This helpfile describes the method for calculating the                  
        reach and freq scores for a case on the combination of                  
        items currently being processed. This type of scoring                   
        is done for each case on every one of the combinations                  
        which are being evaluated.                                              
                                                                                
        The method for determining the importance of each item                  
        in a combination is done as the results files are written,              
        and is described in the TURF.RESULTS helpfile.                          
                                                                                
        This helpfile was last updated on Sept 16, 2006.                        
                                                                                
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              *  general considerations  *                                      
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        INPUT FILE. A TURF run is done on an input file                         
        that contains some numeric items to be analyzed.                        
        The number of analysis items (NV) can be from 1 to 210,                 
        but will often be 20 or 30 or so.                                       
                                                                                
        The file can contain thousands of cases.                                
                                                                                
        CASE.WEIGHT. The file may also have a weight variable                   
        which provides a weight for each case.                                  
        If not, a weight of one is assumed for each case.                       
                                                                                
        SIZE.  A combination size needs to be provided. This is the             
        number of items to be examined in each pass over the data.              
        Suppose NV is 30 and the size is 7. A pass over the data                
        will be done for every different combination of 7 of the                
        30 items, causing 2,035,800 passes.                                     
                                                                                
        In each pass, the number of cases that have been reached                
        by the current combination of items is counted.                         
        The goal is to identify the combination that reaches the                
        largest number of the cases.                                            
                                                                                
        RESPONSE.WEIGHTS.  The response values themselves can be                
        used as weights that reflect the intensity of the response.             
        Using this option causes the responses for each case                    
        to be placed in memory without any change.                              
                                                                                
        When response.weights is not used, the responses for each               
        case are stored in 0/1 form; 0 if the response was indeed               
        zero, and 1 if the response was any value greater than zero.            
        This takes much less memory space.                                      
                                                                                
        ITEM.WEIGHTS.  The items themselves are assumed to be                   
        equally important. In other words, the default is for each of           
        the NV items to have a weight of one in the reach scoring.              
        Different weights can be provided for some or all of the                
        items. These are read from a file associated with the                   
        ITEM.WEIGHTS option.                                                    
                                                                                
        REACH.THRESHOLD.  Finally, the reach threshold, which                   
        defaults to one, can be changed to 3, for example, by saying            
        REACH.THRESHOLD 3. The threshold can be fractional, like 3.5.           
                                                                                
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              *  ------how the reach scoring is done------  *                   
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        A case is reached when its reach score equals or exceeds the            
        reach threshold. Suppose we are scoring a case on a                     
        combination that consists of items V2, V5, V11 and V17.                 
        Remember, the responses are stored internally as 0 or 1                 
        except when the RESPONSE.WEIGHTS option is in use.                      
        The reach score for a given case is:                                    
                                                                                
        V2  response   times   V2's  item weight,  plus                         
        V5  response   times   V5's  item weight,  plus                         
        V11 response   times   V11's item weight,  plus                         
        V17 response   times   V17's item weight.                               
                                                                                
        If that score equals or exceeds the reach threshold,                    
        the case's caseweight is added to the number of cases                   
        that have been reached for that combination.                            
        One is used when there is no CASE.WEIGHT variable.                      
                                                                                
        When responses and items are unweighted and the                         
        threshold is one, a case will have been reached when it                 
        has a positive response on any item in the combination.                 
                                                                                
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              *  ------how the freq scoring is done------  *                    
              **********************************************                    
                                                                                
        The FREQ score for a combination is the sum of the                      
        freq scores of the cases that were reached.                             
                                                                                
        If the case.weight option is not in use, consider each                  
        case to have a weight of one.                                           
        A case's freq score depends on the options in use.                      
                                                                                
        (1) no use of response.weights or item.weights:                         
            Count the positive responses within a case                          
            on the variables in the combination.                                
            Multiply that count by the case's weight.                           
                                                                                
        (2) response weights are used, but not item weights:                    
            Sum the positive responses within a case                            
            on the variables in the combination.                                
            Multiply that sum by the case's weight.                             
                                                                                
        (3) item weights are used, but not response weights:                    
            Sum the item weights for those variables in the                     
            combination that have a positive value.                             
            Multiply that sum by the case's weight.                             
                                                                                
        (4) response weights and item weights are in use:                       
            Sum the item weight times the response value                        
            for those variables in the combination that                         
            have a positive value.                                              
            Multiply that sum by the case's weight.