The deheaping program is for deheaping when respondents use prototypes in giving x-value responses. Now, consider that for 20 a person “heaps” any value between 18 and 22 to because of being uncertain about the exact response that should be given. That person’s mapping/prototype can be designated by [18,20,22] and the person can be referred to as a 5-heaper because the prototype has a width of 5. However, another person may tend to heap responses from 15 to 25 to 20, use the prototype [15,20,25], and can be called a 10-heaper because they heap from 5 below to 5 above. In fact, the program treats the probability of heaping to 20 from 15 or 25 as half of the probability of heaping for other values. In a way the assignment of probabilities of a half can be viewed as making the heaping relate to an interval 10 wide (i.e., 9 + ½ at each end is 10).

So what? Well, having determined the height of a heap at a multiple of 10, say h10, to distribute it “back” one needs to know what proportion of the responses, ρ10(h10), are associated with 10-heapers. If the rest are 5-heapers, their proportion is 1-ρ10(h10). Since one does not know the ρ10(h10), those that apply to a given deheaping must be estimated. Program 3 approaches this estimation by systematically varying the ρ10(h10) that apply to a heap at 10 and one at 20 to find the best values of ρ10(10) and ρ10(20). Getting best must be given a quantitative meaning that is justified. Say best is when a measure is minimized (e.g., as a sum of squares is in may procedures). Then that value must be determined for combinations of ρ10(10) and ρ10(20) to find when a best combination. In that regard, material you download with the program pursues how to get best estimates.

The next page gives information on the flow of estimation.

 DHSW- PROGRAM 3: A Deheaping Program for Estimating Best Heap Sharing Ratios for 10-heaps

Information about the “problem”