ApCIIIVES
FISHERIES RESEARCH BOARD OF CANADA
Translation Series No. 1663
Some demands on mean values in fisheries research
(from "Biological foundations of the fishing industry
and regulations of'marine fisheries")
By S. V. Kozlitina
Original title: 0 nekotorykh trebovaniyakh k srednim v
rybokhozyaistvennykh issledovaniyakh ("Biologicheskie
osnovy rybnogo khozyaistva i regchlirovanie morskogo
rybo1ovstva")
From:
Trudy Vsesoyuznogo Nauchno-Issledovatel'skogo Instituta
Morskogo Rybnogo Khozyaistva i Okeanografii (VNIRO)
(Proceedings of the A11-Union Research Institute of
Marine Fisheries and Oceanography). Publ. by: Pischchevaya
Promyshlennost, Moscow, 67: 362-366, 1969
Translated by the Translation Bureau(NKIW
Foreign Languages Division
Department of the Secretary of State of Canada
Fisheries Research Board of Canada
Biological Station
St. John's, Nfld.
1971
11 pages typescript
Fe-3
DEPARTMENT OF THE SECRETARY OF STATE
TRANSLATION BUREAU
'3
SECRËTARIAT D'ÉTAT
BUREAU DES TRADUCTIONS
•
FOREIGN LANGUAGES
DIVISION
DIVISION DES LANGUES
ÉTRANGÈRES
iW4.:`
CANADA
•.`"
TRANSL ATED FROM - TRADUCTION DE
INTO - EN
Russian
English
AUTHOR - AUTEUR
Kozlitina, S.V.
TITLE IN ENGLISH - TITRE ANGLAIS
Some Demandson.Means Values in FisherieS'Research
In foreign language
,0 nekotoryM1 trebovaniyakh k • sredniM .v rybokhOzyaistvennvkh issledovaniyakIn
•
R5FÇRENCE IN FOREIGN I,ANGUAGE (NAME OF BOOK OR PUBLICATION) IN FULL. TRANSLITERATE FOREIGN CHAIRACTERS.
REFERENCE EN LANGUE ETRANGERE (NOM DU LIVRE OU PUBLICATION) , AU COMPLET.TRANSCRIRE EN CARACTERES PHONETIQUES.
Trudy Vsesoytm-logo nauchno-issledoyatel'skogo instituta morskogo
rybnogo khozyaistva
okeanbgrafiya
REFERENCE IN ENGLISH - IrtFÉRENCE EN' ANGL AIS
of the A11-Union Scientific .-Research Institute of Marine :
Proceedins
,
.
'Fisheries and nceanopiby (vNTPo)
PUBL ISH ER - ÉDITEUR
PAGE„NUMBERS IN ORIGINAL
NUMEROS DES PAGES DANS
DATE OF PUBLICATION
• DATE DE PUBLICATION
L'ORIGINAL
Pishcheyaya promyshlennost'
362366 •
YEAR
ISSUE NO.
VOLUME
ANNÉE
PLACE OF PUBLICATION
LIEU DE PUBLICATION
NUMÉRO
NUMBER OF TYPED PAGES
NOMBRE DE PAGES
DACTYLOGRAPHIÉES
1969
'Moscow
REQUESTING DEPARTMENT
MIN ISTERE-CLIENT
LXVII
Fisheries and Forestry
TRANSLATION BUREAU NO.
NOTRE DOSSIERS°
0650
TRANSLATOR (INITIALS)
TRADUCTEUR (INITIALES)
NKD
Fisheries Research Board
BRANCH OR DIVISION
DIRECTION OU DIVISION
PERSON IREQUESTING
DEMANDE PAR
A.T. Pïnhorn
Biological Station
St. John's Nfdl
YOUR NUMBER
VOT RE DOSSIER N°
.
769-18-14
.
DATE OF REQUEST
DATE DE LA DEMANDE
.
.
.
( R EV. 2/58)
.
-
2 19 71
."1:s.151-ATIC) 7■1 .
.
January 6 › 1971
.
$ 0S-200-10.6
FEB
DATE SOMPLETED
ACHEVE LE
•
.
.
-
e li:v
i3r*
in';on-raf‘ion
TRe+,DUC,ViCi l'-4 NC N
R'.7.VISÉE.
Fe-0
DEPARTMENT OF THE SECRETARY OF STATE
SECRÉTARIAT DiTAT
TRANSLATION BUREAU
BUREAU DES TRADUCTIONS
FOREIGN LANGUAGES DIVISION
DIVISION DES LANGUES ÉTRANGÈRES
CANADA
CLIENTS NO.
N° DU CLIENT
DEPARTMENT
MINISTERE
,...,
Fisheries and Forestry
7 59-18-14
BUREAU NO.
No DU BUREAU
DIVISION/BFIANCH
DIVISION/DIRECTION
Fisheries Research Board
St. Johle .s, NJ
of Canada
LANGUAGE
TRANSLATOR (INITIALS)
LANGUE
TRADUCTEUR (INITIALES)
NKD
Russian
0650
CITY
VILLE
DATE
FEB
-
2 19 71
Source: Trudy Vsesoyuznogo nauchno-issledovatel'skogo instituta
morskogo rybnogo khozyaistva i okeanografii (VNIRO)
[Proceeding of the All-Union Scientific-Research Institute
of Marine Fisheries and Oceanography (VNIR071, Vol, LXVII,
1969.
UDK 639.2001.5
SOME DEMANDS ON MEAN VALUES
IN FISHERIES RESEARCH 1 •
S.V. Kozlitina
hen studying bodies of water, one of the chief methods used in
fishnries research is sampling. When data have been obtained, the
distribution of various non-biotic and biotic indices are plotted,
and deductions are made concerning regions .of high.and low Productivity,.the presence and concentration of pa-rticular organisms,
etc.
Generally, the definitive stage in the initial processing of
1 *. This study- is based on the fund of data at AZNIIRKh (The Azov
Scientific Research Institute of Fisheries), and the references
listed at the end of the paper. '
observational data is the calculation of mean indices which
characterize the value
of certain elements or a definite population.
-
But a meanyalue can be reliable and an objective index
only when certain rule's are observed. when the mèan value is bèing
calculated. Included among the basic rules are the following.
Homogeneity of the data being studied, which is obtained
by means of using data which relate to regions and reservoirs with
insignificant spatial contrasts. Thus, for example, the concentration of ammonia nitrogen, in July 1962, in the water area of the
entire Azov Sea changed from 14.7 to 85,1 mg N/m 3 and the content
of nitrite nïtrogen at the same time varied between 0 and 48,0 mg N/m 3
In the first case the maximum concentration exceeded the
minimum less than six-fold and in the second case the minimum was
exceeded 48-fold, i.e.', it may be assumed that the data obtained
for ammonia nitrogen - are homogeneous and those obtained for nitrite
nitrogen are not homogeneous, Actually, the error in the arithme
tic mean for NH 4 - waa found to be equal to 10% and for NO2, 55%.
From these examples it is evident that the ca1cu14tion of
the mean concentration for the Sea of Azov is only possible for
ammonia nitrogen. In calculating the meah concentration of nitrite
nitrogen it is necessary to isolate regions with characteristic
concentrations,.
The elimination of systematid errors. These include mainly
the instrument errors which'have more or less the same effect on
an entire series of observations.
It is necessary to eliminate
these errors by means of corrections. For example, to the measured temperature of water and air, we add a correction taken
from an authorized Table. When determining the numerical strength
of "tiulka"" in the sea, a correction is made in the catchability ,
,
of the lampara net, etc.
factor
Not infrequently is the instrument• error impossible to
eliminate since researchers, at times, do not know the accuracy
of their apparatus. We can cite the example of the selection of
samples of benthos by means of a benthos-scooper or of zooplankton
by means of Apshtein nets,
Such observations can be used in a
study of changes which are considerably greater in magnitude
than the assumed error,
Gross errors. When processing observations, we must
consider the possibility of errors or external influences which
produce totally inaccurate results.
For example, the observer
records 82 instead of 28, or something gets under the propeller
when rate of flow is being measured, or during trawling the
•
"Azov Kilka" (Clupeonella d. delicatula) according to W.E.
Rickers Russian-Engish Glossary. - translator's note,
/363
the trawl net is caught on the bottom.
The results will obviously
be distorted and values will be obtained which differ sharply from
the other values. It would appear that such a value must be.discarded, however l .one must approach the discarding of such data very
cautiously.
Al),.. measurements represent only a limited sample of
the general population and a value which has a low frequency may
get into the sample. Although the appearance of such a value is
possible, it is not correct to accept -it in the calculations on a
par with the other values; since the probability of such a value
is close to zero, the "drop-out" value would not have a great effect
on the value of mathematical expedtation which is calculated by means
of the formula.
M [xl
i-1
xi
,
where 'y is the probability of the appearance of each value.
Thus, such values can, in exceptional cases, be discarded.
Usually, criteria and rules are applied which permit us to establish
the membership of a random value in the population being examined.
The rule which is most simple and most frequently encountered in
practice is the rule of. "three sigmas" (347- ).
If the value and meah
quadratic deviation crof a measurementare known, then we can find
the approximate error of each measurement, i.e., the deviation of
a measured value from the mean', zi =xi
It is usually considered
unlikely that the absolute value of an error would exeed 3 4er„ Thus,
if kii-? 3a, then the corresponding measurement is considèred to contain a gross error and is discarded.
Sigma is determined by the
fbi-Mula
•
.n 1=1
.
.. •
where Xé is the measured values, and". is the number of measurements.
After the erroneous.data have been eliminated, lt is
neceàsary to calculate the mean value and 0-again. Table' 1 gives
the means of . all observations (m.a.o.), thé means in 'the calculation of which only a single doubtful.value has been discarded
(m.w.d.v,) and the errors of the means.
', , rat5.114111,
•
nOK33àTeA11
,f C.B.H.
cr
.
0u116Ka; %
.
.
Ouni6Ka, %
IniT911J1aNKTOM, 2/.14 3
1,4
47,0
0,5
12,0
TioAbia»
•i e
•
,
• Hirtparià.
Tort atzimi 01101 saeln '.rupta
apbI
30017:18HK• IIIT•
465,0
18,6
347,0
11,7
ma;
1656,10
. 21,4
•1189O .
:
. 1,5
10,5
34,7
Key to Table 1:
3
Zooplankton, mg/m 1
a - Indices, b - Phytoplankton, g/m , c
•d - Tiulka, specimens in one set of a lampara net, e - nitrites,
mg/m 3 , f - m.a.o., g - Error, %, h - m.w.d.v., 1 - Error, %.
The cited data show that without "drop out" values
/364
the errors in the means are much smaller and the means are, as a
result, more exact.. Naturally, subsequent conclusions based on
these means will be more exact. For example, calculated according to the above stated rules, the mean humerical strength of
"tiulka" for a set of a lampara net has changed by 467 specimens,
which when recalculated for the size of the sea comprises a biomass
of 467 thousand centners*.
•
This is very likely the largest catch
Centner = 100 kg. translator's note
of "tiulka" in the Sea of Azov in recent years.
Random error. After having eliminated the systematic errors
and gross errors, the results of the observations will still not
be exact.
Various factors which do not submit to calculatièn have
an effect on them.
sensitive scales.
Let us, for example, weigh something on accurate
If the door of the room slams at the moment the
reading is taken, then the index will deviate in a random direction
and a figure will be obtained'which differs from the correct figure.
A whole series of random factors leading to deviations from the
correct value can be named. Each of these factors producês a
scarcely noticeable deviation, but the tdtal effect of all the factors
may produce a significant error. Such errors are called random errors.
It is impossible to eliminate them and, therefore, by using the
regularites which are characteristic for large populations of random
values, we can generally take into account 'the error in observation
which has been introduced by random causes and the degree of accuracy
of the result of an observation.
We know that random errors in measurement obey the normal
law of distribution, by means of which we can answer a number of
questions which arise in measurement practice;
in particular, we
may indicate the degree of accuracy, the mean quadratic probable
error and greatest possible error of both an individual measurement
and of the arithmetic mean.
In practice, processing is considered to be complete
when the mean quadratic error of the arithmetic mean has been cal-
culated, using the formula
Vn
,
•were -5-is the mean quadratic error of a single measurement which
is determined by formula (1).
•
When recording an arithmetic mean, it is customary to
indicate its mean quadratic error which is usually expressed in
percentages. It is noted that an error is closely connected to
the characteristic distribution of the absolute values of the
variables being studied.
An error is generally smallest when the
distribution is symmetrical (normal) (see the Figure). , It is great-
est when thére is an asymmetrical
it may regch 30-50%;
- distribution (see Figure c) -
when an asymmetric distribution approaches
the distribution of V.I. Smirnova (see Figure h) the mean error
falls between 15 and 5%.
In order to determine the reliability of mean values
which have been obtained, during fisheries research conducted in
the Sea of Azov, the arithmetic means, the quadratic tneans
of an
individual measurement, and the arithmetic mean -of different indices
for Taganrog Bay and the Sea of Azov proper were calculated. Some
of these are given in Tables 1 and 2.
•
It is evident from Table 2 that errors may sometimes
reach a considerable magnitude - 30-50%.
Not infrequently, this
is a result of incorrect initial processing (the "drop out" values
have not been considered); sometimes, it is •the result of a large
/365
range in the fluctuation of the values under consideration.
In the latter case, the arithmetic mean does not serve as a
characteristic of the given series.
•b
fl
IZ
vumeffeeme
Pe4
.
:
602%
JO 5
'
'
214 '
32 r--10
io go
10 15 20
lee
21411
.
.keee
Distribution curves of absolute values
a - oxygen, b - phosphates, c - nitrates and phytoplankton
Table
2
Error (%) in the mean of the concentration of biogennous
elements in the surface layer of Taganrog Bay and the Sea
of Azov proper according to data relating to 1962
--
a
NO,
NO,
NH ,
TaratiporcKuii
.
• ih
•
21,2. 43,9
52,4
16,6
17,4
-
15
Nopr
146pb
•
•
21,9
44,7
30,8
11,2
9,3
17,6
8,6
12,1 10,2
37,1
15,1
10,1
7,8
5,4
10,7
P
opr
•
P am
P'
11,8
.17,3
14,2
9,6
6,4
10;4
3a: HB
CO6cTBeuiio A30pcKoe
0.1b
e•
N (s5tit
9,5
5,5
10,8
12,9
7,8
-
29,4 13,6
9,8 18,7
22,0 15,0
m ope
11,4
6,1
--
15,5
17,7
12,3
7,0
9,6
5.5
6,5 1 7,2
13,9 4,1
5.7 • 18,7
Key to Table:.
a - Month, b f -
p
total, ä - mineral, e -
N organic, c -
total, g- April, h - July 7 i
k - Sea of Azov proper
•
organic,
October, j - Taganrog Bay,
In orderto-obtain a more reliable meanvalue one must
either increase the number of stations - in a trip or use another
• mean .value(for example, the median or the weighted mean).
The
number of stations which are necessary to obtain a mean
.
àpecific.accuracy may be calculated byjneanÉ e the formula:
•
n
F:400 1 2
,
However, it should be noted that an insignificant
decrease in the error of the mean involves a pronounced increase
therefore, it is frequently more
in the number of stations;
rational to use the weighted mean. To this end in terms of the
reservoir being studied, measured values are plotted and isolines
are drawn. Subsequently, the entire reservoir , and the individual
sections between the isolines are weighted, or their areas are
determined by means of a planimeter.
•
'
The weighted mean is determined by means of the. formula
,
where f1 , 4 ...,f ir_
j'b 3 ..sii7e
F.
f;ii+f;-272+...-1-firin
.
',
' F
.
are the areas or weights (mass) of the sections
>between the isolinesLF-h+b+...+f,i
is the'are4 of the entire
.
• reservoir; xi is the arithmetic mean of individual outlined
sections.
The scatter of the weighted mean is calculated by using
the formula
1
o
0‘.
Xb3
Ep
2
21
1
F2
•
'71
•
•••
1 .
mi • •
/366
•
- 10 -
where
e-
xi is the scatter of the arithmetic means of the outlined
sections; in,: is the number of station measurements for individual
outlifed sections.
If the extreme values alone differ sharply and the mean
indices are approximately of the same order, it is more convenient
and accurate to use the median. To this end, all values are arranged
in a descending or ascending order and then the median will be the middl
value if the total number of measurements is odd, or it will • be the
average of the two middle values if the number of measurements is
even.
For example, during sampling in October, 1962, in Taganrog
Bay, the following concentrations of mineral phosphorus (mg/m 3 )
were fixed:
47,6 35,5 21,8 21,4 .20,8 18,4 16,9
7,9
7,3
5,5
1,5
The median is 18.4 mg/m 3 .
From the foregoing it follows that it is necessary to
process a series of measurements in the following sequence.
1.
To determihe the arithmetic mean.
2.
To find the mean quadratic error of an individual
measurement (F- ).
3.
To determine 3crandccompare with e i
,
If led
3 cr,i then
such a measurement should be discarded and the processing should
-
Il -
be done from the beginning.
4.
To determine criof the arithmetic mean and express
in percentages.
5.
In case of large o-Ato determine the weighted average.
The weighted average is a more accurate characteristic
since in determining it the significance pd each measurement is
taken into account.
Bibliography
1. Batuner L.M., Pozin M.E. Mathematicheskie metody
v khimicheskoi tekhnike (Mathematical Methods in Chemical Technology), Goskhimizdat (State Scientific and Technical Publishing
House of Chemical Literature), 1963.
•
2, Velikanov M,A • Oshibki izmereniva i empiricheskie
zavisimosti (Errors in Measurement and Empirical Dependencies)
Gidrometeoizdat (State Scientific and Technical Hydrometeorilogical
Publishing House), 1962.
3, Shigolev V.M. Matematicheskaya obrabotks nablyudenii
(The Mathematical Processing of Observations).
Moscow, Fizmatgiz
(State Publishing House of Literature of Physics
1962,
and Mathematics),