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The software ALPHANAL introduced in the section on randomization can also be used for the analysis of replicated trials regardless of whether the incomplete blocks and/or the replications are physically adjacent to each other.

In this case, open the directory ALPHANAL and click ALPHANAL.exe. The programme starts by asking the “plan file name” (Figure 35), i.e. the name of the randomization file that has been stored at the time it was generated.

FIGURE 35

The first steps in using ALPHANAL for data analysis of replicated trials in incomplete blocks.

FIGURE 36

An example of a data file (*.txt) used in ALPHANAL.

Note that the programme asks for the driver identifier and extension, and therefore it is convenient to store the file in the “ALPHANAL” directory as this avoids typing the drive identifier. After entering the name of the randomization file, the programme asks for the data file name. Also in this case, and for the reasons given above, it is convenient to have the data file in the same directory as the randomization file.

Before proceeding, in Figure 36 we give an example of the format of a data file needed to run ALPHANAL. The file is much simpler that those we have seen so far. As show in Figure 36 the data file is a txt file with an identifier in the first row (in this case, taken from a Stage 3 trial, kernel weight in Farmers 1 in location 07 abbreviated as kw07F1 followed by the data in a single column. Additional traits, as in this case, can be added below each other.

Note however that while the programme can analyse several traits all belonging to the same trial, is not able to analyse trials with different randomizations because it can open only one randomization plan at the time. Therefore, in the case of trials such as those in Stages 2, 3 and 4 planted in a number of farmers’ fields each with a different randomization, each trial has to be analysed separately.

After entering the data file name and extension, there is the option to send the output to the screen, to a printer or to a file. Assuming the output was sent to the screen, it will appear as in Figures 37 and 38.

The first part of the output (Figure 37) describes the structure of data using the information from the randomization file, the levels of the various factors (in this case replications, incomplete blocks and treatment (= entries), followed by the variable name and the raw data.

In the second part of the output (Figure 38) the adjusted means and their ranks are listed by entry number together with the mean of the original values and the original data.

This is followed by the standard statistics and the analysis of variance. Where the data file contains more variables, the outputs for the various variables appear one after the other.

Importing the results of the analysis

The results of the analysis of unreplicated trials and of the replicated trials in rows and columns are stored, as already mentioned, in the files ReportSPUR.txt and ReportSPIB.txt in their respective directories.

The two files have a very similar structure and will be described together, underlining the differences between them.

The two files have a header including the date and the time of the analysis:

FIGURE 37

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This is followed by a description of the file which has just been analysed. Here it has to be noted that the program has been designed to analyse a series of trials with similar structure and this is the reason for the presence of the column “trial”.

This section in the case of the ReportSPUR.txt is as follows:

FIGURE 38

The second (and last) part of the output file of the analysis of incomplete block conducted with ALPHANAL.

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The ReportSPIB.txt is only slightly different:

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The second section (identical in the two files) is a summary of the results. In this section and for each trial and for each variable within each trial, it gives the model selected by the programme as the best model, the efficiency (in %) over the RCB design, the heritability and the standard error of the heritability. Below this line the file gives for each entry (“Genotype”) the Best Linear Unbiased Estimates (BLUEs), the Best Linear Unbiased Predictors (BLUPs) and the Unadjusted means.

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Finally the report gives the Average Standard Error (Av SE), the Average Standard Error of the Difference (Av SED) and the Coefficient of Variation (CV%) for the BLUEs, the BLUPs and the Unadjusted means.

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In the case of replicated trials without spatial analysis, the results are stored in two report files, ReportRCBDmeans.txt with the means and statistical parameters, and ReportRCBDAnovas.txt with the analysis of variance for each variable.

The first file has the following structure:

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After a description of the structure of the file just analysed, the ReportRCBDmeans.txt file lists the means for each variable followed by the Standard Error of the mean (SE mean), the Standard Error of the difference (SE difference), the Least Significant Difference at 5% probability (LSD at 5%), the Grand mean, and the Coefficient of Variability (Exp. error CV%).

At the bottom of the file, the ReportRCBD.txt lists the statistics derived from the Analysis of variance reported separately in the file ReportRCBDAnovas.txt.

All the information available in the Report files should be imported into the same Excel®

files from which we copied the data. This can be done in several ways using various importing features of Excel®_.

In the case of the Spatial Analysis, we usually import in separate sheets the Models (this includes Efficiency, Heritability and its standard error), the BLUEs and the BLUPs as shown in Figures 39 to 41. To show an example of these three sheets we will use the file of the Stage 3 trial shown in Figure 30.

Figure  39 gives an example of the sheet “models” where we collect the spatial models used in the analysis, the efficiency of the design over the RCBD, the heritability and its standard error and for each trial and each variable from the Report files. It will be recalled that in this case “Trial” stands for Farmer. For each spatial model both the number (as in Table  4 from Singh et al., 2003) and the name of the model are given. It will be noticed that the efficiency of the design is often higher, in some cases much higher, than the RCBD, and that in one case the heritability was zero.

The BLUEs and the BLUPs are imported in two separate sheets (Figure 40 and 41), which are very similar, containing for each of the entries tested, the entry number, the unique identifier, Name, Pedigree, row type and seed colour, and then for each variable and each

FIGURE 39

Sheet used to import the spatial models used in the analysis, the efficiency of the design over the RCBD, the heritability and its standard error. Data are from a Stage 3 trial planted by 3 farmers.

TABLE 4.

List of models used to describe spatial variability and analyses

Model No. Block Trend Errors Abbreviation

1 Complete I RCB

2 Complete AR RCBAr

3 Complete ARAR RCBArAr

4 Incomplete I Lat

5 Incomplete AR LatAr

6 Incomplete ARAR LatArAr

7 Complete L I RCBL

8 Complete L AR RCBLAr

9 Complete L ARAR RCBLArAr

10 Incomplete L I LatL

11 Incomplete L AR LatLAr

12 Incomplete L ARAR LatLArAr

13 Complete LCS I RCBLCS

14 Complete LCS AR RCBLCSAr

15 Complete LCS ARAR RCBLCSArAr

16 Incomplete LCS I LatLCS

17 Incomplete LCS AR LatLCSAr

18 Incomplete LCS ARAR LatLCSArAr

KEY I: independent plot errors. L: fixed linear trend along rows. CS: random cubic smoothing spline in column number. AR: first order auto-regressive errors along rows; ARAR: first order auto-regressive error along rows and along columns. Lat: Lattice block model. RCB: randomized complete block model (non-spatial).

FIGURE 40

An example of a sheet used to import the Best Linear Unbiased Estimates (BLUEs) of the genotypic values of the entries tested in a Stage 3 trial grown by 3 farmers.

FIGURE 41

An example of a sheet used to import the Best Linear Unbiased Predictors (BLUPs) of the genotypic values of the entries tested in a Stage 3 trial grown by 3 farmers.

farmer, the respective BLUEs and BLUPs. In both cases the bottom rows of the sheets show mean, minimum and maximum, the Average Standard Error (Av SE), the Average Standard Error of the Difference (Av SED) and the Coefficient of Variation (CV %). These statistics can be used to statistically compare any two varieties.

In the case of Stage 1 trials, such as the one shown in Figure 20, the three sheets (Models, BLUEs and BLUPs) will be the same as described above, with the difference that in the sheet “Models” the column Trial indicate the village and that in the sheets “BLUEs” and “BLUPs” there will be only one value for each genotype and each variable as the trial is usually grown by only one farmer.

Eventually, in the case of the trials in which the replications are planted by different farmers, the full report as shown in page 68 is imported as such in one sheet of the Excel® _file.

The same applies for the output files produced by ALPHANAL.