1. April 20, 2010
To: United States Government
From: Kelan Kline
Re: Analysis of Wheat Crops in Various Growing Conditions
Per your request we have conducted a statistical analysis of the wheat crop in various testing and
growing conditions. We are able to better understand the factors which impact wheat yields
under various growing conditions after our testing and consolidating of the data. The
Government has instructed us to send copies of the analysis to all members of the United Nations
relief agencies working on this issue. This report will help U.N. workers understand which
growing conditions are best suited to be implemented by Afghani farmers to produce the highest
yield.
1. United Nations relief agencies: Please find your copy attached.
2. United Nations relief agencies: Provide acknowledgment of receipt of this email
If you have questions regarding any of the analysis or report, please contact me no later than
May 5th at (585-880-7047) or kelankline@gmail.com.
3. Wheat Analysis
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Recent Research Contract from U.S. Government for
Wheat Analysis
Introduction:
This report delivers the results from a statistical analysis from a recent research contract provided
by the U.S. government. The research was done in order to help United Nations relief agencies
better help Afghani farmers produce the most wheat yield for the lowest cost. The U.S.
government and United Nations have authorized this study in support for the post-war assistance
to Afghani farmers.
The U.S. government has asked a major seed-grain company to provide crop test data on various
strains of wheat seeds, grown under various growing conditions. These conditions included:
amount of rain, variety in soil, fertilizer use, soil type, season, elevation, fungicide, and pesticide.
A total of 200 usable records were compiled for the analysis.
Numerous statistical analysis tools were applied to the data in order to gain an understanding of
the degree to which various factors are associated with advantageous outcomes. Details of the
analysis, including methods used, data preparation issues, and explanations of various in-depth
statistical constructs, appear in Appendix A. Highlights of the statistical analysis are discussed
below. Conclusions and recommendations are made, based on the discussion.
4. Wheat Analysis
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24%
51%
26%
Wheat Type Monsanto 225
delkab
droughtmaster
indian brown
45%
28%
28%
Soil Type
clay
rocky
sandy
40%
60%
Planting Season
Fall
Spring
50%50%
Fungicide Use
No
Yes
The large sample size collected, combined with the statistical methods used, allow us to state that
all conclusions and assertions reached are made with a 95% degree of confidence.
Descriptive Analysis:
We started by providing a brief overview of the data provided by the major seed-grain company.
There were 200 different growing conditions in which the data was collected. From the data
collected we can be 95% confident wheat yield will be between 45.4 bushels and 49.8 bushels.
The averages from these groups are listed below:
Rainfall=7.14 inches per season
Fertilizer=55.58 lbs. per acre
Elevation=2019 meters
The following exhibits show how various characteristics of the test plots are distributed. By
viewing these exhibits, one should be able to understand at a much broader view what the data
collected looked like. A detailed statistical analysis can be found in Appendix A-1 and A-2.
Exhibit 1 – Breakdown of proportions
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29%
21%35%
16%
Pesticide Type
Neither
Joint Worm Only
Both
Root Worm Only
0
100
200
500 1000 1500 2000 2500 +3000
#incategory
Meters
Elevation
0
50
100
2 4 6 8 10 +10
#incategory
Inches per year
Amount of Rain
Exhibit 1 – Breakdown of proportions
continued
Exhibit 2- 81.5% of wheat tested was from an elevation of 2500-3000 meters
As seen in the exhibit above most of the data was taken from a crop field with an elevation of
2500 meters. This is significant in the fact that we do not have data from a lot of different
elevations.
Exhibit 3 – 42.5% of total rainfall was 8-10 inches
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0
20
40
60
80
15 30 45 60 75 100 +100
#ineachcategory
Lbs. Per Acre
FertilizerUse
The above exhibit shows that on average the rainfall is around 8 inch’s. The range we used was 2
inches to above 10 inch’s.
Exhibit 4 – 33.5% of fertilizer used was 60-75 Acers
All of the wheat yield data given to us used between 15 lbs to 100 lbs of fertilizer. The majority
of fertilizer used was 60 lbs per acre.
Summary Analysis:
Impact on crop yields in fall and spring:
This analysis considers whether planting in the fall or spring had a better bushel per acre yield in
wheat. The average yield of wheat was 47.59 bushels. The results of this analysis are shown
below in exhibit 5:
Fall Spring
Mean (Bushels per acre) 40.3 52.4
Test Plots 80 120
Exhibit 5 – Average wheat yield fall vs. spring
The observed difference in averages from fall to spring is very significant. The difference is
around 12 more bushels yield when planting in the spring instead of the fall. From this analysis
7. Wheat Analysis
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planting in the spring would be much more advantageous. See Appendix A-3 for a detailed
statistical analysis.
Impact of soil type on yield:
The next analysis considers if the type of soil that the wheat was planted in had any effect on
yield. Clay soils yielded an average of 52.69 bushels per acre, sandy has an average of 50.18, and
rocky had an average of 36.71. The results of this analysis are below in exhibit 6:
Groups # Plots Average (bushel per acre)
Rocky 55 36.7
Clay 89 52.7
Sandy 56 50.2
Exhibit 6 – Average yield per soil type
The observed difference in averages shows there was not a statistical significant difference
between clay and sandy. When choosing which soil to use, clay and sandy will yield more than
rocky, but there is no advantage in choosing clay or sandy. See Appendix A-4 for a detailed
statistical analysis.
Impact of seedtype on yield:
The next analysis studied whether the type of seed had a statistical significant difference in the
outcome of yield per acre. Indian brown seed shows the largest average yield per acre with
58.29. Results of the analysis are shown below in exhibit 7.
8. Wheat Analysis
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Groups # of plots Average (bushels per acre)
Indian Brown 51 58.3
Delkab Droughtmaster 102 45.3
Monsanto 225 47 40.9
Exhibit 7 – Average yield per seed type
The difference between Indian brown and the other two seed types is statistically significant. See
Appendix A-5 for a detailed statistical analysis. Using Indian brown would be the most
advantageous seed to use to produce the largest amount of yield per acre.
Impact on yield with the use of fungicide:
This analysis studied whether the use of pre-emergence fungicide had a significant impact on the
amount of yield produced. The results from this analysis can be seen below in exhibit 8:
No Fungi Fungi
Average (bushels per acre) 40.9 54.3
# of plots 100 100
Exhibit 8 – Average yield with the use of Fungicide
The analysis shown above is significant in the difference in yield. The use of fungicide increased
the amount of yield by 13 bushels more per acre. The use of fungicide is proven to be beneficial
and we would highly recommend using fungicide. For a detailed statistical analysis see
Appendix A-6.
Impact on yield with the use of pesticide:
The next analysis considered if there was a significant difference in yield with the use of
different pesticides. As stated in Exhibit 9, the average yield when using root worm was 43.13
9. Wheat Analysis
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bushels, joint worm 41 bushels, both pesticides at 57 bushels, and the use of both pesticides was
70 bushels. The results are shown below in exhibit 9.
Type of Pesticide # of plots Average (yield per acre)
Root Worm 32 43.1
Joint Worm 41 45.2
Neither 57 33.9
Both 70 62.2
Exhibit 9 – Average wheat yield with the use of different pesticides
The differences show about are all significant except the difference seen between the use of root
worm and joint worm. To explain further, there is no value added in choosing between the two
pesticides, there is a not a significant difference. We would suggest using both of the pesticides if
the cost of doing so does not out weight the valued added in the increase of yield per acre. The
use of both pesticides together greatly increases the amount of yield in wheat. See Appendix A-7
for a detailed statistical analysis.
Correlation between the use of fertilizer and yield:
This analysis investigated whether it is worth spending the extra money on fertilizer. Fertilizer
can be very expensive so this analysis was extremely important to complete in order to see if
there is a strong correlating1 in the use of fertilizer and the amount of yield produced. As seen in
exhibit 10 below there is a strong correlation between the use of fertilizer and the amount of
yield produced; the analysis identified a .717 correlation.
1 Correlation is a numeric measure of the strength of association between two variables. Correlation coefficients
vary between -1 and 1, with 0 suggesting no association and 1 and -1 suggesting strong associations.The sign of the
correlation coefficients specified whether the variable move in opposite directions (negative correlation) or whether
the variables raise and fall together(positive correlation).
10. Wheat Analysis
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0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120
YeildinBushels
Fertilizer (lbs per acre)
Scatter Chart for Fertilizervs. Yeild
Exhibit 10 – Correlation between fertilizer use and yield
The correlation is a positive correlation as seen above. Exhibit 10 does a great job of
demonstrating the increase in wheat yield with the increase in fertilizer used. If cost efficient,
using more fertilizer will produce a larger wheat yield will be significantly beneficial. From
looking at exhibit 10 the use of 60lbs to 80lbs of fertilizer would be the most cost efficient and
beneficial to wheat yield. For a detailed statistical analysis see Appendix A-8.
Correlation between rainfall and wheat yield:
The next analysis tested the strength of the correlation between the amount of rainfall and the
amount of yield per acre. This is also very important analysis to better understand the
relationship between the amount of rainfall and yield produced per acre. The analysis suggested
a correlation of about .68 for both rainfall and yield per acre. This fairly strong correlation
suggests a close, predictive relationship between these two variables; see exhibit 11. In summary,
the more rainfall the higher the wheat yield will likely be. This being said too much rain would
flood the crops and ruin them for no yield.
11. Wheat Analysis
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0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14
YieldBushels
Rain Fall (Inch)
Scatter Chart Rain vs. Yeild
Exhibit 11 – Correlation between rainfall and wheat yield
In summary the results of this analysis in exhibit 11 show that an increase in rainfall will in turn
increase the amount of wheat yield. We recommend trying to plant in regions that have a good
amount of rainfall. See Appendix A-9 for a detailed statistical analysis.
Correlation between elevation and wheat yield:
This analysis compared elevation to amount of wheat yield. The correlation is negative with a
coefficient of -.45, this meaning that it is not a very strong correlation. Exhibit 12 outlines show
this negative correlation (the tendency for the data points to cluster along a straight downward
line), it also shows a vertical cluster between 2000 meters and 2500 meters, which explains that
the correlation is more complex than what the eye may see.
12. Wheat Analysis
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0
10
20
30
40
50
60
70
80
0 500 1000 1500 2000 2500 3000 3500
YeildinBushels
Elevation (Meters)
Scatter Chart for Elevation vs. Yield
Exhibit 12 – Correlation between elevation and wheat yield
In summary, the higher the elevation the lower the wheat yields per acre. The correlation
between elevation and yield is a complex correlation and it is considered moderate. For a
detailed statistical analysis refer to Appendix A-10.
Predicting wheat yield:
The next analysis was done with the goal of determining what variables would be significant in
predicting wheat yield in bushels per acre using a regression2 analysis. As detailed in Appendix
A-11 and A-12 rain, fertilizer, Indian brown seed, rocky soil, and the use of both pesticides were
found to be the most predictive numeric variables. The left over variables such as elevation,
fungicide, Monsanto 225 seed, Delkab droughtmaster seed, sandy soil, clay soil, fall/spring
2 The use of regression to make quantitative predictions of one variable from the values of other variables.
A regression analysis is used to help point out which variables in an equations have the most significance
in predicting an outcome. Variables are taken out of the equation if they have no significance, which in
turn makes the equation and accurate and simple as possible.
13. Wheat Analysis
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planting, joint worm/root worm/no pesticide were all irrelevant in regard to predicting wheat
yield.
This analysis determined that the following equation is fairly effective in predicting wheat yield,
with approximately 75% of the variation of total wheat yield effectively predicted.
Total yield = 16.50 + 1.71(rainfall) + .27(Lbs. of fertilizer) + 8.76(Indian brown) - 5.53(Rocky
soil) + 9.54(Both Pesticides)
“Indian brown” is set to 1 if Indian brown was used and 0 otherwise. Likewise, “Rocky soil” is
set to 1 if wheat was planted in rocky soil and 0 if it was not. Last “Both Pesticides” is set to 1 if
both pesticides (rootworm/jointworm) were used and 0 if they were not both used. Our equation
suggests that having a good amount of rainfall and fertilizer increases wheat yield. Also, it is
advantageous to use Indian brown seeds, with the addition of using both pesticides. Finally,
planting in rocky soil decreases the amount of yield by a predicted 5.53 bushels per acre. Please
refer to Appendix A-13 for a detailed statistical analysis.
Example estimated wheat yield with predetermined conditions:
In this analysis we examined two hypothetical growing situations and calculated an estimated
yield based on our equation above. Our first example supposes the following conditions: Indian
Brown seed, 5 inches of rainfall per year, and 50 pounds per acre of fertilizer, rocky soil, fall
planting, elevation 1500 meters, no fungicide, and no pesticide. With these variables we were
able to determine an estimate of 41.8 bushels per acre, as seen in our equation below:
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Total yield=16.50 + 1.71(5) + .27(50) + 8.76(1) - 5.53(1) + 9.54(0) = 41.8
Our second growing condition has the following conditions: Monsanto 225 seed, 10 inches of
rainfall per year, 30 pounds per acre of fertilizer, clay soil, spring planting, elevation 500 meters,
fungicide applied, and both pesticides applied. From the above variables we were able to
estimate 51.2 bushels per acre as seen in the equation below:
Total yield=16.50 + 1.71(10) + .27(30) + 8.76(0) – 5.53(0) + 9.54(1) = 51.2
Prediction of wheat yield in three regions of Afghanistan:
In the following analysis we researched three different regions in Afghanistan that could be
possible locations to grow wheat. We found the soil type along with the amount of rainfall for
each region; this information was found on the websites listed below. Other variables were
assumed such as 75 pounds per acre of fertilizer, the use of Indian brown seed (best seed), and no
fungicide or pesticides. The three regions we selected to use as a research and estimate tool are:
Kabul, Herat, and Nili. Starting with Kabul we found 13.22 inches of rainfall and rocky soil,
with this information and the assumed variables we found an estimate of 62.59 bushels per acre.
Second was Herat, we found they had 9.33 inches of rainfall and clay soil, again using these
variables and the assumed variables; we found an estimate of 61.46 bushels per acre. Last was
Nili, we found they had 5.4 inches of rain and rocky soil, once again using these variables and
the assumed variables, we were able to estimate 49.21 bushels per acre. Go to Appendix A-14
for a detailed statistical analysis.
Herat:
http://www.eldoradocountyweather.com/climate/afghanistan/Herat.html
http://upload.wikimedia.org/wikipedia/commons/8/87/Afghanistan_physical_en.png
http://soils.usda.gov/use/worldsoils/mapindex/afghanistan-soil.html
Kabul:
http://www.studentsoftheworld.info/pageinfo_pays.php3?Pays=AFG&Opt=climate
Nili:
http://www.worldweatheronline.com/Nili-weather-averages/Bamian/AF.aspx
15. Wheat Analysis
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Summary and Conclusion:
We were assigned by the U.S. government to conduct a statistical analysis in order to better
understand the factors that impact wheat yield under various growing conditions. This analysis
was performed to aid the United Nations with their continued effort in post-war assistance to
Afghani farmers. The data was provided by a major seed-grain company, 200 samples of various
strains of wheat seeds, and tested plus recorded growing conditions.
We applied numerous statistical analysis tools to the data in order to gain an understanding of the
degree to which various factors are related with advantageous outcomes, and we were successful.
The large sample size, combined with the statistical approaches used, allow us to state that all
assertions made are made with a 95% degree of confidence.
Recommendations:
Many recommendations to the U.S. government and United Nations were included within the
main body of the report. For convenience, they are summarized here:
Planting in the spring did first show up as being advantageous over planting in the fall,
but after our research of three different regions we found that most of the rainfall comes
in the fall season. It would be extremely hard to have good crop yields in the spring with
the little amount of rainfall. (see page 6);
Do not plant in rocky soil; wheat yields are much smaller in rocky soil. (see page 7);
Out of the three seed options to choose to buy from Indian brown will provide the most
yields. Depending on cost, Indian brown is by far the best option. (see page 7);
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Coating the seeds in fungicide is recommended; there is a significant difference in total
yield output with the use of fungicide compared to not using of fungicide. (see page 7);
We would suggest using both of the pesticides if the cost of doing so does not out weight
the valued added in the increase of yield per acre. The use of both pesticides together
greatly increases the amount of yield in wheat. (see page 8);
If cost efficient, using more fertilizer will produce a larger wheat yield which will be
significantly beneficial. (see page 10) ;
We recommend trying to plant in regions that have a good amount of rainfall. The more
rainfall the larger the wheat yield up to the extent of flooding. (see page 11);
Planting at lower elevations should help produce larger wheat yields. Through our
research we found that normally the lower the elevation the better the soil is to plant. The
higher the elevation the more rocky, which we have stated greatly reduces yield. (see
page 12);
Our equation suggests that having a good amount of rainfall and fertilizer increases wheat
yield. Also, it is advantageous to use Indian brown seeds, with the addition of using both
pesticides. Lastly, planting in rocky soil decreases the amount of yield by a predicted
5.53 bushels per acre. (See page 13);
Out of the three regions we researched and estimated, wheat yield for Kabul had the
greatest estimated wheat yield. This in turn suggests that planting in Kabul would
produce more yield than Herat and Nili. (see page 14).
17. Wheat Analysis
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In conclusion, we recommend purchasing Indian brown seed as Indian brown significantly
increase the amount of wheat that is produced compared to the other seeds. We would also
recommend being careful where to plant these seeds as there are many growing conditions that
are extremely important to avoid. An example of one of these would be rocky soil, which would
also take out planting at high elevations since these two things go hand in hand. Also, based on
our research of the three regions in Afghanistan, it is necessary to plant the seeds in the fall, the
reason being, there is not enough rainfall in spring to have a successful yield.
At last, the success of the U.S. government and United Nations post-war assistance to Afghani
farmers will be up to the Afghani. Using the analysis we have provided and executing on the
recommendations given will ensure a successful post-war assistance. We believe this analysis
has been very beneficial to our company, U.S. government, and United Nations. We thank you
for your time and know our statistical analysis has provided the opportunity to help with the
post-war assistance, and save thousands upon thousands of dollars in mistakes that most likely
would have been made.
