UNITED STATES NATIONAL MUSEUM BULLETIN 2 85 



DASAN: Description of Program 



Construction and Handling of Arrays.— The construction 

 and handling of arrays by DASAN is illustrated in Figure 1. 

 Note that the input, referred to as the univariate input array, 

 contributes to and becomes part of a univariate output array. 

 The latter consists of the univariate input array plus any- 

 new variables, other than ratios, which are computed from 

 the input variables. All of the variables represented in the 

 univariate output array may therefore not be univariate 

 in a mathematical sense, but they serve here as the data for 

 a statistical analysis which yields the univariate statistics 

 listed in the introduction. The bivariate array consists only 

 of form ratios, which are computed from pairs of variables 

 drawn from the univariate output array. 



In each of the three arrays, the first variable (first column) 

 consists of specimen identification numbers, with the re- 

 maining variables consecutively numbered from left to right 

 beginning with variable No. 2. 



In the schematic problem illustrated in Figure 1, the uni- 

 variate input array, containing a column of specimen num- 

 bers {a) and five columns of measurements (b through /), 

 becomes a subarray ( A ) within the univariate output array. 

 Two of the original variables, d and /, are modified so that 



and 



d' = 



10.18 



f'=f-9.45 



where 10.18 and 9.45 are constants specified on control cards. 

 Four new subarrays have been generated and included 

 in the univariate output array. The subarray B contains two 

 variables, g and h, where 



b . c 

 g= 



and 



h = d' . e 



These are special computations made possible by the inser- 

 tion of special statements in DASAN, as described in a fol- 

 lowing section. Subarray C consists of variables generated 

 by subtracting one of the variables in the preceding columns 

 from another. Let us suppose that here 



and 



i=b-e 

 i=b-f 



Subarray D consists of variables generated by adding any 

 two of the variables in the preceding columns. For example, 



k=e+h 



Subarray E consists of the logarithms (base 10) of variables 

 in the preceding columns. For example, 



l=log M b 

 and 



m=logioe 



Univariate statistics for all of the variables (except for 

 the specimen identification numbers) in the univariate out- 

 put array are computed. Both univariate and bivariate 

 statistics are computed for the variables in the bivariate 

 array. 



In addition to the bivariate statistics which are computed 

 for each variable (ratio) in the bivariate array, an option 

 exists whereby a bivariate analysis of x and y transformed 

 to logarithms (base 10) may be performed for certain 

 columns, the column numbers of which are specified on a 

 control card. Let us suppose that in the sample problem 

 illustrated in Figure 1 a control card specifies that the 

 variables comprising the ratios appearing in columns 2, 3, 

 5, 6, and 8 in the bivariate array are to be transformed to 

 logs for an additional bivariate analysis. These statistics ap- 

 pear in Array IV. The wavy lines beneath the ratios f'/c, 

 j/d', and l/m mark those variables which were not desig- 

 nated for logarithmic transformation and for which the 

 bivariate statistics from Array III are merely repeated (with 

 the exception of the coordinates of the end points of the 

 lines of best fit or regressions, which have been altered and 

 are no longer valid ) . 



In the bivariate array for this same sample problem, the 

 ratio l/m is the ratio of one log (log b) to another (log c) . 

 Such ratios which are constructed from variables previously 

 transformed to logarithms in the univariate output array 

 cannot be processed to yield correct univariate and bivariate 

 statistics. These invalid statistics are indicated by a wavy line 

 in Arrays II and III. Note that correct bivariate statistics 

 for this same ratio (log b /log c) appear under bjc in 

 Array IV. 



If the horizontal dimension of an output array exceeds 

 the width of standard output paper, the array must be 

 broken into segments, each of which can be printed on the 

 computer paper. This has been done in the sample output 

 (see listing of sample output) . 



Flow of Control. — The flow of control through DASAN is 

 schematically represented in Figure 2, and the main steps 

 followed by the program during an execution involving all 

 subroutines are listed below: 



DASAN (main) 



1. Control cards, variable formats, and data are read in. 



2. Subroutine RAWTAB is called if so indicated by 

 option. 



