The number of fishing trials required for comparing the efficiency of fishing gears was investigated. A unique solution to this problem did not appear to exist because of the heterogeneity of the experimental material. Sequential experimentation and analysis have been found to be a practical approach to this problem. By this, the experiment can be terminated almost after 35 days fishing for catches with standard error per unit as per cent of the mean about 30% or less (after logarithmic transformation). For data with mean catches less than 1.5 kg analysis of variance approach does not appear to be meaningful

Kesavan Nair, A.K.

Aquatic Commons

Fish. Techno!. (1982) 19, 49-53 49 
Investigations on the umber of Trials 
Statistical omparison of Fishing 
uired for 
A. K. KESA VAN NAIR 
Central Institute of Fisheries Technology, Cochin-682 029 
!he n_umber of fishi?g trials r~quired f?r comparin~ the efficiency of fishing gears 
was mvest1gated. A umque solutwn to this problem did not appear to exist because· 
of the heterogeneity of the experimental material. Sequential experimentation and 
analy~is have been fou~d to be a practical approach to this problem. By this, t.he 
expenment can be termmated utmost after 35 days' fishing for catches with standard 
error per unit as per cent of the mean about 30% or less(after logarithmic transforma-
tion). For data with mean catches less than 1.5 kg analysis of variance approach does 
not appear to be meaningful. 
To compare the efficiency of fishing gears, 
one of the statistical designs used is the ran-
demised block design where a block is 
constituted by consecutive hauls made in the 
same area on the same day. The fishing 
gears tested for their relative efficiencies 
form the treatments. For economy and 
to get quick results, the optimum number 
of trials are useful. Solution on the number 
of trials requir~ information on the e~timate 
of variance (o-) in the population and a spe-
cification of the largest confidence interval to 
be tolerated or the smallest mean difference. 
Simple estimate of the sample size as well 
as estimates specifying the probability of 
success are given by Panse & Sukhatme 
(1957), Snedecor (1961), Cochran & Cox 
(1963) and Kempthorne (1967). Informa-
tion on the variance is normally obtained 
from a previous experiment or from a know-
ledge of the range. Pause & Sukhatme 
(1957) have stated that in the absence of 
information on the variability, the number 
of replicatioris should be sufficient to ensure 
at least about 12 degrees of freedom (d.f) for 
error. Tables on the number of replications 
required for a given probability of obtaining 
a significant result have been given by 
Cochran & Cox (1963). These numbers 
correspond to a range of 2 to 20 in the 
standard error per unit expressed as per cent 
of the mean. For large values of standard 
error as per cent of the mean, the number 
of replicates are to be worked out. Formula 
to work out the number of blocks relevant 
Vol. 19, 1982 
to randomised block experiments has been 
given in Snedecor (1961). Results of an inv-
estigation conducted to estimate the optimum 
number of trials are reported in this com-
munication. 
Materials and Methods 
The present investigation on the num-
ber of replicates is an empirical study using 
three sets of data. The data were arranged 
sequentially for 10, 15, 20, 25, 30 and 35 
days. At each stage the number of blocks 
were estimated using the formula. 
given by Snedecor (1961). Here, 'a' is the 
number of treatments tested, f = (a-1) 
(b-1) corresponding to a.large value of b, So, 
the standard error per umt (an estimate of o-), 
fo, d.f. corresponding to the mean square 
So 2 and 8, the least population difference 
in the means, the proposed experiment i& 
expected to detect with p = 0.75. The 
values of Qa, f and Ff, fo orginally tabulated 
by May (1952) and Merrington & Thom-
pson (1943) respectively were taken from 
Snedecor (1961). For a given number of 
blocks b, the lowest differences in the mean~ 
which the experiment would detect, were 
worked out from, 
50 
Qa, f (so) tv'Ff, fo 
8 = "" b ............ 2 
The variation in the estimates of para-
meters when based on increasing number 
of blocks and also the relationship between 
some estimated parameters were studied 
graphically. 
Results and Discussio!l 
The mean (m), So 2 , standard error per 
unit as percent of the mean (So x 100) and 
ill 
b, estimated from consecutive trials of 10, 15, 
A. K. KESAVAN NAIR 
20, 25, 30 and 35 days (using MICRO 2200 
of Hindustan Computers) after logarithmic 
transformation for the three sets are 
given in Table 1. The b's were estimated 
for detecting 20% or more difference in 
the means (8 =20% of the mean) with 
p = 0.75. The standard error per unit 
as per cent of the mean ranged between 
17 to 40% for the first set, 14 to 24% for 
the second and 53 to 74% for the third. 
Thus the expel"iment'll mLterial appeared 
to be hetnogeneous. From its relationship 
with the number of blocks used to estimate, 
the estimated number of blocks were found 
to be more stable and realistic for sets 1 
Table 1. Showzng the mean, standard error per unit, standard error per unit as percent of the 
mean and b, computed from 10, 15, 20, 25, 30 and 35 days offishing trials. 
A. Set I 
No. of 
days 
10 
15 
20 
25 
30 
35 
B. Set 2 
10 
15 
20 
25 
30 
35 
C. Set 3 
10 
15 
20 
25 
30 
35 
Mean 
(m) 
0.2756 
0.4063 
0.5435 
0.6293 
0.6699 
0.7475 
0.4084 
0.5401 
0.6505 
0.6889 
0.7845 
0.8471 
0.3008 
0.2880 
0.2578 
0.2375 
0.2285 
0.2391 
Standard 
error 
per unit 
(So) 
0.10984 
0.09561 
0.09103 
0.18425 
0.20201 
0.20059 
0.09767 
0.09735 
0.08962 
0.11922 
0.12506 
0.14996 
0.17570 
0.15193 
0.14743 
0.13764 
0.16174 
0.17717 
Standard 
error per 
unit as 
per cent of 
the mean 
(So/m x iOCl) 
39.8 
23.5 
16.7 
29.3 
30.1 
26.8 
23.9 
18.0 
13.8 
17.3 
15.9 
17.7 
58.4 
52.7 
57.2 
57.9 
70.8 
74.1 
NS = Not significant, * - Significant at 5% level, 
*':' = Significant at 1% level, *** = Significant at 0.1% level 
b 
62 
21 
10 
30 
32 
25 
23 
12 
7 
11 
9 
11 
133 
103 
116 
117 
173 
188 
Significance of 
difference 
between 
treatments 
NS 
... 
... 
:.-:{ 
NS 
NS 
NS 
*: 
·'· .,. 
* ~:~ 
, ... ,, .. 
~.~ .-,~ 
'" 
.,. 
** 
... 
... 
*~!-! 
':'** (P <" 
' 
0.1) 
**':' (P< 0.1) 
,:,,:,,~ (P< 0.1) 
':'*~' (P< 0.1) 
FISHERY TECHNOLOGY 
STATISTICAL COMPARISON OF FISHING GEAR EFFICIENCY 51 
and 2 (Fig. 1). Set 3, for which the 
estimated numbers of blocks are larger, 
the estimates do not stabilize but increase 
, .. 
"" 
140 
120 
100 
•• 
Fig. 1. 
_,,, 
... , 
______ , 
.. 
"' 
.. 
Relation between estimated number of 
blocks and number of blocks used for 
estimation 
with increasing number of blocks from 
which the estimates were made. Thus the 
large sample property of estimates was not 
found to be satisfied for this set within the 
available range of values. ·· This is because 
eo 
-111 
lO 
10 
" 
zo 
" " HO OF OAY.S 
Fig. 2. Relation between standard error per unit 
as percentage of the mean and number of 
days 
the estimated number of blocks increases 
with increase in the standard error per unit 
and as found from Fig. 2, the estimated 
standard error as per cent of the mean 
increases when the number of blocks (days), 
Vol. 19, 1982 
lBO 
160 
140 
129 
100 
~ 
0 
() 
z ao 
60 
40 
20 
Fig. 3. 
0 20 40 60 eo 
9 E PER UNIT AS PERCENTAGE OF THE MEAk , 
Kelation between estimated number of 
blocks and standard error per unit as 
percentage of the mean 
from which this is estimated, increases. 
The standard error per unit as per cent of 
the mean: are also relatively larger (above 
50%) for this set. To know how much 
larger the estimated number of blocks 
should be for larger increase in standard 
error per unit as per cent of the mean, 
figure 3 is employed. A common curve 
appears to adequately represent the three 
sets of data. The figure shows that for 
standard error larger than about 30% of 
the mean large number of blocks are required. 
For such sets of data (as in set 3), the esti-
mation of number of blocks do not seem 
to be useful, because . experiments requiring 
very large number of replications are not 
desirable from practical and economic points 
of view. Such data calls for other mtthod 
of handling. As found from Fig. 4, 
larger standard errors per unit as per cent 
52 
80 
70 
so 
•o 
~ 
40 
./ 
!0 
20 
10 
. . 
.. 
•- T 
0 -ll 
•-ill 
O·t 0 !I o a o e o 1 O•D 0 t 
Fig. 4. 
tHAN CATCH(S. (lilt Ulllll) 
Relationship between mean catch and 
S 0 as per cent of the mean 
of the mean are associated with smaller mean 
catches, the rate of increase in the former 
being rapid for decrease in the latter below a 
certain level. For instance, for the mean 
catch less than 0.4 (1.5 kg in original scale), 
the standard error as per cent goes above 40. 
Thus, when the catch is very poor, standard 
error as per cent of the mean and consequently 
the number of blocks required becomes very 
large making the analysis of variance ~ess 
meaningful. The fact that when the availa-
bility of fish in the exploited area is very poor, 
catches will not reflect the efficiency of 
gears supports this conclusion. 
With variations in the number of blocks, 
changes in ihe level of significance of the 
difference in treatment effects could be 
observed (Table 1). For set 3, though the 
significance level was very high (P < 0.1), 
the 8 - value computed from equation (2) 
for 35 blocks was 46.1% of the mean showing 
that the experiment would detect only 
treatment effects as large as 46.1 %. But 
the corresponding 8 - values for sets 1 and 2 
were 16.7 and 11.0% of the mean respectively, 
which agree with the originally set 8 - value 
A. K. KESA VAN NAIR 
of 20% or less. These results also supp.ort 
the observations made in the precedmg 
paragraph. 
In conclusion, as a practical procedure, 
the accumulated data can be analysed 
sequentially at the ends of 10, 15, 20 ...... days 
and depending on the standard error as 
per cent of the mean, a decision on the num-
ber of trials can be made with 35 days' 
trial. If the standard error per unit as per 
cent of the mean stabilizes at about 30% 
or below, the experiment can be stopped 
and the decision at this stage can be taken 
as conclusive. The population which gives 
rise to such sets of data is probably less 
affected by fluctuations in the availability 
of fish because the replenishment · and 
removal balance the sub-populations in 
the exploited area. For such data, analysis 
of variance as applied to randomised block 
design can be reasonably attempted after 
logarithmic transformation. But when the 
catches are poor, say, with· a mean catch 
less than 1.5 kg, standard error per unit 
will increase necessitating experimentation 
in very large number of blocks which would 
be impractical as well as uneconomical and 
analysis of variance approach would not be 
useful for such data. 
Cochran & Cox (1963) and Tippet (1952) 
have discussed the usefulness of sequential 
experimentation when the treatments can 
be applied to a unit in definite time sequence 
and when the process of measurement is 
very rapid so that the yield or response on 
any unit is known before the experimenter 
treats the next unit in the time sequence. 
It can be seen that these conditions are 
fully satisfied for fishing experiments. The 
sequential experimentation has also the 
advantage that the experimenter can stop 
the experiment and examine the accumulated 
results before deciding whether to continue 
the experiment or not. 
The author is grateful to Dr. C. C. Panduranga 
Rao, Director, Dr. P. N. Kaul and Shri K. Krishna 
Rao all of Central Institute of Fisheries Technology 
for ~ncouragement, to Dr. K. Alagaraja, Scientist, 
Central Marine Fisheries Research Institute, Cochin 
for critically going through the manuscript and 
suggesting improvements and to Shri H. Krishna 
Iyer for helpful comments. 
FISHERY TECHNOLOGY 
STATISTICAL COMPARISON OF FISHING GEAR EFFICIENCY 53 
References 
Cochran, W. G. & Cox, G. M. (1963) 
Experimental Design. John Wiley & 
Sons, New York, 611 p 
May, J. M. (1952) Biometrika 39, 192 
Kempthorne, 0. (1967) The Design and 
Analysis of Experiments. Wiley Eas-
tern University Edition. Wiley Eastern 
Pvt. Ltd., New Delhi, 628 p 
Vol. 19, 1982 
Panse, V. G. & Sukhatme, P. V. (1957) 
Statistical Methods for Agricultural 
Workers, Indian Council of Agricul-
tural Research, New Delhi, 361 p 
Snedecor, G. W. (1961) Statistical Methods. 
The Iowa State College Press, Ames, 
Iowa U. S. A., 534 p 
Tippet, L. H. C. (1952) Technological 
Application of Statistics. John Wiley & 
Sons, Inc., London, 186 p 


Investigations on the number of trials required for statistical comparison of fishing gears

http://aquaticcommons.org/18380/1/FT19.1_049.pdf

Investigations on the number of trials required for statistical comparison of fishing gears

Abstract

Similar works

Full text

Available Versions

Aquatic Commons