

ORIGINAL ARTICLE 

Year : 2017  Volume
: 40
 Issue : 1  Page : 3443 


Naturally occurring radionuclide transfer from soil to vegetables in some farmlands in Ghana and statistical analysis
Theophilus Adjirackor^{1}, Emmanuel Ofori Darko^{2}, Frederic Sam^{3}
^{1} Nuclear Regulatory Authority, Department of Radiological and Nonionizing installation, Atomic Energy, Kwabenya; Department of Business Administration and Computer Sciences, Dominion University College, Accra, Ghana ^{2} Department of Waste and Environmental, Radiation Protection Institute, Accra; Department of Health Physics and Radiation Protection, University of Ghana, School of Nuclear and Allied Sciences, Cape Coast, Ghana ^{3} Department of Physics, University of Cape Coast, Cape Coast, Ghana
Date of Submission  02Mar2017 
Date of Decision  05Mar2017 
Date of Acceptance  18Mar2017 
Date of Web Publication  24Apr2017 
Correspondence Address: Theophilus Adjirackor Nuclear Regulatory Authority, Atomic Energy, Ghana. Dominion University College, Accra Ghana
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.RPE_11_17
Distribution studies of natural radionuclides in soil, statistical analysis of activity concentrations, and transfer factors (TFs) from soil to the vegetables grown in some selected farming communities within the Greater Accra Region in Ghana were carried out. The measurements were carried out through a gammaray spectrometry. The mean activity concentrations of ^{226}Ra, ^{228}Ra, and ^{40}K in the fertilized soils were 20.0 ± 3.9 Bq/kg, 39.0 ± 7.0 Bq/kg, and 143.6 ± 23.3 Bq/kg, respectively. For the nonfertilized soils, mean activity concentrations were found to be 12.07 ± 2.55 Bq/kg for ^{226}Ra, 27.1 ± 6.3 Bq/kg for ^{228}Ra, and 87.8 ± 18.5 Bq/kg for ^{40}K. These results were compared with reported ranges in the literature from other location in the world. The TF for ^{226}Ra, ^{228}Ra, and ^{40}K from fertilized soil to vegetables was evaluated. ^{226}Ra TF values from fertilized soil to vegetables were found to be higher in lettuce in Farm 6. The highest TF for ^{40}K and ^{228}Ra was found in cauliflower in Farm 4. ^{40}K TF was higher than those values reported in other studies. The activity concentration in fertilized and unfertilized soil exhibited slightly positively skewed, negatively skewed, leptokurtic, and platykurtic distribution in terms of skewness and kurtosis. The activity concentration of natural radionuclides in fertilized and unfertilized soil is statistically insignificant at 5% level of significance using independent ttest. Pearson's correlation coefficient exhibited a negative correlation between ^{226}Ra and ^{228}Ra in fertilized soil and ^{226}Ra and ^{228}Ra in vegetables but was statistically insignificant while ^{40}K in fertilized soil exhibited a positive correlation with ^{40}K in vegetables and was statistically significant at 5% level of significance with a coefficient of determination of 1%, 61%, and 10% for ^{226}Ra, ^{40}K, and ^{228}Ra, respectively. Keywords: Fertilized soil, natural radioactivity, transfer factor, unfertilized soil, vegetables
How to cite this article: Adjirackor T, Darko EO, Sam F. Naturally occurring radionuclide transfer from soil to vegetables in some farmlands in Ghana and statistical analysis. Radiat Prot Environ 2017;40:3443 
How to cite this URL: Adjirackor T, Darko EO, Sam F. Naturally occurring radionuclide transfer from soil to vegetables in some farmlands in Ghana and statistical analysis. Radiat Prot Environ [serial online] 2017 [cited 2018 May 27];40:3443. Available from: http://www.rpe.org.in/text.asp?2017/40/1/34/205048 
Introduction   
Radionuclide uptake by plants from contaminated soil represents a key step of radionuclide input into human food chain; this phenomenon is described by soil–plant transfer factor (TF) that is defined as the ratio between plant specific activity and soil specific activity. Plants are the primary recipients of radioactive contamination leading to the food chain radionuclides, following atmospheric releases of radionuclides. The TF is a value used in evaluation studies on the impact of routine or accidental releases of radionuclide into the environment for most important agricultural products. The soiltoplant TF is regarded as one of the most important parameters in environmental safety assessment needed for nuclear facilities. This parameter is necessary for environmental transfer models which are useful in prediction of the radionuclide concentrations in agriculture crops for assessment of dose to man.^{[1]}
Humans and other organisms in their environment are under continuous exposure from radiation due to natural radioactive material found in earth's crust and cosmic rays. In addition, they receive the radiation exposure from medical and industrial sources. The most important natural radionuclides are ^{226} Ra,^{40} K,^{228} Rawith different physical and chemical properties enter into the physical and biological environments.^{[2]}^{226} Ra with halflife 1620 (years) belonged to ^{238} U chain is one of the main pollutants in the natural radiation environment, and it is found widely in different ecosystems. Higher solubility of this element than uranium causes this element to be washed out by the surface. This element is chemically similar to calcium, and it is absorbed by plants through the soil and then through the food chain and enters the human's body. Almost 70% of ^{226} Ra is accumulated in the bones and the rest is spread to soft tissues of the body.^{[3]} Therefore, it is necessary to pay attention to radioactivity pollution and their mechanism of absorption. Amount of radioactive pollution in various food and plants according to their absorption capacity is different. Consumed diet, consumed dosage, preparation site, and ways of preparing food, whether vegetable or animal influence the ingestion pattern of radionuclides. With the increased public concern and awareness about radioactivity in the environment, this study has been carried out to analyze statistically the amount of each natural radionuclide transfer from soil to vegetables grown in some selected farming communities within the Greater Accra Region in Ghana. The results would be useful for establishing a database in the area under consideration and represent a basis to assess any future changes in the radioactivity background levels due to modern agricultural technologies or any artificial influences around the area.
Description of study area
The study area is Accra, the capital of Ghana, located in the southern part of Ghana. It stretches along the Gulf of Guinea near the Atlantic Ocean covering about 170 km ^{2} (65 miles ^{2}) and lies on the latitude 5° 36' 19'' N (degree min second) and longitude 0° 13' 0'' W. The city lies within the Coastal Savanna zone. The almost flat and featureless Accra plain descends gradually to the Gulf of Guinea from a height of 150 m. The topography at the east of the city is marked by ridges and valleys while the west is marked by low plains containing broader valleys, with around low hills with a few rocky headlands. The land is mostly flat and covered with grass and scrub, with thick patches of coconut palms along the coastlines. The annual rainfall is low; averaging 810 mm is distributed over <80 days. The main wet seasons fall between the months of March and June and a minor rainy season around October. The mean temperature varies from 75.2°F (24°C) in August to 80.6°F (27°C) in March. It has a low evaluation and its soil nature is clayish and has been Ghana's capital since 1877.^{[4]}
Materials and Methods   
The equipment, procedures, and statistical analysis used in the study are presented in this section and they include as follows:
Mathematical equations used in calculating the activity concentrations and Transfer factors from fertilized soil to vegetables.
Skewness and kurtosis will be used to determine if the naturally occurring radionuclides are symmetrically or asymmetrically distributed using SPSS version 16.0 developed by IBM in New York, USA since inferential statistics such as the ttest require that the distribution of the variables analyzed is normally distributed or at least approximately normally distributed.
Independent t test to establish whether the differences in the two means (activity concentration in fertilized soil and activity concentration in unfertilized soil) are statistically significant or the difference is due to chance or sampling error.
Correlation analysis (R) between activity concentration in fertilized soil and the activity concentration in vegetables and the extent at which the variation in activity concentration in fertilized soil affects the variation of activity concentration in vegetables using coefficient of determination (R^{2}).
Sampling and sample preparation
Sampling was done at seven different farms within the Greater Accra Region, namely, Abgobga farms, Dworwulu Farm 1, Dworwulu Farm 2, CSIR farm, KorleBu farm, Castle farm, and Mallam junction farm and was regarded as F1, F2, F3, F4, F5, F6, and F7, respectively, as shown in [Figure 1]. These sites were selected in such a way that most of them had been using fertilizer for many years in different amounts. Fertilizers were applied by means of broadcasting so that each soil profile receives almost uniform amounts of fertilizer. The fertilized soil of Farm 1 (F1), Farm 2 (F2), Farm 3 (F3), Farm 4 (F4), Farm 6 (F6), and Farm 7 (F7) was under regular cultivation practices which have been going on for about 35 years while Farm 5 (F5) was over 65 years. The land use in the selected areas is mainly agricultural and residential. The soil texture varied gradually from approximately pure clay to pure sand.
Samples of soil and vegetables were randomly collected from fertilized sites from different farming communities within the Greater Accra Region. Three soil samples were taken from the associated soil of each vegetable, chosen at random within each site, and three unfertilized soil samples were collected from sites distant from each of the cultivated sites to evaluate the impact of the application of phosphate fertilizers. A total of 60 soil samples were collected, of which 39 soil samples were from cultivated sites and 21 soil samples from uncultivated sites, and the collected samples were transferred to tightly closed labeled polyethene. Seven types of vegetable samples were harvested at random from each farm where available, namely, cabbage, cauliflower, gboma, Chinese cabbage, lettuce, radish, and sweet pepper. The samples were transferred to the laboratory for preparation and measurement. Vegetable samples were washed in distilled water, were cut and peeled when necessary, and were freezedried at 20°C for 24 h after which they were crushed into fine powder. For activity concentration measurement, each product was prepared into Marinelli beakers. The beakers were closed by screw caps and plastic tape was wrapped over the caps and weighed with an electronic balance and then stored for about 4 weeks before measurement. This step was necessary to ensure that radon gas is confined within the volume and that the daughters will also remain in the sample.
Measurement and analysis of spectra
The activity concentrations of the samples were determined by nondestructive analysis using a computerized gammaray spectrometry system with high purity germanium. The relative efficiency of the detector system was 25%, with a resolution of 1.8 keV at 1.33 MeV of ^{60} Co. The gamma spectrometer is coupled to conventional electronics connected to a multichannel analyzer card installed in a desktop computer. A software program called MAESTRO 32 of ORTEC, USA was used to accumulate and analyze the data manually using a spreadsheet (Microsoft Excel) to calculate the natural radioactivity concentrations in the sample. The detector is located inside a cylindrical lead shield of 5 cm thickness with internal diameter of 24 cm and height of 60 cm. The lead shield is lined with various layers of copper, cadmium, and Plexiglas, each 3 mm thick. A counting time of 14 h was used to acquire spectral data for each sample. The activity concentrations of the uranium series were determined using gammaray emissions of ^{214} Pb at 351.9 keV (35.8%) and ^{214} Bi at 609.3 keV (44.8%) for ^{226} Ra, and for the ^{232} Thseries, the emissions of ^{228} Ac at 911 keV (26.6%),^{212} Pb at 238.6 keV (43.3%), and ^{208} Tl at 583 keV (30.1%) and 2614.7 keV (35.3%) were used. The ^{40} K activity concentration was determined directly from its emission line at 1460.8 keV (10.7%), while activities of ^{226} Ra and ^{228} Ra were calculated based on the weighted mean value of their respective decay products in equilibrium. The secular equilibrium of daughter products of Useries (^{226} Ra) and Thseries (^{226} Ra) is generally assumed for soil activity concentrations; however, it is not true for vegetation or other migrationdependent matrices. Therefore, here in this paper, the ^{228} Ra and ^{226} Ra concentrations are used for both soil and vegetation for determination of TFs. The TF does not represent for the transfer of ^{238} U and ^{232} Th radionuclides.
The activity concentrations of the radionuclides in the samples were calculated using the expression:
Where M is the mass of sample (kg), N_{sam} is the net counts for the sample in the peak range, P_{E} is the gamma emission probability, T_{c} is the counting time, and ɛ is the photopeak efficiency.
The minimum detectable activity (MDA) was calculated according to Currie equation:^{[5]}
Where MDA is in Bq/kg, σ is the statistical coverage factor = 1.645 at 95% confidence level, and N_{B} is the background counts at the region of interest of a certain radionuclide.
The weight used for MDA calculation was 0.178 kg which is the weight of an empty Marinelli beaker.
The MDA derived from background measurements was approximately 0.12 Bq/kg for ^{226} Ra, 0.11 Bq/kg for ^{228} Ra, and 0.15 Bq/kg for ^{40} K. Concentration values below these detection limits have been taken in this work to be below the minimum detection limit.
Transfer factors
The soiltoplant (vegetable) TFs were determined according to the relation:
Where TF is transfer factor of vegetable soil; Cv is the activity concentration of radionuclides in Bq/kg dry vegetable weight; C s is the activity concentration of radionuclides in Bq/kg dry soil weight (Chibowski and Gładysz, 1997; Chibowski and Gładysz, 1999).^{[6],[7]}
The dry weight was preferred because the amount of radioactivity per kilogram dry weight is much less variable than the amount per unit fresh weight. It reduces uncertainties.^{[1]}
Statistical analysis
Skewness
Skewness is the degree of departure from the symmetry of a distribution. A normal distribution is symmetrical. A nonsymmetrical distribution is described as being either negatively or positively skewed. A normal distribution has a skewness of zero, and the mean, mode, and median are the same. A positive value indicates a positive skew and the mean is greater than the mode or the mean is on the right of the peak value (mode), while a negative value indicates a negative skew where the tail is longer on the left and the mean is less than the mode or the mean is on the left of the peak value (mode).
Kurtosis
Kurtosis indicates the degree of “flatness” or “peakedness” in a distribution relative to the shape of normal distribution or describes the shape of a distribution and how dataset is clustered or spread around the mean. Kurtosis can either be mesokurtic, platykurtic, or leptokurtic. Platykurtic describes a statistical distribution with extremely dispersed points that results in a smaller peak (lower kurtosis) than curves typically seen in a normal distribution, and because this distribution has a low peak and corresponding thin tails, it is less clustered around the mean than are mesokurtic and leptokurtic distributions.
A normal distribution has a kurtosis of zero and is called mesokurtic. If a distribution is peaked (tall and skinny), its kurtosis value is >0 and it is said to be leptokurtic and has a positive kurtosis. If, on the other hand, the kurtosis is flat, its value is <0 or platykurtic and has a negative kurtosis. Data with low kurtosis (platykurtic) tend to have a flat top near the mean rather than a sharp peak and data with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have a heavy tail (leptokurtic).
Independent ttest
Ttest is a statistical tool used to infer differences between small samples based on the mean and standard deviation. It is a powerful statistics that enables a researcher to determine that the differences obtained between two groups are statistically significant. When two groups are independent of each other, it means that the sample drawn came from two populations.
The independent ttest means were used to establish whether the differences in the two means (activity concentration in fertilized soil and activity concentration in unfertilized soil) are statistically significant or due to chance using the relation.
Where X_{mean_1} is the mean activity concentration of fertilized soil, X_{mean_2 } is the mean activity concentration of unfertilized soil, Var_{1} is the variance of fertilized soil, Var_{2} is the variance of nonfertilized soil, and n_{1} and n_{2} are the number of observations of fertilized and unfertilized soil, respectively.
Hypothesis for independent t test
Ho: μ1= μ2
There is no significant difference between the mean activity concentration of natural radionuclides in fertilized soil and mean activity concentration in unfertilized soil.
Ha: μ1 ≠ μ2
There is a significant difference between the mean activity concentration of natural radionuclides in fertilized soil and mean activity concentration in unfertilized soil.
The decision rule
Reject the null hypothesis if T calculated >T critical.
Accept null hypothesis if T calculated < T critical.
Correlation analysis
The linear relationship between two variables is evaluated from two aspects: the strength of the relationship (correlation) and the causeeffect association (regression). Correlation is used to denote association between two quantitative variables, assuming that the association is linear.
The strength of a relationship is indicated by the size of the correlation coefficient: the larger the correlation, the stronger the relationship. A strong relationship exists where cases in one category of the X variable usually have a particular value on the Y variable, while those in a different value of X have a different value on Y.
The correlation coefficient is a number between 0 and ± 1. If there is no relationship between the values, the correlation coefficient is zero or very low. As the strength of the relationship between the values increases, it does the correlation coefficient. Thus, the higher the correlation coefficient, the better is the relationship.
The correlation coefficient (R) is computed using the Pearson's R.
To establish the relationship between the activity concentration in fertilized soil and the activity concentration in vegetables and to determine the significance of the relationship, the activity concentration in vegetables directly depends on the activity concentration in fertilized soil.
Dependent variable (Y)  Activity concentration of natural radionuclides in vegetables.
Independent variable (X)  Activity concentration of natural radionuclides in fertilized soil.
A correlation analysis was also performed between the three natural radionuclides.
Significance of the correlation coefficient using ttest
Pearson correlation is a measure of the strength of a relationship between two variables, but any relationship should be assessed for its significance as well as its strength. The correlation coefficient computed from a sample indicates the strength of the relationship in the sample. To generalize a linear relationship to the population, the significant test needs to be performed.
Hypothesis for regression coefficient
H0: R = 0  There is no linear relationship between activity concentration in fertilized soil and activity concentration in vegetables.
H1: R ≠ 0  There is a linear relationship between activity concentration in fertilized soil and activity concentration in vegetables.
Using the relation:
where n is the number of observation, R is the regression coefficient, and T is the ttest
The decision rule
Reject the null hypothesis if T calculated >T critical.
Accept null hypothesis if T calculated <T critical.
The coefficient of determination (R^{2}) is a single summary number that tells us how much variation in one variable (independent variable) is directly related to variation/variance in another variable (dependent variable).
The square of the product moment correlation coefficient R is known as the coefficient determination (R^{2}).
Results and Discussion   
Specific activity
In the soils of agricultural areas from where the vegetables were collected, the concentrations of ^{226} Ra,^{40} K, and ^{228} Ra ranged from 10.7 ± 5.6 to 40.7 ± 3.3 Bq/kg, 80.6 ± 4.8 to 245.4 ± 2.3 Bq/kg, and 20.2 ± 2.7 to 76.7 ± 1.6 Bq/kg, respectively, with an average of 23.8 ± 2.5 Bq/kg, 199.7 ± 3.67 Bq/kg, and 43.6 ± 2.2 Bq/kg for fertilized soil. For nonfertilized fields, activity concentrations of these radionuclides in the soils were found to be within 5.1 ± 0.4–23.9 ± 1.3 Bq/kg for ^{226} Ra, 18.7 ± 5.7–170.0 ± 3.7 Bq/kg for ^{40} K, and 3.2 ± 2.3–48.1 ± 1.8 Bq/kg for ^{228} Ra, with an average of 14.0 ± 5.9 Bq/kg for ^{226} Ra, 120.9 ± 4.7 Bq/kg for ^{40} K, and 29.4 ± 2.0 Bq/kg for ^{228} Ra.
When fertilized and nonfertilized soils were compared in terms of their natural radionuclide concentrations, it was found that fertilized soils contain slightly higher concentrations than nonfertilized soils as shown in [Table 1]. [Table 2] shows the literature values for naturally occurring radionuclides in fertilized and nonfertilized soils in some studies around the world. [Table 2] also shows the average concentrations obtained in the present study for comparison and it revealed that the activity concentration in fertilized and nonfertilized soil due ^{226} Ra,^{228} Ra, and ^{40} K of the areas studied in Ghana was higher than the activity concentration of fertilized and nonfertilized soil obtained by Ahmed et al. in Egypt (Qena)^{[2]} but lower than the activity concentration of soil obtained by Bikit et al. in Yugoslavia (Vojvodina).^{[8],[9]}  Table 1: Measured average activity concentration of ^{226}Ra, ^{40}K, ^{228}Ra in fertilized and unfertilized soil
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 Table 2: Comparison of the average activity concentrations of ^{228}Ra, ^{226}Ra, and ^{40}K in fertilized and nonfertilized soils with published reports
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Activity concentration in vegetables
Activity concentrations of ^{226} Ra,^{40} K, and ^{228} Ra radionuclides in frequently grown vegetables from seven different fields are presented in [Table 3]. In the vegetables collected from agricultural fields, the activity concentrations of ^{226} Ra,^{40} K, and ^{228} Ra were found to range from 2.4 ± 0.2 Bq/kg to 13.4 ± 1.1 Bq/kg, 489.7 ± 3.9–2755.7 ± 2.0 Bq/kg, and 0.8 ± 0.06–5.3 ± 0.4 Bq/kg, with an average of 6.3 ± 3.0 Bq/kg, 1675 ± 719.4 Bq/kg, and 3.3 ± 1.4 Bq/kg, respectively. The highest concentrations of ^{226} Ra,^{40} K, and ^{228} Ra were observed in F3 lettuce followed by F6 lettuce and F2 Chinese cabbage while the lowest concentrations of ^{226} Ra,^{40} K, and ^{228} Ra were observed in F1 cauliflower, F1 cabbage, and F1 cauliflower, respectively. [Table 4] shows the average concentrations obtained in the present study and previous studies for comparison and it revealed that the activity concentration of ^{226} Ra,^{232} Th, and ^{40} K in vegetables of the areas studied in Ghana was higher than the activity concentration reported in worldwide by the UNSCEAR, 2000^{[15]} and in Egypt by Badran et al.^{[9]} but less than those reported in Turkey by Ekdal et al. and Bolca et al.^{[11],[12]}  Table 3: Activity concentration of ^{226} Ra, ^{40}K, and ^{228}Ra (Bq/kg) in vegetable from each farm
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 Table 4: Comparison of the average activity concentrations of ^{228}Ra, ^{226}Ra, and ^{40}K in vegetables determined in present study with other studies
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Transfer factors of ^{226} Ra,^{40} K, and ^{228} Ra in fertilized soil and vegetables
The TFs of ^{226} Ra,^{40} K, and ^{228} Ra in the analyzed soil and vegetables are presented in [Table 5]. The average values of TF were 0.53, 13.29, and 0.10, respectively. [Table 4] shows the TFs with their respective farms. The highest TF of 1.22 for ^{226} Ra was found in lettuce in Farm 6. The mean TF of 0.53 is higher than the result published by Hasan et al., 2010.^{[6]}  Table 5: Mean activity concentration and transfer factors of ^{226} Ra, ^{40}K, and ^{228}Ra (Bq/kg) in soil and vegetable from each farm
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The highest TF of 21.27 and 0.17 for ^{40} K and ^{228} Ra, respectively, was found in cauliflower in Farm 4 and the mean TFs for all vegetables for ^{40} K and ^{228} Ra were 13.29 and 0.10, respectively. These results are higher than the results published by Hasan et al., 2010, Ashwood et al., 2013, and Aswood et al., 2013.^{[16]}
Result predicted that potassium has the highest TF. This was due to the fact that potassium is an important element to fertile the crop. The higher TF of potassium was not a risk because it has insignificant contribution to internal dose as ^{40} K content in the human body is homeostatically controlled.^{[15]}
The concentration of radium in the part of the plant species depends on the radium content of soil, including its availability to the plant and the metabolic characteristics of the plant species. In view of the fact that the radium content of soil varies fairly widely, corresponding variations in radium levels in land crops may be expected. Chemical factors such as the amount of exchangeable calcium in the soil will determine the rate at which radium will be absorbed by plants.^{[17]}
The uptake of the isotope from soil by vegetables depends on various interrelated soil properties, including texture, clay content, dominant clay minerals, cation exchange capacity, exchangeable cations, pH, and organic matter contents. It also varies depending on the chemical and physical forms of the radionuclides, plant species, stage of growth, etc.^{[18]} Hence, because soil and plant characteristics strongly affect TF values, caution is necessary when TF values are used as the sole parameter to predict radionuclide uptake by plants in seminatural ecosystems.^{[19]}
Statistical analysis
Skewness and kurtosis for ^{226} Ra,^{40} K, and ^{228} Ra in fertilized and unfertilized soil
Ttest requires that the distribution of the variables analyzed is normally distributed or at least approximately normally distributed. Statistics from [Table 6] shows that the distribution of activity concentration of ^{226} Ra in both fertilized and unfertilized soil is positively skewed; thus, the mean activity concentration of ^{226} Ra is greater than modal activity concentration of measured soils, or soils that measured relatively lower concentrations of ^{226} Ra are more than those that measured higher concentrations. The positive kurtosis of fertilized and unfertilized soil shows that the distribution of activity concentration of ^{226} Ra is leptokurtic. Leptokurtic describes a statistical distribution where the concentrations of ^{226} Ra are clustered around the mean activity concentration in the soils, and the distribution will tend to have a distinct peak near the mean, decline rather rapidly, and have a heavy tail.  Table 6: Skewness and kurtosis for ^{226}Ra, ^{40}K, and ^{228}Ra in fertilized and unfertilized soil
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Statistics from [Table 6] shows that the distribution of activity concentration of ^{40} K in both fertilized and unfertilized soil are positively skewed; thus, the mean activity concentration of ^{40} K is greater than the modal activity concentration or soils that measured relatively lower concentrations of ^{40} K are more than those that measured higher concentrations. The negative kurtosis of fertilized soil shows that the distribution of activity concentration of ^{40} K is platykurtic. Platykurtic describes a statistical distribution with extremely dispersed concentration of ^{40} K in fertilized soil, and the distribution will tend to have a flat top near the mean rather than a sharp peak. The positive kurtosis of unfertilized soil shows that the distribution of activity concentration of ^{40} K is leptokurtic, describing a statistical distribution where the concentration of ^{40} K is clustered around the mean activity concentration in unfertilized soils, and the distribution will tend to have a distinct peak near the mean, decline rather rapidly, and have a heavy tail.
Statistics from [Table 6] also shows that the distribution of activity concentration of ^{228} Ra in fertilized soil is positively skewed; thus, the mean activity concentration of ^{226} Ra fertilized soil is greater than the modal activity concentration, or the soils that measured relatively lower concentrations of ^{228} Ra are more than those that measured higher concentrations. The activity concentration of ^{228} Ra in unfertilized soil is negatively skewed; thus, the mean activity concentration of ^{228} Ra in unfertilized soil is less than the modal activity concentration, or soils that measured a relatively higher concentration of ^{228} Ra are more than those that measured a lower concentration. The positive kurtosis of fertilized soil shows that the distribution of activity concentration of ^{228} Ra is leptokurtic, describing a statistical distribution where the concentration of ^{228} Ra is clustered around the mean activity concentration in fertilized soils, and the distribution will tend to have a distinct peak near the mean, decline rather rapidly, and have a heavy tail. The negative kurtosis of unfertilized soil shows that the distribution of activity concentration of ^{228} Ra is platykurtic, describing a statistical distribution with extremely dispersed concentration of ^{228} Ra in unfertilized soil, and the distribution will tend to have a flat top near the mean rather than a sharp peak.
Independent ttest
The asymmetry of the measured activity concentration of naturally occurring radionuclides in fertilized and unfertilized soil is not that significant and can be seen as slightly symmetric, slightly mesokurtic, or slightly normally distributed which statistically buttress the computation of independent ttest to compare if the mean activity concentration for the natural radionuclides is the same or the difference may be due to chance or sampling error. [Table 7] shows the mean activity concentration, variance, and T values for the naturally occurring radionuclides ^{226} Ra,^{40} K, and ^{228} Ra to determine if the difference in activity concentration of fertilized and unfertilized soil is statistically significant.  Table 7: Mean, variance, standard deviation, and T values of ^{226}Ra, ^{40}K, and ^{228}Ra for fertilized and unfertilized soil
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The mean activity concentration of ^{226} Ra,^{40} K, and ^{228} Ra in fertilized soil is 20.0, 143.6, and 39.0, respectively, and for unfertilized soil is 12.1, 82.8, and 27.1, respectively. The T values of 1.59, 1.74, and 0.98 for ^{226} Ra,^{40} K, and ^{228} Ra, respectively, being less than the critical T value at 5% level of significance (P < α) shows that the difference in activity concentration of naturally occurring radioactive materials in fertilized and unfertilized soil is statistically insignificant; thus, the difference between the mean activity concentration of natural radionuclides in fertilized and unfertilized soil may be due to chance or sampling error; hence, the null hypothesis is accepted and alternative hypothesis is rejected. This could also mean that agricultural fertilizers do not have significant impact on the transfer of natural radionuclides to soil.
The standard deviation of activity concentration of ^{226} Ra,^{40} K, and ^{228} Ra in fertilized soil is 10.19, 61.50, and 18.44, respectively, and in unfertilized soil is 6.74, 48.98, and 16.54, respectively. This shows that activity concentration of ^{226} Ra,^{40} K, and ^{228} Ra is more dispersed in fertilized soil as compared to unfertilized soil.
Correlation coefficient (R) and coefficient of determination (R^{2})
[Table 7] shows the correlation coefficient and coefficient of determination of the naturally occurring radionuclides ^{226} Ra,^{40} K, and ^{228} Ra to determine the relationship between natural radionuclides in fertilized soil and vegetables. The results show that there is a negative correlation (R_{Ra}= −0.114, R_{Th}= −0.324) between ^{226} Ra and ^{228} Ra in fertilized soil and vegetable; thus, an increase in activity concentration of ^{226} Ra and ^{228} Ra in fertilized soil will lead to a decrease in activity concentration of ^{226} Ra and ^{228} Ra in vegetables grown on the same farmland and a strong positive relationship (R_{K} = 0.78) for ^{40} K between fertilized soil and vegetables; thus, an increase in activity concentration of ^{40} K in fertilized soil will lead to an increase in activity concentration of ^{40} K in vegetables grown on the same farmland, but a T value of −0.26 and −0.77 for ^{226} Ra and ^{228} Ra, respectively, being less than the critical T value at the 5% level of significance (P < α) shows that the correlation coefficients of ^{226} Ra and ^{228} Ra between fertilized soil and vegetables are statistically insignificant; thus, there is not enough statistical proof that a negative relationship exists between ^{226} Ra and ^{228} Ra in soil and ^{226} Ra and ^{228} Ra in vegetables grown on such soil. Hence, the relationship seen in the sample may be due to mere chance or sampling error and might not give a true reflection of the phenomena in the population.
However, since the calculated T value (2.77) of ^{40} K is greater than the critical T value,^{40} K is statistically significant at the 5% level of significance (P< α). Thus, there is enough statistical proof that a positive relationship exists between ^{40} K in soil and ^{40} K in vegetables grown on the same soil. The null hypothesis is accepted for ^{226} Ra and ^{228} Ra but rejected for ^{40} K at the 5% level of significance.
The coefficient of determination of the naturally occurring radionuclides shows that 1%, 61%, and 10% variation or variance of ^{226} Ra,^{40} K, and ^{228} Ra, respectively, in vegetables is attributed to the variation or variance in activity concentration of ^{226} Ra,^{40} K, and ^{228} Ra in fertilized soil.
Conclusions   
Natural radionuclide transfer and statistical analysis of naturally occurring radioactive materials in soils and vegetables from some selected farmlands in Ghana were studied. It was found that the natural radionuclides of ^{226} Ra (^{238} U series),^{228} Ra as well as ^{40} K are the main radiological constituents of soil and vegetable samples in the study area.
The analysis revealed that the activity concentrations of the natural radionuclides in soil and vegetables in general are within the range of values reported in other countries, apart from ^{40} K which was slightly higher as depicted by their transfer ratios.
The study also revealed that there is a no significant difference in activity concentration of fertilized soil and unfertilized soil, which concludes that agricultural fertilizers do not have a significant effect on the transfer of natural radionuclides to soil, but the standard deviation revealed that activity concentration of natural radionuclides is more dispersed in fertilized soil as compared to unfertilized soil.
^{40} K exhibited a strong positive correlation between fertilized soil and vegetables.
Finally, the result revealed that the correlations of ^{226} Ra and ^{228} Ra are statistically insignificant apart from ^{40} K that was statistically significant at 5% level of significance and this may be due to the fact that potassium helps regulate plant metabolism and affects water pressure regulation inside and outside of plant cells or helps regulate the flow of water through the plant. It is important for good root development, and for these reasons, potassium is critical to plant stress tolerance and essential for overall plant health.
Data obtained in this research revealed that extensive application of phosphate fertilizers to soils may slightly enhance the activity concentrations of natural radionuclides. Considerable variability was evident in levels of ^{226} Ra,^{228} Ra, and ^{40} K from all the farm sites and all vegetables species investigated. The data of vegetables are not large enough to fully utilize statistical parameters in the present study; however, it gives procedures and highlights the need of further generation data.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7]
