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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 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 Xaxis: Environmental Index, EI Y1axis: 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 rightclick. Choose the Properties command. Choose OK when finished making the changes. Change fonts for titles: Main (24 points) Subtitle (14 points) Xaxis and Yaxis (12 poin C, 12. _p c? fv Change: Xaxis scale (10 points) r r  Xaxis major and minor grid style color to white Yaxis scale (10 points) Yaxis 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, rightclick, 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 rightclick 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 (Yaxis) and pH is the independent variable (Xaxis). 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: Xaxis (C4..C11) Legend (A3) 1st. series (A4..A11) Change titles: Main: Environmental Characterization Subtitle: Maize, Manaus, 1989 Xaxis: pH Yaxis: 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$15) 0.15 15.00 1.39 3.58 3.68 0.10 10.00 1.89 341 3.56 0.05 5.00 2.92 3.07 3.33 0.03 2.50 4.30 2.62 3.01 0.01 1.00 6.97 1.75 2.39 0.01 0.50 9.93 0.78 1.71 0.00 0.05 31.60 6.34 3.30 31. To compare the risk associated with these two treatments, graph the probabilities. 3 la. Use one of the previous graphs as a basis for these and edit it using the graphics menu. To change main title, subtitle, and axis titles use GraphicsTitles. Enter text in the appropriate edit fields, and choose OK. Main: Risk Estimation Subtitle: Land Class PF1 Xaxis: Risk (%time below Yaxis value) Y1axis: Yield (t/ha) Click OK 3 lb. Series for this graph will be: Xaxis (14..I11) , Legend (K3..L3) 1st. series (K4..K11) 2nd. series (L4...LI1) Make additional changes if needed. STEP 5 c Define final recommendation domains. 32. View the risk analysis graph and decide final recommendation domain. Figure 12. 1 2 3 4 5 6 7 8 9 10 11 13 14 :J  Compare results using alternative evaluation criteria. 33. Go to a new page in your notebook. In cell Al type the name for this table: Alternative Evaluation Criterion, kg /$ 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 15 of this exercise using the alternative criterion. GOOD LUCK! , ,STEP 6 