into the present statistical survey as an aid 

 to whoever might find it necessary to con- 

 vert the catch figures reported. As can best 

 be ascertained, this factor, 1.680, was origi- 

 nally arrived at by calculating the ratio be- 

 tween a standard barrel (210 pounds) of whole 

 shrimp and its yield of headless shrimp. We 

 are not certain which species of shrimp was 

 involved in this initial calculation, but the 

 resulting value has since been adopted for 

 use with the four major kinds, namely, the 

 brown shrimp, Penaeus aztecus; pink shrimp. P. 

 d uorarum v/hite shrimp, P. setiferus; and seabob, 

 Xiphopeneus ^royeri. Conversely, its reciprocal, 

 0.595, permits shrimp buyers and statistical 

 agents to convert heads-on landings to heads- 

 off units. Hence for a commercial species of 

 any size, about 125 pounds of heads-off shrimp 

 may ostensibly be expected from every stand- 

 ard barrel of heads-on shrimp. Because these 

 complementary factors are employed in 

 business transactions, especially in areas 

 where heads-on landings of small shrimp 

 predominate, their accuracy is of vital con- 

 cern. 



Since 1956, when the present statistical 

 survey was inaugurated, questions have arisen 

 periodically as to the statistical reliability 

 of the above-mentioned factors. Recent studies 

 of conditions in Gulf of Mexico shrimp stocks 

 as revealed by commercial fishery statistics 

 reemphasized the need to give these factors 

 the appraisal that many have felt has been 

 long overdue. In connection with population 

 studies underway at various points along the 

 Gulf coast, shrimp measurement data of 

 several kinds have accumulated. These include 

 weights of the whole and corresponding head- 

 less portions of shrimp representing the major 

 commercial species. For all species, 

 measurements sufficient to provide quite pre- 

 cise estimates of the whole-headless (and 

 vice versa) ratio were found to be available. 

 For some, additional data were secured so 

 that the ratio's variability according to area, 

 season, and sex could be determined, 



MATERIAL AND METHODS 



Brown, pink, and white shrimp of all sizes 

 from the smallest juvenile to the largest 

 adult are treated in the following analysis. 

 Only medium-size and a few large adults 

 represent the seabob and rock shrimp, 

 Sicyonia brevirostris, a commercially po- 

 tential but not as yet utilized species. All 

 specimens except those of pink shrimp came 

 from the east Texas-western Louisiana area. 

 The pink shrimp were taken in Biscayne Bay 

 (Florida) and the Gulf of Mexico just north of 

 the Dry Tortugas. 



Individuals were secured by sampling com- 

 mercial bait shrimp (inshore) catches, by 

 sampling commercial (offshore) landings prior 

 to their processing at dockside plants, and 

 from biological samples taken by research 

 vessels operating on inshore waters and at 

 sea. After excess moisture was removed, 

 weights of individual whole and corresponding 

 beheaded shrimp were recorded to the nearest 

 one-tenth gram in most cases, and to the 

 nearest one-hundredth gram in the remainder. 

 Beheading proceeded in as uniform a manner 

 as possible, using techniques commonly em- 

 ployed in the shrimp industry. 



RESULTS AND DISCUSSION 



If a straight line best characterizes the 

 relationship between two variables, then the 

 method of least squares provides the most 

 efficient estimate of their mean ratio, com- 

 monly referred to as the regression coeffi- 

 cient. For each species, inspection of paired 

 data (whole and headless weights) indicated 

 that a straight-line relationship did prevail, 

 this being subsequently confirmed by means 

 of appropriate statistical tests. Employing the 

 least squares method, I fitted straight lines 

 to the data and obtained the desired esti- 

 mates. These, together with the correspond- 

 ing prediction equations, are summarized in 

 table 1, 



Actually, two regressions of the form 

 Y = A + BX are called for under the present 

 circumstances, depending upon which conver- 

 sion factor (or regression coefficient, B) is of 

 interest. Assuming that both factors, the one 

 relating headless to whole weight, and the one 

 relating whole to headless weight, are equally 

 useful, the regressions of headless on whole 

 weight (Y on X) and whole on headless weight 

 (X on Y) were computed. Theoretically, if 

 "sampling" error were nil and the paired 

 variates perfectly correlated, the coefficient 

 of the one regression should equal the recip- 

 rocal of the coefficient of the other, and vice 

 versa. Examination of the plots and subse- 

 quent fitting of the regressions revealed that, 

 in the case of the brown, pink, and white 

 shrimp, the data did in fact very nearly 

 meet these requirements. The error proved 

 so negligible and the variates so closely 

 correlated that both regressions merged as 

 one. This "common" regression is depicted 

 for the brown, pink, and white shrimp re- 

 spectively, in figures 1-3, which are pre- 

 sented merely as devices (nomographs) for 

 graphic conversion. Observe that they permit 

 (1) simple weight conversion in individual 

 shrimp, (2) conversion from simple weight 

 to corresponding number-per-pound units and 



