 objects of type bar, line. These objects represent Good, Bad.

This bin information contains the frequencies of “Good” and “Bad,” and bin statistics. Avoid having bins with frequencies of zero because they lead to infinite or undefined (NaN) statistics. Use the modifybins or autobinning functions to bin the data accordingly.

For numeric data, a common first step is "fine classing." This means binning the data into several bins, defined with a regular grid. To illustrate this point, use the predictor 'CustIncome'.

cp = 20000:5000:60000;

sc = modifybins(sc,'CustIncome','CutPoints',cp);

bininfo(sc,'CustIncome')

ans=11×6 table
           Bin           Good    Bad     Odds         WOE       InfoValue 
    _________________    ____    ___    _______    _________    __________

    {'[-Inf,20000)' }      3       5        0.6      -1.2152      0.010765
    {'[20000,25000)'}     23      16     1.4375     -0.34151     0.0039819
    {'[25000,30000)'}     38      47    0.80851     -0.91698      0.065166
    {'[30000,35000)'}    131      75     1.7467     -0.14671      0.003782
    {'[35000,40000)'}    193      98     1.9694    -0.026696    0.00017359
    {'[40000,45000)'}    173      76     2.2763      0.11814     0.0028361
    {'[45000,50000)'}    131      47     2.7872      0.32063      0.014348
    {'[50000,55000)'}     82      24     3.4167      0.52425      0.021842
    {'[55000,60000)'}     21       8      2.625      0.26066     0.0015642
    {'[60000,Inf]'  }      8       1          8        1.375      0.010235
    {'Totals'       }    803     397     2.0227          NaN       0.13469

plotbins(sc,'CustIncome')

Figure contains an axes. The axes with title CustIncome contains 3 objects of type bar, line. These objects represent Good, Bad.

Step 2a. Automatically bin the data.

Use the autobinning function to perform automatic binning for every predictor variable, using the default 'Monotone' algorithm with default algorithm options.

sc = autobinning(sc);

After the automatic binning step, every predictor bin must be reviewed using the bininfo and plotbins functions and fine-tuned. A monotonic, ideally linear trend in the Weight of Evidence (WOE) is desirable for credit scorecards because this translates into linear points for a given predictor. The WOE trends can be visualized using plotbins.

Predictor = 'ResStatus';
plotbins(sc,Predictor)

Figure contains an axes. The axes with title ResStatus contains 3 objects of type bar, line. These objects represent Good, Bad.

Unlike the initial plot of 'ResStatus' when the scorecard was created, the new plot for 'ResStatus' shows an increasing WOE trend. This is because the autobinning function, by default, sorts the order of the categories by increasing odds.

These plots show that the 'Monotone' algorithm does a good job finding monotone WOE trends for this dataset. To complete the binning process, it is necessary to make only a few manual adjustments for some predictors using the modifybins function.

Step 2b. Fine-tune the bins using manual binning.

Common steps to manually modify bins are:

Use the bininfo function with two output arguments where the second argument contains binning rules.
Manually modify the binning rules using the second output argument from bininfo.
Set the updated binning rules with modifybins and then use plotbins or bininfo to review the updated bins.

For example, based on the plot for 'CustAge' in Step 2a, bins number 1 and 2 have similar WOE's as do bins number 5 and 6. To merge these bins using the steps outlined above:

Predictor = 'CustAge';
[bi,cp] = bininfo(sc,Predictor)

bi=8×6 table
         Bin         Good    Bad     Odds        WOE       InfoValue
    _____________    ____    ___    ______    _________    _________

    {'[-Inf,33)'}     70      53    1.3208     -0.42622     0.019746
    {'[33,37)'  }     64      47    1.3617     -0.39568     0.015308
    {'[37,40)'  }     73      47    1.5532     -0.26411    0.0072573
    {'[40,46)'  }    174      94    1.8511    -0.088658     0.001781
    {'[46,48)'  }     61      25      2.44      0.18758    0.0024372
    {'[48,58)'  }    263     105    2.5048      0.21378     0.013476
    {'[58,Inf]' }     98      26    3.7692      0.62245       0.0352
    {'Totals'   }    803     397    2.0227          NaN     0.095205

cp([1 5]) = []; % To merge bins 1 and 2, and bins 5 and 6
sc = modifybins(sc,'CustAge','CutPoints',cp);
plotbins(sc,'CustAge')

Figure contains an axes. The axes with title CustAge contains 3 objects of type bar, line. These objects represent Good, Bad.

For 'CustIncome', based on the plot above, it is best to merge bins 3, 4 and 5 because they have similar WOE's. To merge these bins:

Predictor = 'CustIncome';
[bi,cp] = bininfo(sc,Predictor)

bi=8×6 table
           Bin           Good    Bad     Odds         WOE       InfoValue 
    _________________    ____    ___    _______    _________    __________

    {'[-Inf,29000)' }     53      58    0.91379     -0.79457       0.06364
    {'[29000,33000)'}     74      49     1.5102     -0.29217     0.0091366
    {'[33000,35000)'}     68      36     1.8889     -0.06843    0.00041042
    {'[35000,40000)'}    193      98     1.9694    -0.026696    0.00017359
    {'[40000,42000)'}     68      34          2    -0.011271    1.0819e-05
    {'[42000,47000)'}    164      66     2.4848      0.20579     0.0078175
    {'[47000,Inf]'  }    183      56     3.2679      0.47972      0.041657
    {'Totals'       }    803     397     2.0227          NaN       0.12285

cp([3 4]) = []; % To merge bins 3, 4, and 5
sc = modifybins(sc,'CustIncome','CutPoints',cp);
plotbins(sc,'CustIncome')

Figure contains an axes. The axes with title CustIncome contains 3 objects of type bar, line. These objects represent Good, Bad.

For 'TmWBank', based on the plot above, it is best to merge bins 2 and 3 because they have similar WOE's. To merge these bins:

Predictor = 'TmWBank';
[bi,cp] = bininfo(sc,Predictor)

bi=6×6 table
         Bin         Good    Bad     Odds       WOE       InfoValue
    _____________    ____    ___    ______    ________    _________

    {'[-Inf,12)'}    141      90    1.5667    -0.25547     0.013057
    {'[12,23)'  }    165      93    1.7742    -0.13107    0.0037719
    {'[23,45)'  }    224     125     1.792    -0.12109    0.0043479
    {'[45,71)'  }    177      67    2.6418     0.26704     0.013795
    {'[71,Inf]' }     96      22    4.3636     0.76889     0.049313
    {'Totals'   }    803     397    2.0227         NaN     0.084284

cp(2) = []; % To merge bins 2 and 3
sc = modifybins(sc,'TmWBank','CutPoints',cp);
plotbins(sc,'TmWBank')

Figure contains an axes. The axes with title TmWBank contains 3 objects of type bar, line. These objects represent Good, Bad.

For 'AMBalance', based on the plot above, it is best to merge bins 2 and 3 because they have similar WOE's. To merge these bins:

Predictor = 'AMBalance';
[bi,cp] = bininfo(sc,Predictor)

bi=5×6 table
             Bin             Good    Bad     Odds       WOE       InfoValue
    _____________________    ____    ___    ______    ________    _________

    {'[-Inf,558.88)'    }    346     134    2.5821     0.24418     0.022795
    {'[558.88,1254.28)' }    309     171     1.807    -0.11274    0.0051774
    {'[1254.28,1597.44)'}     76      44    1.7273    -0.15787    0.0025554
    {'[1597.44,Inf]'    }     72      48       1.5    -0.29895    0.0093402
    {'Totals'           }    803     397    2.0227         NaN     0.039868

cp(2) = []; % To merge bins 2 and 3
sc = modifybins(sc,'AMBalance','CutPoints',cp);
plotbins(sc,'AMBalance')

Figure contains an axes. The axes with title AMBalance contains 3 objects of type bar, line. These objects represent Good, Bad.

Now that the binning fine-tuning is completed, the bins for all predictors have close-to-linear WOE trends.

Step 3. Fit a logistic regression model.

The fitmodel function fits a logistic regression model to the WOE data. fitmodel internally bins the training data, transforms it into WOE values, maps the response variable so that 'Good' is 1, and fits a linear logistic regression model. By default, fitmodel uses a stepwise procedure to determine which predictors should be in the model.

sc = fitmodel(sc);

1. Adding CustIncome, Deviance = 1490.8954, Chi2Stat = 32.545914, PValue = 1.1640961e-08
2. Adding TmWBank, Deviance = 1467.3249, Chi2Stat = 23.570535, PValue = 1.2041739e-06
3. Adding AMBalance, Deviance = 1455.858, Chi2Stat = 11.466846, PValue = 0.00070848829
4. Adding EmpStatus, Deviance = 1447.6148, Chi2Stat = 8.2432677, PValue = 0.0040903428
5. Adding CustAge, Deviance = 1442.06, Chi2Stat = 5.5547849, PValue = 0.018430237
6. Adding ResStatus, Deviance = 1437.9435, Chi2Stat = 4.1164321, PValue = 0.042468555
7. Adding OtherCC, Deviance = 1433.7372, Chi2Stat = 4.2063597, PValue = 0.040272676

Generalized linear regression model:
    status ~ [Linear formula with 8 terms in 7 predictors]
    Distribution = Binomial

Estimated Coefficients:
                   Estimate      SE       tStat       pValue  
                   ________    _______    ______    __________

    (Intercept)     0.7024       0.064    10.975    5.0407e-28
    CustAge        0.61562     0.24783    2.4841      0.012988
    ResStatus       1.3776     0.65266    2.1107      0.034799
    EmpStatus      0.88592     0.29296     3.024     0.0024946
    CustIncome     0.69836     0.21715     3.216     0.0013001
    TmWBank          1.106     0.23266    4.7538    1.9958e-06
    OtherCC         1.0933     0.52911    2.0662      0.038806
    AMBalance       1.0437     0.32292    3.2322     0.0012285


1200 observations, 1192 error degrees of freedom
Dispersion: 1
Chi^2-statistic vs. constant model: 89.7, p-value = 1.42e-16

Step 4. Review and format scorecard points.

After fitting the logistic model, by default the points are unscaled and come directly from the combination of WOE values and model coefficients. The displaypoints function summarizes the scorecard points.

p1 = displaypoints(sc);
disp(p1)

      Predictors              Bin              Points  
    ______________    ____________________    _________

    {'CustAge'   }    {'[-Inf,37)'       }     -0.15314
    {'CustAge'   }    {'[37,40)'         }    -0.062247
    {'CustAge'   }    {'[40,46)'         }     0.045763
    {'CustAge'   }    {'[46,58)'         }      0.22888
    {'CustAge'   }    {'[58,Inf]'        }      0.48354
    {'CustAge'   }    {'<missing>'       }          NaN
    {'ResStatus' }    {'Tenant'          }    -0.031302
    {'ResStatus' }    {'Home Owner'      }      0.12697
    {'ResStatus' }    {'Other'           }      0.37652
    {'ResStatus' }    {'<missing>'       }          NaN
    {'EmpStatus' }    {'Unknown'         }    -0.076369
    {'EmpStatus' }    {'Employed'        }      0.31456
    {'EmpStatus' }    {'<missing>'       }          NaN
    {'CustIncome'}    {'[-Inf,29000)'    }     -0.45455
    {'CustIncome'}    {'[29000,33000)'   }      -0.1037
    {'CustIncome'}    {'[33000,42000)'   }     0.077768
    {'CustIncome'}    {'[42000,47000)'   }      0.24406
    {'CustIncome'}    {'[47000,Inf]'     }      0.43536
    {'CustIncome'}    {'<missing>'       }          NaN
    {'TmWBank'   }    {'[-Inf,12)'       }     -0.18221
    {'TmWBank'   }    {'[12,45)'         }    -0.038279
    {'TmWBank'   }    {'[45,71)'         }      0.39569
    {'TmWBank'   }    {'[71,Inf]'        }      0.95074
    {'TmWBank'   }    {'<missing>'       }          NaN
    {'OtherCC'   }    {'No'              }       -0.193
    {'OtherCC'   }    {'Yes'             }      0.15868
    {'OtherCC'   }    {'<missing>'       }          NaN
    {'AMBalance' }    {'[-Inf,558.88)'   }       0.3552
    {'AMBalance' }    {'[558.88,1597.44)'}    -0.026797
    {'AMBalance' }    {'[1597.44,Inf]'   }     -0.21168
    {'AMBalance' }    {'<missing>'       }          NaN

This is a good time to modify the bin labels, if this is something of interest for cosmetic reasons. To do so, use modifybins to change the bin labels.

sc = modifybins(sc,'CustAge','BinLabels',...
{'Up to 36' '37 to 39' '40 to 45' '46 to 57' '58 and up'});

sc = modifybins(sc,'CustIncome','BinLabels',...
{'Up to 28999' '29000 to 32999' '33000 to 41999' '42000 to 46999' '47000 and up'});

sc = modifybins(sc,'TmWBank','BinLabels',...
{'Up to 11' '12 to 44' '45 to 70' '71 and up'});

sc = modifybins(sc,'AMBalance','BinLabels',...
{'Up to 558.87' '558.88 to 1597.43' '1597.44 and up'});

p1 = displaypoints(sc);
disp(p1)

      Predictors               Bin              Points  
    ______________    _____________________    _________

    {'CustAge'   }    {'Up to 36'         }     -0.15314
    {'CustAge'   }    {'37 to 39'         }    -0.062247
    {'CustAge'   }    {'40 to 45'         }     0.045763
    {'CustAge'   }    {'46 to 57'         }      0.22888
    {'CustAge'   }    {'58 and up'        }      0.48354
    {'CustAge'   }    {'<missing>'        }          NaN
    {'ResStatus' }    {'Tenant'           }    -0.031302
    {'ResStatus' }    {'Home Owner'       }      0.12697
    {'ResStatus' }    {'Other'            }      0.37652
    {'ResStatus' }    {'<missing>'        }          NaN
    {'EmpStatus' }    {'Unknown'          }    -0.076369
    {'EmpStatus' }    {'Employed'         }      0.31456
    {'EmpStatus' }    {'<missing>'        }          NaN
    {'CustIncome'}    {'Up to 28999'      }     -0.45455
    {'CustIncome'}    {'29000 to 32999'   }      -0.1037
    {'CustIncome'}    {'33000 to 41999'   }     0.077768
    {'CustIncome'}    {'42000 to 46999'   }      0.24406
    {'CustIncome'}    {'47000 and up'     }      0.43536
    {'CustIncome'}    {'<missing>'        }          NaN
    {'TmWBank'   }    {'Up to 11'         }     -0.18221
    {'TmWBank'   }    {'12 to 44'         }    -0.038279
    {'TmWBank'   }    {'45 to 70'         }      0.39569
    {'TmWBank'   }    {'71 and up'        }      0.95074
    {'TmWBank'   }    {'<missing>'        }          NaN
    {'OtherCC'   }    {'No'               }       -0.193
    {'OtherCC'   }    {'Yes'              }      0.15868
    {'OtherCC'   }    {'<missing>'        }          NaN
    {'AMBalance' }    {'Up to 558.87'     }       0.3552
    {'AMBalance' }    {'558.88 to 1597.43'}    -0.026797
    {'AMBalance' }    {'1597.44 and up'   }     -0.21168
    {'AMBalance' }    {'<missing>'        }          NaN

Points are usually scaled and also often rounded. To do this, use the formatpoints function. For example, you can set a target level of points corresponding to a target odds level and also set the required points-to-double-the-odds (PDO).

TargetPoints = 500;
TargetOdds = 2;
PDO = 50; % Points to double the odds

sc = formatpoints(sc,'PointsOddsAndPDO',[TargetPoints TargetOdds PDO]);
p2 = displaypoints(sc);
disp(p2)

      Predictors               Bin             Points
    ______________    _____________________    ______

    {'CustAge'   }    {'Up to 36'         }    53.239
    {'CustAge'   }    {'37 to 39'         }    59.796
    {'CustAge'   }    {'40 to 45'         }    67.587
    {'CustAge'   }    {'46 to 57'         }    80.796
    {'CustAge'   }    {'58 and up'        }    99.166
    {'CustAge'   }    {'<missing>'        }       NaN
    {'ResStatus' }    {'Tenant'           }    62.028
    {'ResStatus' }    {'Home Owner'       }    73.445
    {'ResStatus' }    {'Other'            }    91.446
    {'ResStatus' }    {'<missing>'        }       NaN
    {'EmpStatus' }    {'Unknown'          }    58.777
    {'EmpStatus' }    {'Employed'         }    86.976
    {'EmpStatus' }    {'<missing>'        }       NaN
    {'CustIncome'}    {'Up to 28999'      }    31.497
    {'CustIncome'}    {'29000 to 32999'   }    56.805
    {'CustIncome'}    {'33000 to 41999'   }    69.896
    {'CustIncome'}    {'42000 to 46999'   }    81.891
    {'CustIncome'}    {'47000 and up'     }     95.69
    {'CustIncome'}    {'<missing>'        }       NaN
    {'TmWBank'   }    {'Up to 11'         }    51.142
    {'TmWBank'   }    {'12 to 44'         }    61.524
    {'TmWBank'   }    {'45 to 70'         }    92.829
    {'TmWBank'   }    {'71 and up'        }    132.87
    {'TmWBank'   }    {'<missing>'        }       NaN
    {'OtherCC'   }    {'No'               }    50.364
    {'OtherCC'   }    {'Yes'              }    75.732
    {'OtherCC'   }    {'<missing>'        }       NaN
    {'AMBalance' }    {'Up to 558.87'     }    89.908
    {'AMBalance' }    {'558.88 to 1597.43'}    62.353
    {'AMBalance' }    {'1597.44 and up'   }    49.016
    {'AMBalance' }    {'<missing>'        }       NaN

Step 5. Score the data.

The score function computes the scores for the training data. An optional data input can also be passed to score, for example, validation data. The points per predictor for each customer are provided as an optional output.

[Scores,Points] = score(sc);
disp(Scores(1:10))

disp(Points(1:10,:))

    CustAge    ResStatus    EmpStatus    CustIncome    TmWBank    OtherCC    AMBalance
    _______    _________    _________    __________    _______    _______    _________

    80.796      62.028       58.777         95.69      92.829     75.732      62.353  
    99.166      73.445       86.976         95.69      61.524     75.732      62.353  
    80.796      62.028       86.976        69.896      92.829     50.364      62.353  
    80.796      73.445       86.976         95.69      61.524     75.732      89.908  
    99.166      73.445       86.976         95.69      61.524     75.732      62.353  
    99.166      73.445       86.976         95.69      92.829     75.732      62.353  
    53.239      73.445       58.777        56.805      61.524     75.732      62.353  
    80.796      91.446       86.976         95.69      61.524     50.364      49.016  
    80.796      62.028       58.777         95.69      61.524     75.732      89.908  
    80.796      73.445       58.777         95.69      61.524     75.732      62.353

Step 6. Calculate the probability of default.

To calculate the probability of default, use the probdefault function.

pd = probdefault(sc);

Define the probability of being “Good” and plot the predicted odds versus the formatted scores. Visually analyze that the target points and target odds match and that the points-to-double-the-odds (PDO) relationship holds.

ProbGood = 1-pd;
PredictedOdds = ProbGood./pd;

figure
scatter(Scores,PredictedOdds)
title('Predicted Odds vs. Score')
xlabel('Score')
ylabel('Predicted Odds')

hold on

xLimits = xlim;
yLimits = ylim;

% Target points and odds
plot([TargetPoints TargetPoints],[yLimits(1) TargetOdds],'k:')
plot([xLimits(1) TargetPoints],[TargetOdds TargetOdds],'k:')

% Target points plus PDO
plot([TargetPoints+PDO TargetPoints+PDO],[yLimits(1) 2*TargetOdds],'k:')
plot([xLimits(1) TargetPoints+PDO],[2*TargetOdds 2*TargetOdds],'k:')

% Target points minus PDO
plot([TargetPoints-PDO TargetPoints-PDO],[yLimits(1) TargetOdds/2],'k:')
plot([xLimits(1) TargetPoints-PDO],[TargetOdds/2 TargetOdds/2],'k:')

hold off

Figure contains an axes. The axes with title Predicted Odds vs. Score contains 7 objects of type scatter, line.

Step 7. Validate the credit scorecard model using the CAP, ROC, and Kolmogorov-Smirnov statistic

The creditscorecard class supports three validation methods, the Cumulative Accuracy Profile (CAP), the Receiver Operating Characteristic (ROC), and the Kolmogorov-Smirnov (K-S) statistic. For more information on CAP, ROC, and KS, see Cumulative Accuracy Profile (CAP), Receiver Operating Characteristic (ROC), and Kolmogorov-Smirnov statistic (KS).

[Stats,T] = validatemodel(sc,'Plot',{'CAP','ROC','KS'});

Figure contains an axes. The axes with title Cumulative Accuracy Profile (CAP) curve contains 6 objects of type patch, line, text.

Figure contains an axes. The axes with title Receiver Operating Characteristic (ROC) curve contains 3 objects of type patch, line, text.

Figure contains an axes. The axes with title K-S Plot contains 6 objects of type line, text. These objects represent Cumulative Bads, Cumulative Goods.

disp(Stats)

            Measure              Value 
    ________________________    _______

    {'Accuracy Ratio'      }    0.32225
    {'Area under ROC curve'}    0.66113
    {'KS statistic'        }    0.22324
    {'KS score'            }     499.18

disp(T(1:15,:))

    Scores    ProbDefault    TrueBads    FalseBads    TrueGoods    FalseGoods    Sensitivity    FalseAlarm      PctObs  
    ______    ___________    ________    _________    _________    __________    ___________    __________    __________

     369.4       0.7535          0           1           802          397                 0     0.0012453     0.00083333
    377.86      0.73107          1           1           802          396         0.0025189     0.0012453      0.0016667
    379.78       0.7258          2           1           802          395         0.0050378     0.0012453         0.0025
    391.81      0.69139          3           1           802          394         0.0075567     0.0012453      0.0033333
    394.77      0.68259          3           2           801          394         0.0075567     0.0024907      0.0041667
    395.78      0.67954          4           2           801          393          0.010076     0.0024907          0.005
    396.95      0.67598          5           2           801          392          0.012594     0.0024907      0.0058333
    398.37      0.67167          6           2           801          391          0.015113     0.0024907      0.0066667
    401.26      0.66276          7           2           801          390          0.017632     0.0024907         0.0075
    403.23      0.65664          8           2           801          389          0.020151     0.0024907      0.0083333
    405.09      0.65081          8           3           800          389          0.020151      0.003736      0.0091667
    405.15      0.65062         11           5           798          386          0.027708     0.0062267       0.013333
    405.37      0.64991         11           6           797          386          0.027708      0.007472       0.014167
    406.18      0.64735         12           6           797          385          0.030227      0.007472          0.015
    407.14      0.64433         13           6           797          384          0.032746      0.007472       0.015833