Calculating adaptability analysis using Quattro Pro 6.0

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Title:
Calculating adaptability analysis using Quattro Pro 6.0
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13 leaves : ; 28 cm.
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Creator:
Bastidas, Elena P
Hildebrand, Peter E
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State University System of Florida
Place of Publication:
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Subjects / Keywords:
Quatro Pro   ( lcsh )
Agricultural systems -- Research -- Data processing   ( lcsh )
Agriculture -- Research -- On-farm   ( lcsh )
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non-fiction   ( marcgt )

Notes

Statement of Responsibility:
Elena Bastidas, Peter E. Hildebrand.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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oclc - 624802941
ocn624802941
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AA00007206:00001

Full Text







CALCULATING ADAPTABILITY ANALYSIS
USING QUATTRO PRO 6.0

Elena Bastidas
and
Peter Hildebrand



INTRODUCTION

Adaptability Analysis (AA) is a comparison of the response of different experimental treatments
to environment. It is used with multilocational testing to assess potential interaction of treatment by
environment. Environment is measured by the mean yield of all treatments at each location, and is
expressed as an environmental index, "EI". The response of each treatment is estimated from a linear
(Y, = a + bEI) or quadratic (Y, = a + bEI + cEI2) equation.


STEP 1. Calculate a measure of environments: Environmental Index, EL

1. Type in Table number and name in cell Al. (Refer to Table 1 in the AA guide)

2. To get lines under table title in cell A2 touch the back slash (\) and equal (=) keys followed by
. Copy.to other cells.

3. Columns are treatments and rows are farms. Write column names starting in cell A3.

4. Enter data in matrix.

5. In first blank column (F), label row 3 as "EI" for environmental index. In row 4 of this column,
using @AVG(B4..E4) calculate farm mean which is the environmental index for first farm listed
in cell A4. Then using this cell as source, copy this function to remaining cells in same column.

6. At foot of matrix, leave one blank row for convenience, and in column A label Col Avg. In
column 2 of this row, calculate the mean for the first treatment using @AVG(B4..B11). Copy
to other cells in the row.












Figure 1. Initial matrix.

SA A B C D E F G


Table 1. Maize Trials (t/ha), Manaus, Brazil, Singh, 1990.


FP PCW
0.15 0.15
0 1.1
0 0
0.25 1.1
0.15 0.7
2.2 1
2.5 1.4
0.2 0.7


TSP


1.3
3.4
0.15
1.6
3.4
4.2
4.5
3.5


2.85
4.4
0.65
2.8
3.6
3.6


El
@AVG(B4..E4)
@AVG(B5..E5)
@AVG(B6..E6)


1
2\
3
4
5
6
7
8
9
10
11
12
13 |


7. Adjust column width, center align column heading, and fix decimal points to two.

Figure 2. Column width adjusted, aligned column heading, and decimal points fixed to two.


A A B C I E F


Table 1. Maize Trials (t/ha), Manaus, Brazil, Singh, 1990.


FARM
1
2
3
4
5
6
7
8

Col. Avg.


FP
0.15
0.00
0.00
0.25
0.15
2.20
2.50
0.20


PCW
0.15
1.10
0.00
1.10
0.70
1.00
1.40
0.70


TSP
1.30
3.40
0.15
1.60
3.40
4.20
4.50
3.50


CM
2.85
4.40
0.65
2.80
3.60
3.60
4.00
4.00


0.68 0.77 2.76 3.24


El
1.11
2.23
0.20
1.44
1.96
2.75
3.10
2.10

1.86


8. Sort entire data matrix using /BlocklSort command. Range to sort will be (A4..F11) and the
primary sort (1st. Sort key) will be the column with the El (F4..F11). Sort in Descending order
(blank box under ascending). Click OK. The purpose of this sort is to facilitate partitioning
the data set into recommendation domains for calculating the distribution of confidence
intervals for risk analysis.


FARM


Col. Avg. @AVG(B4..B11)


1
2
3
4
5
6
7
8
9
10
11
12
13












Figure 3. Matrix sorted by EI.

A A B C D E F
1 Table 1. Maize Trials (t/ha), Manaus, Brazil, Singh, 1990.

3 FARM FP PCW TSP CM El
4 7 2.50 1.40 4.50 4.00 3.10
.5 6 2.20 1.00 4.20 3.60 2.75
6 2 0.00 1.10 3.40 4.40 2.23
7 8 0.20 0.70 3.50 4.00 2.10
8 5 0.15 0.70 3.40 3.60 1.96
9 4 0.25 1.10 1.60 2.80 1.44
10 1 0.15 0.15 1.30 2.85 1.11
11 3 0.00 0.00 0.15 0.65 0.20
12
13 Col. Avg. 0.68 0.77 2.76 3.24 1.86

C STEP 2 Relate treatment response to environment.

STEP 2 a Plot observations

9. To graph the observations choose /GraphicsjNew Graph. The New Graph box menu appears.

10. Enter a name for the graph (FP for the first treatment observations). Assign data blocks to X-
Axis (F4..F11), including the first series (B4..B11) and Legend (B3) for first treatment (FP).

11. Choose O.K. A graph window opens and displays the new graph. Once you created the graph
you can change its type and edit it.

1 la. To add a main title, subtitle, and axis titles to the graph use GraphicsiTitles. Enter
text in the appropriate edit fields, and choose OK.
Main: Researchers' Criterion
Subtitle: Maize, Manaus, 1989
X-axis: Environmental Index, EI
Y1-axis: Yield (t/ha)
Click OK

1 lb. To edit different parts of the graph use the object inspector. Select the object you
want to change and right-click. Choose the Properties command. Choose OK when
finished making the changes.
Change fonts for titles:
Main (24 points)
Subtitle (14 points)
X-axis and Y-axis (12 poin








C-,


12.
_p c? fv


Change:
X-axis scale (10 points) -r r- -
X-axis major and minor grid style color to white
Y-axis scale (10 points)
Y-axis scale to High of 5 (because the highest data point is less than
5) and Low O, increment of 1, number of minors, ).

To delete line connecting data points click on the line and right click, change
line to no line.

Make copies of the graph you created as a basis for the other graphs. To copy, move from the
graph window to the notebook using /Window. Click the Speed Tab button to display the
Object page. Select the graph, click the copy icon once and click the paste icon as many times
as graphs you want to create (in this case 3 times). To change the name of the graphs select
the graph, right-click, choose properties, and modify the name (PCW, TSP AND CM).


13. To edit a graph double click the graph icon. Make changes following the Graphics menu.
Follow the same procedures to graph all treatments observations.


STEP 2b View Observations

14. View observations and tentatively decide on the type of relationship, linear or quadratic, of each
treatment to environment. To view the FP observations go to /Windows and double click FP.

15. Return to notebook using /Windows, Speed Tab.

16. To confirm your decision regarding shape of relationship, Calculate linear and quadratic
regressions using the formulas: y = a + bEI for linear or y = a + bEI + cEI^2 for quadratic
relationship.

16a. Add an additional column title to the data matrix in column G for El square (E^2). In
cell G4 type the formula (+F4A2). Copy this formula to the rest of the column.











Figure 4. Data matrix for regressions.

SA A B C D E F G
1 Table 1. Maize Trials (t/ha), Manaus, Brazil, Singh, 1990.

3 FARM FP PCW TSP CM El El^2
4 7 2.50 1.40 4.50 4.00 3.10 9.61
5 6 2.20 1.00 4.20 3.60 2.75 7.56
6 2 0.00 1.10 3.40 4.40 2.23 4.95
7 8 0.20 0.70 3.50 4.00 2.10 4.41
8 5 0.15 0.70 3.40 3.60 1.96 3.85
9 4 0.25 1.10 1.60 2.80 1.44 2.07
10 1 0.15 0.15 1.30 2.85 1.11 1.24
11 3 0.00 0.00 0.15 0.65 0.20 0.04
12 .
13 Col. Avg. 0.68 0.77 2.76 3.24 1.86



16b. Use /ToolslNumeric Toolslkegressioi command. The independent variable for all
linear regressions will be the column with the El (F4..F11). The dependent variables
will be the columns with the yield data. For the first treatment, the Y values will be
(B4...B 11). Output address will start in cell A18. Mark compute intercept. Click
OK. In cell A18 type FP to identify it from the other regression outputs. For this
exercise the linear regressions will be placed below one another separated by a space
between each regression output (A28 for PCW linear regression output, A38 for TSP,
etc.) Both column F and G will be the independent variable for all quadratic
regressions (F4..G11). The quadratic regression outputs will start in cell F18 for FP,
F28 for TSP, etc.


16c. After regressions for all treatments have been calculated, move to the next available
column in the spreadsheet, leave a blank column and label the next cell in row 3 as
EST FPL for estimated linear regression for FP. This column will be the estimated
values of Y taken from the regression equation for treatment 1. In row 4 of this
column write the formula for estimating Y for the environmental index value "El" for
the corresponding farm. The constant for the first regression is in cell (D19), and the
regression coefficient "b" is in (C25). The formula:

+$D$19+$C$25*$F4 -

Then copy this formula down the column for the other farms. Repeat this procedure
for the quadratic regression for FP with the following formula. The constant for the
quadratic regression is in cell (119), the regression coefficient "b" is in (H25) and the
regression coefficient "c" is in (125) column F contains the environmental index and

















column G contains the El square, then the calculation will appear in cell J4 as:


+$I$ 19+$H$25 *$F4+$I$25*$G4


Figure 5. Regression outputs and estimated responses.


A B I C I D I E I F I


Table 1. Maize Trials (t/ha), Manaus, Brazil, Singh, 1990.


FARM FP
7 2.50
6 2.20
2 0.00
8 0.20
5 0.15
4 0.25
1 0.15
3 0.00

Col. Avg. 068




FPL Kegressio
Constant
Std Err of Y Est
R Squared
No. of Observations
Degrees of Freedom

X Coefficient(s)
Std Err of Coef.


PCW TSP CM El
1.40 4.50 4.00 3.10
1.00 4.20 3.60 2.75
1.10 3.40 4.40 2.23
0.70 3.50 4.00 2.10
0.70 3.40 3.60 1.96
1.10 1.60 2.80 1.44
0.15 1.30 2.85 1.11
0.00 0.15 0.65 0.20

0.77 2.76 3.24 1.86


n Output:


0.813182
0.313017


-0.83203
0.768256
0.529375
8
6


G I


EI^2
9.61
7.56
4.95
4.41
3.85
2.07
1.24
0.04


FPQ Regression Output:
Constant
Std Err of Y Est
R Squared
No. of Observations
Degrees of Freedom


X Coefficient(s)
Std Err of Coef.


H I I I J I K I


L I


Table 2. Estimated Responses.

ESTFPL ESTFPQ ESTPC ESTPC
+$D$19+$C$25*$F4
1.40422 +$1$19+$H$25*$F5+$1$25*$G
0.977299 0.666438
0.875651 0.482707
0.763839 0.304231
0.336918 -0.14952
0.072634 -0.24956
-0.66939 0.208803


0.45493
0.490169
0.840348
8
5


-1.36157 0.654664
0.724919 0.209777


17. To graph the estimates follow the procedure in 12, 13.


Use speed tab to go the graphs. Copy FP graph. Rename the new graph FPLQ (linear,
quadratic). Double click to edit the graph. Add the estimated linear series (I4..I11) in second
series and quadratic (J4..J11) responses in third series.


Add legends by selecting the appropriate line and right click. After entering legends, the line
style and symbols can be modified. To delete the symbols on the regression line click auto size
and change the weight to 0.


Looking at the graph decide on type of relationship. Repeat this process when necessary.



STEP 3 Assess interaction of treatments with environments. j


18. Graph all 4 selected treatment responses in a single graph.
i


IA


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26


__~-_ ,,














Use different types of lines for each treatment. To edit lines use the object inspector. Select
and right-click the objects you want to change and choose the Properties command.


STEP 4 Characterize the environments

19. Go to a new page in your notebook. In cell Al type the name for this table Environmental
Characteristics. For column titles refer to Table 3 of the AA guide.

20. Copy the El as values (F4..Fll) from first page to (A4..All) of your new page using
BlocklValues command.

21. In column B type in the land class corresponding to each of the Els. Enter pH, ECEC, Al Sat.
and P2 O data in the following columns.


Figure 6. Environmental Characteristics data.


B A B C D E F
1 ENVIRONMENTAL CHARACTERISTICS
2 ======= ======= ======= ======= ======= ===
3 El LND CLS pH ECEC Al sat P205
4 3.10 PF1 5.20 4.21 58.30 7.40
5 2.75 PF1 5.10 3.45 69.10 7.10
6 2.23 SF1 4.60 2.29 91.70 4.50
7 2.10 PF1 4.50 2.26 79.20 6.80
8 1.96 PF2 4.60 2.45 80.00 5.00
9 1.44 SF2 4.10 3.12 94.80 2.80
10 1.11 SF2 4.20 1.99 90.70 2.00
11 0.20 WL 3.90 1.35 94.80 0.10



22. You can relate the El to any of the environmental characteristic by regression. As an example,
relate El to pH. In this process El becomes the dependent variable (Y-axis) and pH is the
independent variable (X-axis). For this reason the next step is to sort the entire data matrix by
independent variable (pH).













Figure 7. Environmental Characteristics data sorted by pH.

B A B C D E F
1 ENVIRONMENTAL CHARACTERISTICS
2 -------======= ======= ======= =======---------------------
3 El LND CLS pH ECEC Al sat P205
4 3.10 PF1 5.20 4.21 58.30 7.40
5 2.75 PF1 5.10 3.45 69.10 7.10
6 1.96 PF2 4.60 2.45 80.00 5.00
7 2.23. SF1 4.60 2.29 91.70 4.50
8 2.10 PF1 4.50 2.26 79.20 6.80
9 1.11 SF2 4.20 1.99 90.70 2.00
10 1.44 SF2 4.10 3.12 94.80 2.80
11 0.20 WL 3.90 1.35 94.80 0.10


22a. To graph, follow the same procedures as in step 2 (View observations).
Graph the observations for pH. Series for this graph will be:
X-axis (C4..C11)
Legend (A3)
1st. series (A4..A11)
Change titles:
Main: Environmental Characterization
Subtitle: Maize, Manaus, 1989
X-axis: pH
Y-axis: Environmental Index, EI
Make other changes using the object inspector if necessary.

22b. Decide on the type of relationship by looking at the plot observations. Skip one
column and in column H1 construct a matrix for regression calculations and graph.
Type in table name: Data for graph and regression. In row 3 type column names pH,
pH^2 (if needed) and Est EI.
Copy data for the pH column to H3.
Calculate the pH^2 (if needed).

22c. Do regression, using ToolsJNumeric ToolsjRegression
independent variable (H4..H11) if linear or (H4...I11) if quadratic
dependent variable (A4..A11)
output (A16)
Calculate the estimate EI using the formula:
(+$D$17+$c$23*$H4) if linear
(+$D$ 17+$c$23 *$H4+$D$23 *$I4) if quadratic














Figure 8. Regression and graph data.

B A B C D E F G H | I J | K
1 ENVIRONMENTAL CHARACTERISTICS DATA FOR GRAPH AND REGRESSION
2 ======= ======= ======= ======= ======= ======= ======= ===="== ======= r.== =
2----------------------------------------
3 El LND CLS pH ECEC Al sat P205 pH pH^2 Est El
4 3.10 PF1 5.20 4.21 58.30 7.40 5.20 27.04 2.96
5 2.75 PF1 5.10 3.45 69.10 7.10 5.10 26.01 2.88
6 1.96 PF2 4.60 2.45 80.00 5.00 4.60 21.16 2.18
7 2.23 SF1 4.60 2.29 91.70 4.50 4.60 21.16 2.18
8 2.10 PF1 4.50 2.26 79.20 6.80 4.50 20.25 1.99
9 1.11 SF2 4.20 1.99 90.70 2.00 4.20 17.64 1.28
10 1.44 SF2 4.10 3.12 94.80 2.80 4.10 16.81 1.01
11 0.20 WL 3.90 1.35 94.80 0.10 3.90 15.21 0.40
12
13
14
15
16 Regression Output:
17 Constant -26.7743
18 Std Err of Y Est 0.266035
19 R Squared 0.941255
20 No. of Observations 8
21 Degrees of Freedom 5
22
_23 X Coefficient(s) 10.71749 -0.96135
24 Std Err of Coef. 5.106889 0.557792




22d. Graph the estimated response. Add the additional series (J4..J11) to the pH
observations graph.



STEP 5 Define recommendation domains.

STEP 5 a Tentative recommendation domains.

23. Go to a new page in your notebook. In cell Al type the name for this table: Recommendation
Domains and Risk Analysis. Leave a blank row.

24. Copy the El and land class data from second page (A3..B11) to third page (A3..Bll)using
BlocklValues command.

25. In the new page sort the El and land class (A3..B11) by environmental index. /BlocklSort
because we are going to copy data from the first page that is already sorted by El

26. Copy treatment titles and data from first page (B3..E11) to third page (C3..F11). Block the
source and do a copy and paste.













Figure 9. Recommendation domains and risk analysis data.


C A B C D E F
1 RECOMMENDATION DOMAINS AND RISK ANALYSIS
2 ======= ======= ======= ======= =======
3 El LND CLS FP PCW TSP CM .
4 3.10 PF1I 2.50 1.40 4.50, 4.00
5 2.75 PF1- 2.20 1.00 4.20- .3.60 -
6 2.23 SF1 0.00 1.10 3.40 4.40
7 2.10 PF1- 0.20 0.70 3.50- 4.00 ,
8 1.96 PF2 0.15 0.70 3.40 3.60
9 1.44 SF2 0.25 1.10 1.60 2.80
10 1.11 SF2 0.15 0.15 1.30 2.85
11 0.20 WL 0.00 0.00 0.15 0.65

27. Sort entire data matrix by Land Class in ascending order. y= 4 '

Figure 10. Recommendation domains and risk analysis data so~ed by land cl

S A B C D E F
1 ENVIRONMENTAL CHARACTERISTICS
2 ======= -====== ==--=== -- -----------
3 El 'IND CLS p ECEC Al sat P205
4 2.10 PFI 4.50 2.26 79.20 ,6.80
5 2.75 PF1 5.10 3.45 69.10 7.10
6 3.10 PF1 .20 4.21 58.30" 7.40
7 1.96 4.0 2.45 80o0 5.00'
8 2.23 F1 4.60 2.29 .70 4,50
9 1.4 SF2 4.10 2 94.80 /2.80
10 1/1 SF2 4.20 1.9 90.70 '2.00
11 ,0.20 WL 3.90 1 5 94.80 0.10



STEP 5 b Determine risk associated with the new technology.

28. Decide on tentative recommendation domains. Refer to pages 11 and 12 of the AA guide. The
distribution of confidence intervals is calculated from the treatment values over all farms if there
is only one recommendation domain represented, or over the farms within a determined
recommendation domain. In this case the 3 observations in PF1 will represent one
recommendation domain and the other land classes will represent a second domain. If the data
set is going to be split, then calculations will be done for the observations within each
recommendation domain. The following example is to examine the risk associated with TSP
and CM when applied in PF1.

28a. Type: in cell A 13 Average of PF1, in (A14) STDS (Sample standard deviation) of
PF1, in (A15) Square root ofn.

28b. Calculate:
average of the PF1 values for TSP in cell (E13) using the function @AVG(E4..E6)










11

copy to (F13).
Sample Standard deviation in cell (E14) using @STDS(E4..E6) copy to (F14)
Square root of 3 (for the 3 TSP observations representing PF1) in cell (E15)
@SQRT(3).

29. In cell H1 type in the table name: Risk Analysis, and title columns (alpha; prob; t.df=3; TSP;
CM) for risk estimation. Refer to Table 4 in AA guide. "
fc---
29a. Enter:
alpha values starting in cell (H4)
probability values starting in cell (14)
"t" table values for degrees of freedom= 2 starting in cell (J4)

Figure 11. Risk analysis data.


C A B C D E F
1 RECOMMENDATION DOMAINS AND RISK ANALYSIS
2 ======= ======= ======= ===== -- --
3 El LND CLS FP PCW TSP CM
4 3.10 PF1 2.50 1.40 4.50 4.00
5 2.75 PF1 2.20 1.00 4.20 3.60
6 2.23 SF1 0.00 1.10 3.40 4.40
7 2.10 PF1 0.20 0.70 3.50 4.00
8 1.96 PF2 0.15 0.70 3.40 3.60
9 1.44 SF2 0.25 1.10 1.60 2.80
10 1.11 SF2 0.15 0.15 1.30 2.85
11 0.20 WL 0.00 0.00 0.15 0.65
12
13 AVG OF PF1 4.03. 4.00 -
14 STDS OF PF1 =. 0.57 af&A- O
15 SQUARE ROOT OF n = 1.73


30. Calculate the probability of values for PF1 below the confidence interval (measure of the level
of risk associated with the technology) in the tentative recommendation domain (PF1) for TSP
and CM using the formula: Y (t, s /n).

30a. In cell (K4) use the formula (+$E$13-$J4*$E$14/$E$15). Copy the formula to other
cells in the column. Copy the formula in to cell L4. Edit to modify it should be
(+$F$13-$J4*$F$14/$E$15). Copy the formula to other cells in the column.















Risk analysis graph data.


C A C D E F 0 H I J K L M N


RECOMMENDATION DOMAINS AND RISK ANALYSIS
" == = .=L = -=-== = = == == ---== .= =----- .-.===
El LND CLS FP PCW TSP CM
3.10 PF1 2.50 1.40 4.50 4.00
2.75 PF1 2.20 1.00 4.20 3.60
2.23 SF1 0.00 1.10 3.40 4.40
2.10 PF1 0.20 0.70 3.50 4.00
1.96 PF2 0.15 0.70 3.40 3.60
1.44 SF2 0.25 1.10 1.60 2.80
1.11 SF2 0.15 015 1.30 285
0.20 WL 0.00 0.00 0.15 0.65
AVG OF PF1 4.03 4.00
STDS OF PF1 0.57 0.40
SQUARE ROOT OF n 1.73


RISK ANALYSIS
ALPHA PROBE t,df=2 TSP CM
0.25 25.00 0.82 +$E$13-($J4'$E$14/$E$15)
0.20 20.00 1.06 3.69 +$F$13-($J5*F$$14/$E$15)
0.15 15.00 1.39 3.58 3.68
0.10 10.00 1.89 341 3.56
0.05 5.00 2.92 3.07 3.33
0.03 2.50 4.30 2.62 3.01
0.01 1.00 6.97 1.75 2.39
0.01 0.50 9.93 0.78 1.71
0.00 0.05 31.60 -6.34 -3.30


31. To compare the risk associated with these two treatments, graph the probabilities.


3 la. Use one of the previous graphs as a basis for these and edit it using the graphics
menu. To change main title, subtitle, and axis titles use Graphics|Titles. Enter text
in the appropriate edit fields, and choose OK.
Main: Risk Estimation
Subtitle: Land Class PF1
X-axis: Risk (%time below Y-axis value)
Y1-axis: Yield (t/ha)
Click OK


3 lb. Series for this graph will be:
X-axis (14..I11) ,
Legend (K3..L3)
1st. series (K4..K11)
2nd. series (L4...LI1)


Make additional changes if needed.



STEP 5 c Define final recommendation domains.


32. View the risk analysis graph and decide final recommendation domain.


Figure 12.


1
2
3
4
5
6
7
8
9
10
11
13
14
:J -












Compare results using alternative evaluation criteria.


33. Go to a new page in your notebook. In cell Al type the name for this table: Alternative
Evaluation Criterion, kg /$ cash cost. Leave a blank row .

34. Copy the Farm title and numbers (A3..A11) from 1st. page to new page using Block and Copy
and Paste commands. Copy also column titles for treatments (B3...G3).

35. Convert t/ha from page 1 to kg/$cash cost. First convert tons to kg by multiplying by 1000
then divide by the cash cost for FP/12. In cell B4 enter the formula +A:B4* 1000/12 copy
this formula to the other cells in the column. For PCW the formula vill be
gr -t e1:C4* 1000/208 because cash cost for PCW is 208. Copy this formula to the other cells
in the column. Repeat procedure for all treatments.


Figure 12.


Recommendation domains and risk analysis data sorted by land class.


FARM
7
6
2
8
5
4
1
3


B I C I D I E F G
TIVE EVALUATION CRITERION, kg/$cash cost.

FP PCW TSP CM El E^2
(+A:B4*1000/12) 3.10 9.61
183.33 (+A:C5*1000/208) 2.75 7.56
0.00 5.29 (+A:D6*1000/98) 2.23 4.95
16.67 3.37 35.71 (+A:E7*1000/127)
12.50 3.37 34.69 28.35
20.83 5.29 16.33 22.05
12.50 0.72 13.27 22.44
0.00 0.00 1.53 5.12


36. Repeat steps 1-5 of this exercise using the alternative criterion.


GOOD LUCK!


, ,STEP 6