come differentiable until the newly hatched 

 larva transforms from a naupllus into a 

 protozoea. This transformation involves de- 

 velopment (extension) of theabdomenor "tail." 

 In a sense, therefore, it would be possible at 

 the earliest stages in a shrimp's life history 

 to obtain a "whole" but no "headless" weight. 

 Hence the true regression of headless on 

 whole weight (Y on X) should contain a negative 

 value for A, that of whole on headless weight 

 (X on Y) a positive value, the values in both 

 cases being of a very low order of magnitude. 



In the present case, the variation about the 

 fitted line was unquestionably sufficient to 

 result in a general departure in the sign of the 

 observed A. from that expected. Statistically, 

 however, none of the observed A's in the 

 eight regressions computed for the five species 

 in table 1 differed significantly from zero. This 

 suggested a simple proportional relationship 

 between the two weight measurements and 

 prompted refitting the regression lines through 

 zero. The resulting equations are given in 

 column 3 of table 1. Except for slight depar- 

 tures attributable to the rounding process, 

 each member of the five pairs of factors 

 tabulated is the reciprocal of the other. Ob- 

 serve also that these new factors do not differ 

 greatly from the comparable values presented 

 in column 2. They are preferred over the latter, 

 however, and hence recommended for use in 

 future computations involving mass conversion 

 of catch weights in the case of each species 

 represented. As an example of how these 

 factors might be employed, assume a fisherman 

 lands 987 pounds of whole brown shrimp (any 

 or all sizes) but can obtain payment only on 

 the basis of headless weight. Appropriate 

 conversion would be made using the first 

 equation given in column 3 of table 1. Hence 



Predicted headless weight(Y) = 0,620(987) =612 pounds. 



Again, suppose the monthly landings of white 

 shrimp from a particular area totaled 3,175, 550 

 pounds in terms of headless weight, but that 

 landings in terms of whole weight were needed 

 to satisfy some requirement of a biological 

 study utilizing such data. The appropriate 

 conversion is made using the sixth equation 

 in column 3 of table 1. Thus 



Prediaed whole weight (ft) = 1.543(3,175,550) = 4.899,874 

 pounds. 



Factors for each species together with their 

 95 percent confidence limits are given in 

 column 4 or 5 (table 1), according to the 

 conditions for A under which they were cal- 

 culated. Note that confidence limits under the 

 assumption that A ^ are considerably nar- 

 rower than under the alternate assumption. 

 This follows from the fact that the slope (or 



regression coefficient) is restricted in its 

 variation by the condition that the regression 

 line pass through zero. 



All of the foregoing estimates of factors 

 relating headless to whole weights (and vice 

 versa) in commercial shrimps constitute sig- 

 nificant departures from the traditional 0.595 

 (and 1.680). Moreover, statistical comparison 

 of regressions by means of covariance analysis 

 indicated that regression coefficients (or con- 

 version factors), on the whole, differed sig- 

 nificantly between species, although those for 

 the brown and pink shrimp on the one hand, 

 and the white shrimp and seabob on the other, 

 did not. 



Further speculation as to factor differences 

 between sex, geographic locale, and season 

 (within species) prompted additional testing 

 using the same statistical technique. Paired 

 measurements for representatives of each 

 sex were secured over a 5-month period for 

 pink shrimp. The difference between sexes 

 proved highly significant statistically, but in 

 the case of the factor relating headless to 

 whole weight (Y on X), the maximum devia- 

 tion from the value given in columns 3 and 5 

 of table 1 was only two units in the second 

 decimal place. In general, the headless weight 

 (relative to the whole weight) of males slightly 

 exceeded that of females. It is assumed that 

 a similar difference would also hold for closely 

 related species in other areas. 



Factors calculated for pink shrimp sampled 

 at two widely separated locations in Florida, 

 namely, Biscayne Bay (Miami) and the Gulf 

 of Mexico (north of Dry Tortugas), also 

 differed statistically. Although sexes were 

 about equally represented in the sample from 

 each location, part of the difference could 

 have been due to the fact that the sample 

 from Dry Tortugas was largely obtained at 

 a somewhat later season than that from 

 Biscayne Bay. Again, the maximum deviation 

 of the whole-to-headless factors derived for 

 each area was only two units in the second 

 decimal place from the average value given 

 in column 5 of table 1, a departure not quite 

 approaching practical significance. 



Seasonal differences in whole-to-headless 

 conversion factors were tested by using meas- 

 urements of white shrimp sampled throughout 

 the year in the east Texas coastal area. Based 

 on data grouped arbitrarily under two seasons, 

 March-August and September-February, they 

 also proved statistically significant. Maximum 

 deviation of seasonal factors from that com- 

 puted using the combined data was again only 

 two units in the second decimal place. The 

 possible effects of inequitable representation 



