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Archive of SID
J. Agric. Sci. Technol. (2006) Vol. 8: 15-23
15
Physical Attributes of Garlic (Allium sativum L.)
A. A. Masoumi1*, A. Rajabipoor2, L. G. Tabil3 and A. A. Akram2
ABSTRACT
Some physical attributes of two common types of Iranian garlic cloves (white and pink)
were identified and compared. A machine vision system was used to determine three di-
mensions and both major and minor projected areas of garlic cloves at a moisture content
of 42.4% w. b. The geometric mean diameter and sphericity were calculated, as well as
the unit mass and volume of cloves were measured. In the moisture range from 34.9 to
56.7% w.b., the unit density, bulk density and porosity for both types were measured. Re-
sults showed that the unit density, bulk density and porosity of cloves were affected sig-
nificantly by moisture content (p<0.01). The type of garlic had a highly significant effect
on the unit density and porosity (P<0.01), and a significant effect on the bulk density
(P<0.05). The relationship between volume and dimensions of cloves was established using
regression analysis. The effect of moisture content on physical properties of cloves was
also expressed by appropriate equations.
Keywords: Garlic, Machine vision, Physical attributes.
_____________________________________________________________________________
1 Department of Agricultural Machinery, Faculty of Agriculture, Isfahan University of Technology, Isfa-
han, Islamic Republic of Iran.
2 Department of Agricultural Machinery, Faculty of Agriculture, University of Tehran, Karaj, Islamic Re-
public of Iran.
3 Department of Agricultural and Bioresource Engineering, University of Saskatchewan, 57 Campus Drive,
Saskatoon, SK, Canada S7N 5A9.
* Corresponding author.
INTRODUCTION
Garlic (Allium sativum L.) has been culti-
vated since ancient times all over the world
especially in Asia. Garlic has medicinal
properties and it is an important ingredient
in the leading cuisines around the world.
Garlic as a spice is utilized in both fresh and
dehydrated state in the food industry. It is
dehydrated into different products such as
flakes, slices, and powders (Ahmad, 1996).
Garlic does not produce seeds, so it must
be propagated vegetatively with garlic
cloves as the most common planting mate-
rial. The yield quality of garlic is affected by
planting methods and clove rates and sizes
(Nourai, 1994; Matlob and Khalel, 1986).
Lack of basic engineering properties of this
planting material is a problem identified in
the development of new methods of sowing
the garlic crop, development of new equip-
ment for processing and control strategies
for crop storage. A number of researchers
have worked on the physical properties of
garlic (Madamba et al., 1993, 1995, 1997;
Pezzutti and Crapiste, 1997; Park et al.,
1981; Bhatt et al., 1998; Sharma and Prasad,
2002).
Madamba et al., (1993) measured the
length, width, and thickness of garlic slices
by using vernier caliper. Song and Litch-
field, (1991) measured the length and width
of seed grains by using a computer imaging
system while using a caliper to measure the
third dimension. Tabil et al., (1999) used an
image analysis program to determine the
size and shape characteristics of some spe-
cialty crops such as chickpeas, lentils and
peas including the length of the longest and
shortest axes, cross section area, perimeter
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_________________________________________________Masoumi, Rajabipoor, Tabil and Akram
16
of the object, circularity and roundness of
each seed. Olaoye, (2000) used an overhead
projector to project the image of the nut
samples on a plain cardboard sheet to char-
acterize the shape.
Sizes of materials usually play a significant
role under approximately the same operating
conditions (Gupta and Das, 1997), as shown
by Marjana (1996) who investigated the ef-
fects of the size of cloves on the yield of
garlic.Gupta and Das (1997) reported a cor-
relation among various dimensions of sun-
flower seeds. The influence of moisture con-
tent on several physical properties was re-
ported by some researchers (Madamba et al.,
1994; Joshi et al., 1993).
Information on the physical attributes of
garlic cloves is not available in the literature.
The objective of this study was to determine
the physical attributes of garlic cloves in-
cluding their dimensions, unit density, bulk
density, porosity. Models were developed to
express the relationship between volume and
dimension as well as determining the mois-
ture-dependent physical attributes of garlic
cloves in the moisture range of 34.9 to 56.7
% w.b.
MATERIALS AND METHODS
Sample Preparation
Garlic bulbs (white and pink) were ob-
tained locally in the region of Marvdasht,
Fars province Iran. Freshly harvested garlic
bulbs were randomly collected from differ-
ent farms. Similar with local practice, the
bulbs were dried by spreading them in a
thin-layer inside a darkroom with open win-
dows near the farms for 15 days. Samples
were stored in a cabinet at 5oC. The sample
bulbs were randomly selected from the bulk
sample and their outer covering manually
removed and cracked before the experi-
ments.
The moisture content of the cloves was de-
termined by following the ASAE S352.2
standard method (ASAE, 1999). Each sam-
ple weighing about 10 g, was placed in a
convection oven set at 130°c for 50 minutes.
The desired sample moisture levels were
prepared. Samples with lower moisture con-
tent were dried by placing in a oven at 60°c
and spread in a thin layer. The sample cloves
with higher moisture contents were prepared
by adding distilled water. Before beginning
the experiments the required quantity of the
samples was placed in room temperature for
12 hours (Visvanathan et al., 1996).
Determination of Dimensions, Mass and
Volume
Seventy-five cloves of each type were ran-
domly selected from the bulk of the samples
with their initial moisture and packed in la-
beled bags individually for easy identifica-
tion. Size and shape characteristics were de-
termined by using a computer imaging sys-
tem. The sample cloves were placed on the
black backplate under the camera individu-
ally and the image was acquired and the im-
ages analyzed using a Sony DXC-151A
CCD color video camera (Sony Corporation,
Japan), light stand, Matrox Meteor RGB
capture card, Pentium III 700 PC, and Ma-
trox Inspector Software version 2.1 (Matrox
electronic systems, Quebec, Canada). In or-
der to increase the accuracy of measuring
the size and shape, significant contrast be-
tween the samples and background was re-
quired that was obtained by using the black
sheet under samples as background and ad-
justing the lights, camera height, brightness,
zoom and focus. Each clove was individu-
ally placed on a black sheet in its natural
position with its length parallel to the y-
coordinate and its image was taken. Then it
was rotated 90 degrees to its major axis to
take a second image. An 80-mm needle and
a 10-mm square rubber with a 5 mm thick-
ness was used to keep and rotate each clove
on its major axis. The features of both im-
ages of each clove including area, perimeter,
feret x and feret y (the dimensions of the
minimum bounding box of the clove in the
horizontal and vertical axes, respectively)
were saved in Excel Workbook format for
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Physical Attributes of Garlic __________________________________________________
17
further analysis. The average of feret y in
both images of each clove was reported as
the major dimension (mm). The longer and
shorter of feret x in both images were re-
ported as intermediate and minor dimensions
(mm) of cloves, respectively.
The bulk clove sample was classified into
three categories-namely small, medium and
large-based on the unit mass of the cloves.
The distribution of cloves by number and
size for each category of unit mass was de-
termined.
The geometric mean diameter (Dp) of the
cloves was calculated by using the following
relationship (Mohsenin, 1986):
3
1
(LWT)
p
D= (1
where L, W and T are the length, width and
thickness in mm, respectively. The spheric-
ity (φ) of the cloves was calculated using the
following equation (Mohsenin, 1986):
L
)LWT(
=
3
1
Φ (2
The volume of each clove was measured
using the gas comparison multipycnometer
(Quanta Chrome Corporation, Boynton
Beach FL, U.S.A). The pycnometer had cell
cups of a volume of 6, 18, and 150 cm3.
Some of the sample cloves were larger than
the smallest cell and partially occupied the
large cell, so a more accurate calibration of
the system was needed. The system was
calibrated as follows. Actual and measured
volumes of different unit sizes were com-
pared by using the known volume of steel
spheres. The average diameter of each
sphere was measured by a digital caliper
(resolution of 0.01 mm), to calculate its ac-
tual volume. Combinations of spheres were
placed in different cell cups for volume de-
termination by the gas pycnometer. The
measurement was repeated three times. The
data was analyzed to find the relationship
between actual and measured volumes by
using different cells for different unit sizes.
To obtain the mass, each clove was weighed
using an electronic weighing balance (Qhaus
scale corp. G 160D, W. Germany) reading to
0.0001 g.
Physical Properties of Cloves
The bulk and unit densities as well as po-
rosity of the various garlic cloves at different
moisture contents were determined. Bulk
density, ρb, was calculated from the mass
and volume of the circular container with a
known volume that was filled by the sample
cloves. The cloves were dropped from a
hopper into the container at a height of 200
mm and excess cloves were removed by
passing a wooden stick across the top sur-
face using 5 zigzag motions (Madamba et
al., 1993).
Unit density, ρp is defined as the ratio of
the mass of the bulk of cloves to its volume
(Joshi et al., 1993). The average value of the
densities was taken from three replications
for each moisture content of each type of
garlic.
The porosity, ε of bulk cloves expressed in
a percentage was calculated from the bulk
and unit densities by using the following
relationship (Jha, 1999):
100
-
=ε
p
bp ×
ρ
ρ
ρ
(3
where ρb and ρp are the bulk density and the
unit density.
Data Processing and Analysis
All the tests were conducted on two various
garlic cloves commonly grown in Iran
(white and pink). SAS PROC MEANS,
FREQ and CORR were used to determine
the maximum, minimum, mean, standard
error, frequency distribution, and correlation
of dimensions of cloves. The relationship
between the volume and dimensions of
cloves was established using regression
analysis and the relationship between the
physical properties of cloves and levels of
moisture content was determined.
Model coefficients were determined using
the SAS routines, REG for linear models
and NLIN for non-linear models (SAS,
2001). The analysis of variance (ANOVA)
and comparison of means were performed
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_________________________________________________Masoumi, Rajabipoor, Tabil and Akram
18
using PROC ANOVA. The coefficient of
multiple determination (R2) and the mean
square error (MSE) of models and the varia-
tion of predicted values with respect to
measured values as well as the distribution
of the residuals with respect to the estimated
coefficients were used to evaluate the mod-
els for fit to the experimental data.
RESULTS AND DISCUSSION
Dimensions and Size Distribution of
Garlic Cloves
Table 1 shows the size distribution of both
the white and pink garlic clove samples at a
42.4% moisture content (w.b.). About 36%
and 38.67% of the white and pink cloves,
respectively, had a mass ranging from 3-5 g,
whereas 28% and 37.33% of the white and
pink cloves, respectively, had a mass less
than 3 g, (small). The larger (mass greater
than 5 g) white and pink cloves were 36%
and 24% of cloves, respectively.
The mean values of 75 measurements for
the major, intermediate and minor dimen-
sions as well as the major and minor pro-
jected areas of white cloves were found to
be 31.71 mm, 19.91 mm, 15.41 mm, and
473.83 mm2, 377.88 mm2, respectively. The
corresponding values for pink cloves were
30.56 mm, 18.72 mm, 15.15 mm, 427.59
mm2 and 352.76 mm2, respectively.
The unit mass and volume of white cloves
were found to be 4.28 g and 4410 mm3, re-
spectively. The values for pink cloves were
3.68 g and 3809 mm3, respectively.
Table 2 shows the Pearson correlation co-
efficients of cloves at a moisture content of
42.4% (w.b.). These values indicate a high
correlation among all the parameters of both
cloves. For both types, the major dimension
of the cloves were also closely related to the
Table 1. Size and distribution of white and pink garlic cloves at 42.4% moisture content (w. b.).
Size category
a
Type
Physical attributes
Total Small Medium Large
White
Percent of sample
By number 100 28 36 36
By mass 100 12.5 34.98 52.52
Average dimensions
Major (a), mm 31.71±0.46 27.41 ± 0.97 32.38 ± 0.41 34.40 ± 0.29
Intermediate (b), mm 19.91±0.47 14.50 ± 0.49 20.63 ± 0.41 23.39 ± 0.30
Minor (c), mm 15.41±0.45 11.06 ± 0.39 15.39 ± 0.46 18.81 ± 0.54
Major projected area (A1), mm2 473.8±16.1 303.3 ± 19.2 485.6 ± 14.8 594.6 ± 13.1
Minor projected area (A2), mm2 377.9±14.6 227 ± 13.4 377.4 ± 10.8 495.7 ± 15.8
Unit mass (M), g 4.28±0.22 1.19 ± 0.15 4.16 ± 0.11 6.25 ± 0.21
Unit volume (V), mm3 4401±213 2122 ± 212 4387 ± 129 6188 ± 260
Pink
Percentage of sample
By number 100 37.33 38.67 24
By mass 100 19.07 40.99 39.94
Average dimensions
Major (a), mm 30.56±0.54 26.10 ± 0.74 31.89 ± 0.35 35.39 ± 0.59
Intermediate (b), mm 18.72±0.46 14.73 ± 0.50 20.16 ± 0.37 22.62 ± 0.54
Minor (c), mm 15.15±0.41 12.24 ± 0.45 15.39 ± 0.33 19.29 ± 0.68
Major projected area (A1), mm2 427.6±16.6 281.3 ± 14.4 470.8 ± 13.2 585.4 ± 20.8
Minor projected area (A2), mm2 352.8±14.15 241±12.8 364.7± 8.43 507.4 ± 21.8
Unit mass (M), g 3.68±0.21 1.88 ± 0.12 3.90± 0.11 6.13 ± 0.26
Unit volume (V), mm3 3809±199 2114±132 4101±151 5974±260
a Small <3g; Meduium 3-5g; Large>5g.
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Physical Attributes of Garlic __________________________________________________
19
intermediate dimension. The geometric
mean diameter and sphericity of cloves were
calculated. Table 3 shows these values for
both white and pink cloves.
Unit Volume
The relationship between unit volume and
dimensions of cloves for both types of garlic
were established using the following regres-
sion analyses:
)c(Ln62.0)b(Ln16.1
)a(Ln2.173.0)
Vw
(Ln
+
++−=
(R2=0.96) (4
)c(Ln61.0)b(Ln67.0
)a(Ln4.136.0)
Vp
Ln(
+
+
+−=
(R2=0.93) (5
where (Vw) and (Vp) are the unit volume of
white and pink cloves (mm3) and a, b , and c
are the major, intermediate and minor di-
mensions (mm), respectively. Mohsenin
(1986) reported the same model for corn
with various coefficients. As Table 2 shows
the correlation between volume and the ma-
jor and minor dimensions of white and pink
garlic cloves at 42.4% moisture content
(w.b.) was close but the corresponding val-
ues for intermediate dimensions of white
garlic cloves were larger than pink garlic
cloves. The same results can be observed
from Equations 7 and 8.
Unit Density
Type and moisture level had a significant
effect (P<0.01) on the unit density of garlic
cloves as revealed by a one-way analysis of
variance. The Duncan multiple range test
indicated that, at each moisture level, the
mean unit density for both types of cloves
was significantly different (P<0.01).
The unit density of the white and pink gar-
lic clove samples were found to decrease
from 1142 to 1106 and 1184 to 1108 kg/m3,
respectively, when the moisture content in-
creased from about 34.9 to 56.7 %w.b. (Fig-
ure 1). The relationship between unit density
and moisture content for both types of
cloves is shown as:
Table 2. Correlation of white and pink garlic cloves dimensions, volume and mass at 42.4% mois-
ture content (w. b.).
Type A2(mm2) A1(mm2) a(mm) b(mm) c(mm) V(mm3)
White
A1(mm2)
a (mm)
b (mm)
c (mm)
V (mm3)
M (g)
0.8024**
0.7701**
0.8108**
0.9680**
0.9230**
0.9411**
1
0.9007**
0.9719**
0.6763**
0.9192**
0.9164**
1
0.8305**
0.6172**
0.8187**
0.8089**
1
0.7122**
0.9232**
0.9157**
1
0.8473**
0.8756**
1
0.9793**
Pink
A1(mm2)
A (mm)
B (mm)
c (mm)
V (mm3)
M (g)
0.8497**
0.8776**
0.7966**
0.9641**
0.9308**
0.9367**
1
0.9177**
0.9633**
0.7303**
0.9020**
0.9209**
1
0.8533**
0.7524**
0.8768**
0.8762**
1
0.6933**
0.8571**
0.8785**
1
0.8577**
0.8601**
1
0.9692**
**Significant at 1% level.
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_________________________________________________Masoumi, Rajabipoor, Tabil and Akram
20
2
cc M0.1+9.1M-13607=
ρp(w)
(R2=0.93) (6
2
cc M0.18+20M-1667.8=
ρp(p)
(R2=0.94) (7
ρp(w) and ρp(p) represent the unit density of
white and pink garlic cloves (kg/m3), respec-
tively and Mc is the percentage of moisture
content ( w. b.). Madamba et al. (1994) pro-
posed the second degree polynomial model
to predict the apparent density of garlic
cloves (cv. Early California) as follows:
0.1M-2.6M1267.2=
ap
2
cc
+
ρ
(R2=0.93) (8
where ρ(ap) is the apparent density kg/m3. As
shown in Equations 6 to 8, the difference in
coefficients may be due to the garlic variety.
Bulk Density
In this study, significant differences
(P<0.01) in bulk density were found be-
tween the two types and moisture levels of
cloves. The mean bulk density for both types
of cloves were significantly different
(P<0.05).
The bulk density for white and pink garlic
cloves was found to increase from 468.8 to
612.8, and 510.2 to 672 kg/m3, respectively,
while the moisture level increased from
about 34.9 to 56.7 % w.b. (Figure 1). The
second degree polynomial model was found
to predict bulk density values for both types
of garlic, shown as:
0.25M+
c
16.1M-725.8=
ρb(w) 2
c
(R2=0.96) (9)
2
ccp(b) 0.17M+8.61M-591.8=ρ
(R2=0.94) (10)
where ρb(w) and ρb(p) are the bulk density of
white and pink garlic cloves (kg/mm3), re-
spectively. Some researchers such as (Joshi
et al. 1993) expressed the bulk density of
pumpkin seeds as a function of moisture
content using the second degree polynomial
model. Modamba et al. (1993) proposed the
linear model for bulk density of garlic slices
as a function of moisture content and slice
thickness.
Porosity
The relationship between porosity and
400
600
800
1000
1200
30 35 40 45 50 55 60
Moisture content,% w.b.
Density,kg/m
3
U-density-w B-densit y-w U-density-p B-density-p
Figure 1. Effect of moisture content on unit and bulk densities of white
and pink garlic cloves.
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Physical Attributes of Garlic __________________________________________________
21
moisture content of both cloves is given in
Figure 2. The porosity decreased from 59 to
45% and 57 to 39% for white and pink garlic
cloves, respectively, when the moisture con-
tent increased from about 34.9 to 56.7% w.b.
The results revealed a high significant effect
of both moisture content and garlic type on
the porosity (P<0.01). The variation in po-
rosity with respect to moisture can be ex-
pressed by the following equations:
)0.94=(R 0.68M-83.49=
w2
c
ε (11
0.93)=(R 0.82M-86.9=
p2
c
ε (12
where εw and εp are the porosity of white and
pink garlic cloves (%) respectively.
Madamba et al. (1993) proposed a linear
model as a function of moisture content and
of garlic slice thickness also showed de-
creasing porosity with respect to the increas-
ing moisture content of garlic slices.
CONCLUSION
The average major, intermediate and minor
dimensions as well as the major and minor
projected areas of white garlic cloves were
31.71 mm, 19.91 mm, 15.41 mm and 473.8
mm2 and 377.9 mm2 , respectively; the cor-
responding values for pink garlic were 30.56
mm, 18.72 mm, 15.15 mm and 427.6 mm2
and 352.8 mm2, respectively. The values of
average unit mass and volume were 1.19 g
and 2122.4 mm3, respectively, for white gar-
lic cloves and 1.88 g and 214.4 mm3, respec-
tively, for pink garlic.
35
40
45
50
55
60
33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
M oist ur e conten t, % w .b.
Poro sity %
porosity-w Porosity-p
Figure 2. Effect of moisture content on porosity of white and pink garlic clove.
Table 3. Geometric mean diameter and sphericity of white and pink garlic cloves at 42.4%
moisture content (w. b.).
Geometric mean diameter (mm) Sphericity
Type Range Mean Range Mean
White 12.43 – 27.55 21.25 (3.74) 0.58 - 0.91 0.72 (0.08)
Pink 11.14 - 28.38 20.46 (3.77) 0.57 – 0.87 0.74 (0.07)
Each value is a mean of 75 measurements. The standard deviation is given in parentheses.
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_________________________________________________Masoumi, Rajabipoor, Tabil and Akram
22
The mean values of geometric mean di-
ameter and sphericity of white garlic cloves
were 21.25 mm and 0.72, respectively, while
corresponding values for pink garlic were
20.46 mm and 0.74, respectively.
The unit density, bulk density and porosity
of cloves were found to be dependent on
moisture content. The unit density and po-
rosity decreased when the moisture content
increased, while bulk density increased with
increasing of moisture content. The type of
garlic also significantly affected the above
named physical properties.
ACKNOWLEDGMENTS
The authors would like to acknowledge the
Department of Agricultural and Bioresource
Engineering, University of Saskatchewan for
technical support; we also appreciate the
help extended by Mr. Bill Crerar during the
experimental work.
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Physical Attributes of Garlic __________________________________________________
23
Physical Properties of Selected Special
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Engng Res. 63:19-26.
ﻲﻜﻳﺰﻴﻓ تﺎﻴﺻﻮﺼﺧﺮﻴﺳ )Allium sativum L. (
ا. ﻲﻣﻮﺼﻌﻣ ل ، . ج . ،ﻞﻴﺒﺗع.رﻮﭘ ﻲﺒﺟر و ا.مﺮﻛا
هﺪﻴﻜﭼ
ﻪــﺒﺣ ﻲــﻜﻳﺰﻴﻓ تﺎﻴــﺻﻮﺼﺧو تﺎــﺼﺨﺸﻣ زا ﻲــﻀﻌﺑ ﺮﻴــﺳ يﺎــﻫﻲﻣﻮــﺑناﺮــﻳا رد رد و ﺪﻴﻔــﺳ عﻮــﻧ ود
و ﻦﻴــﻴﻌﺗ ﻲﺗرﻮــﺻ ﺪﻧﺪــﺷ ﻪــﺴﻳﺎﻘﻣ ﺮﮕﻳﺪــﻜﻳ ﺎــﺑ.ﻦﻴــﺷﺎﻣ ﻢﺘــﺴﻴﺳ زا ﻲﺋﺎــﻨﻴﺑ ﺢﻄــﺳ ،ﻲﻠــﺻا دﺎــﻌﺑا ﻦﻴــﻴﻌﺗ ياﺮــﺑ
ﺗو ﻪــﻨﻴﻤﻛ هﺪــﺷ ﺮﻳﻮــﺼ ﻪﭼﺮﻴــﺳ ﻪﻨﻴــﺸﻴﺑ ﻲﺘﺑﻮــﻃر ياﻮــﺘﺤﻣ ﺎــﺑ ﻲــﺸﻳﺎﻣزآ يﺎــﻫ4/42) %ﺮــﺑ ﺮــﺗ نزو سﺎــﺳا (
ﺪــﻳدﺮﮔ هدﺎﻔﺘــﺳا . و ﻪﺒــﺳﺎﺤﻣ ﺎــﻬﻧآ ﺖــﻳوﺮﻛ و ﻲــﺳﺪﻨﻫ ﻦﻴﮕﻧﺎــﻴﻣ ﺮــﻄﻗﻦﻴــﻨﭽﻤﻫ ﺎــﻫ ﻪﭼﺮﻴــﺳ ﻢــﺠﺣ و مﺮــﺟ
ﺪﻧﺪـــﺷ يﺮـــﻴﮔ هزاﺪـــﻧا. مﺮـــﺟ ،ﻪﭼﺮﻴـــﺳ صﻮـــﺼﺨﻣ مﺮـــﺟ ﻞﻣﺎـــﺷ ﻲـــﻜﻳﺰﻴﻓ تﺎﻴـــﺻﻮﺼﺧ زا ﻲـــﺧﺮﺑ
و ﻞــﻠﺧو هدﻮــﺗ صﻮــﺼﺨﻣ ﺮــﻫ جﺮــﻓ دو ﻲﺘﺑﻮــﻃر هدوﺪــﺤﻣ رد ﺮﻴــﺳ يﺎــﻫ ﻪــﺒﺣ عﻮــﻧ 9/ 34 % ﻲــﻟا
7/56) %ﺮــﺑ ﺮــﺗ نزو سﺎــﺳا ( ﺪﻧﺪــﺷ يﺮــﻴﮔ هزاﺪــﻧا. ﺲﻧﺎــﻳراو ﻞــﻴﻠﺤﺗو ﻪــﻳﺰﺠﺗ)ANOVA ( ﺎــﻫ هداد
يراد ﻲــﻨﻌﻣ رﺎﻴــﺴﺑ ﺮﻴﺛﺄــﺗ ﺎــﻫ ﻪﭼﺮﻴــﺳ ﻲﺘﺑﻮــﻃر ياﻮــﺘﺤﻣ ﻪــﻛ داد نﺎــﺸﻧ)1 ./.P < ( مﺮــﺟ ﺮﻳدﺎــﻘﻣ ﺮــﺑ
و ﻞــﻠﺧ ناﺰــﻴﻣ و هدﻮــﺗ صﻮــﺼﺨﻣ مﺮــﺟ ،ﺎــﻫ ﻪﭼﺮﻴــﺳ صﻮــﺼﺨﻣ جﺮــﻓ ﺖــﺷاد ﺎــﻬﻧآ . ﺶﻳﺎــﻣزآ ﻦــﻳا رد
و ﻞــﻠﺧ و ﻪﭼﺮﻴــﺳ صﻮــﺼﺨﻣ مﺮــﺟ ﻦﻴــﺑ يراد ﻲــﻨﻌﻣ رﺎﻴــﺴﺑ توﺎــﻔﺗ هﺪــﺷ هدﺎﻔﺘــﺳا يﺎﻫﺮﻴــﺳ عاﻮــﻧا جﺮــﻓ
ﺪــﻳدﺮﮔ هﺪﻫﺎــﺸﻣ)1./.P<( ود هدﻮــﺗ صﻮــﺼﺨﻣ مﺮــﺟ ﻦﻴــﻨﭼ ﻢــﻫ ، ﻲــﻨﻌﻣ توﺎــﻔﺗ ﻲــﺸﻳﺎﻣزآ ﻪﭼﺮﻴــﺳ عﻮــﻧ
ﺪﻨﺘــﺷاد يراد)5 ./.
P<.( دﺎــﻌﺑاو ﻢــﺠﺣ ﻦﻴــﺑ ﻪــﻄﺑار ﻪﭼﺮﻴــﺳ ر شور زا هدﺎﻔﺘــﺳا ﺎــﺑ ﺎــﻫ ﺖــﺳﺪﺑ نﻮﻴــﺳﺮﮔ
ﺪــﻧﺪﻣآ. ﻲــﺿﺎﻳر ﻂــﺑاور ﻂــﺳﻮﺗ ﺎــﻬﻧآ ﻲــﻜﻳﺰﻴﻓ صاﻮــﺧ ﺮــﺑ ﺎــﻫ ﻪﭼﺮﻴــﺳ ﻲﺘﺑﻮــﻃر ياﻮــﺘﺤﻣ ﺮــﺛا ﻦﻴــﻨﭼ ﻢــﻫ
ﺪﻧﺪﺷ نﺎﻴﺑ ،ﺪﻧدﻮﺑ هﺪﺷ ﻲﺑﺎﻳزرا ﺲﻧﺎﻳراو ﺰﻴﻟﺎﻧآ زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﻛ ﻲﺒﺳﺎﻨﻣ.
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