1 Making the Most of Modified Stability Analysis:
2 Finding "Best Fit" Regressions and Determining Specific Adaptation
3 to Recommendation Domains 1
4 by
5 John T. Russellt, Peter E. Hildebrand*, and Clifton K. Hiebsch' 2
6
7 Abstract
8 Modified stability analysis is a simple, powerful and flexible tool in the analysis of onfarm trials. As currently
9 used, however, too much emphasis is often placed on the rote calculation and graphical representation of linear
10 regression on an environmental index, on the statistics (R2, etc.) associated with the regressions, and on finding the
11 "most stable" treatment, variety, practice, etc. In addition, final "recommendation domains" are sometimes simply
12 described as high or lowyielding (or "good" or "poor") environments, with little attempt to relate these
13 characteristics to environmental characteristics that farmers and extension personnel can identify prior to planting.
14 These practices tend to limit the practical usefulness of modified stability analysis. An example of modified stability
15 analysis of four years' data from onfarm sorghum variety tests in North Cameroon is used to illustrate several steps
16 to ensure getting the most useful information from the method. These steps include the plotting of data points, by
17 treatment, the comparison of various regression models, and the association of environmental index with non
18 experimental environmental variables. Emphasis is placed on identifying technologies specifically suited to
19 particular recommendation domains, and not broadly adapted to (or stable over) all environments.
20
21
22 Contribution from the Institute of Food and Agricultural Sciences, Univ. of Florida, Gainesville, FL, 32611,
23 Journal Series R03513. Research supported by Institute of Agronomic Research, Republic of Cameroon, and
24 United States Agency for International Development (ACPO/SAFGRAD and NCRE/IITA).
25 2 t Zanzibar Smallholder Support Project, Ministry of Agriculture, Box 159, Zanzibar Town, Tanzania.
26 t Corresponding author; Department of Food and Resource Economics, P.O. Box 110240, University of
27 Florida, Gainesville, Florida, 326110240, USA.
28 Department of Agronomy, University of Florida, Gainesville, Florida, 32611, USA.
1 Introduction
2 Modified stability analysis (MSA) is increasingly used by farming systems research
3 practitioners for the analysis of onfarm trials (Hildebrand, 1984; Hildebrand and Poey, 1985).
4 Its strength is that it allows, through simple regression analysis, evaluation of treatmentby
5 environment interactions of onfarm trial treatments and identification of specific adaptation of
6 treatments to particular groups of farmers and environments, i.e., to specific recommendation
7 domains (Hildebrand, 1990).
8 As currently employed, however, its usefulness is often limited. It is sometimes used
9 as if it were a simple stability analysis, to determine which variety, treatment, practice, etc., is
10 most "stable" across all onfarm trial sites. The implication is that the most broadly adapted,
11 or most stable variety or treatment is the superior one. In fact, the use of MSA to determine
12 specific adaptation to particular environments, rather than broad, general adaptability, is a major
13 reason the method is said to be "modified" stability analysis. Even when specific adaptation is
14 recognized as a goal of the analysis, frequently little more is drawn from the analysis than that
15 some treatments are better in "good" environments and others better in "poor" environments.
16 Further, too much emphasis is given to reporting, comparing, and discussing regression
17 statistics such as the slope (b) and coefficient of determination (R2) of the various regression
18 lines. These statistics are at best problematic, given the wellknown logical difficulties with this
19 type of regression of "dependent" variables on an independent variable directly derived from and
20 correlated to them (Freeman, 1973). They are also largely irrelevant to the purpose of
21 determining specific adaptation, at least in determining whether and how to delineate separate
22 recommendation domains.
3
1 Conversely, it is unusual that concerted attempts are made to identify and analyze the
2 important environmental characteristics that determine the goodness or poorness of the trial
3 environments. More seriously, too little attention is paid to determining which environmental
4 variables can be identified by farmers and extension personnel to decide the recommendation
5 domain into which a given farm environment will fall. If farmers knew before planting, whether
6 their field would be "highyielding" or "lowyielding," domains could reasonably be delineated
7 along these lines. But farmers can rarely predict, at least in the semiarid tropics where widely
8 variable rainfall causes large fluctuations in yield, whether the yield from any given field will
9 be above or below a given threshold of average yields. Recommendations to farmers should be
10 made on the basis of some characteristics) of their environment that farmers can identify
11 beforehand. Finally, users of MSA need to assess better the degree to which the environments
12 chosen for a trial are representative of the range of environments in the research domain.
13 After recommendation domains are decided upon, recommendations within a domain are
14 often made on the basis of differences between the predicted regression lines within each
15 domain. Those predictions, however, are based in part on data in the other domain(s). It is
16 preferable (both more honest and more accurate), once domains are determined by comparison
17 of the regression lines over environments, to analyze the results by recommendation domain.
18 This allows determination not just of mean differences among treatments within a domain but
19 also of the variability, error, and risk associated with those estimates of mean differences. The
20 present paper addresses these concerns and presents a number of guidelines and ideas for getting
21 the most information out of modified stability analysis of onfarm agronomic trials. It attempts
4
1 to illustrate an effective series of steps in MSA, using data from a series of multiyear onfarm
2 sorghum variety trials in North Cameroon.
3 The case used in this paper involves the development, testing, and extension of an
4 improved, shortcycle, photoperiodinsensitive sorghum variety, S35. This variety was tested
5 during four years of onfarm "preextension" tests. These tests, conducted in a vast area called
6 the Center North Zone, were a collaborative effort between the parastatal cotton development
7 agency SODECOTON and Cameroon's Institute of Agronomic Research (IRA). Despite
8 promising results in the onfarm tests and extensive recommendation of S35 by SODECOTON
9 throughout the Center North Zone, widespread adoption never occurred. It was remarked that
10 in some areas .35 was much in demand and well adopted. In other, more numerous areas,
11 however, the variety was poorly accepted by farmers. In effect, there were at least two
12 recommendation domains for the variety S35.
13 Analyses presented here were initially undertaken to determine if use of MSA could have
14 predicted and avoided the loss of time, expense and effort of extending this variety throughout
15 an entire research domain when in fact it was adapted to only a part of the domain (Russell,
16 1991). The results illustrated clearly the importance of the concerns with MSA listed above,
17 including finding the best fit of the response across environments, conducting adequate
18 environmental characterization, and ensuring representativeness of the sample of trial
19 environments.
1 Materials and Methods
2 A data set was compiled containing yield, date of seeding, and rainfall data from 239 on
3 farm varietal trials of an improved shortcycle sorghum variety compared to locally adapted
4 traditional varieties. These trials took place in North Cameroon from 1984 to 1987 (Testing and
5 Liaison Unit, 1986; Testing and Liaison Unit, 1987; Johnson, 1988). Each trial included other
6 varieties; the present analysis, however, concerns only the data on S35 and locals. Tests in 1984
7 were done in two geographical groups, while in 1985 there were in two groups with different
8 target ranges of seeding dates. In 1986 there was just one set of tests. All tests in 1984, 1985
9 and 1986 had one replicate per onfarm site. In 1987 one set of tests had a single replicate per
10 test site and another set had two replicates; for the analyses presented here, the yields of those
11 tests with two replicates were averaged over replicates.
12 The treatment called "locals" was not a single variety; each collaborating farmer selected
13 a locally adapted variety as a local check. Given the huge number of local sorghum types in
14 North Cameroon, and their diversity and local adaptation, this approach was preferable to
15 imposing one local type on all farmers, some of whom had never grown and would never grow
16 it.
17 Each onfarm test was conducted on a 0.25hectare field (i.e., 50 m X 50 m), with a
18 collaborating farmer chosen by the local SODECOTON field extension agent, and monitored
19 throughout the season by that agent. Betweenrow spacing was 0.80 m; withinrow spacing was
20 0.40 m between hills. Plants were thinned, beginning seven days after planting, to two per hill,
21 resulting in densities of 62,500 plants ha1'. In 1984, seeding dates were 20 June to 10 July,
22 choice of preceding crop was left to the farmer, and all sites were fertilized with 611325 kg
6
1 NPK ha'1. In 1985, fertilizer was reduced to just 46 kg N ha1, and all sites had cotton as the
2 preceding crop. Test conditions in 1986 and 1987 were as in 1985 except that recommended
3 date of seeding was 10 to 20 June, to avoid favoring the early maturing, improved varieties
4 (Johnson, 1988). Means and standard errors from analysis of variance of these trials, as well
5 as mean rainfall and mean date of seeding, are presented in Table 1. Standard errors for each
6 test group were calculated from the yields of all varieties tested in that group.
7 Modified stability analysis was performed both on the combined data set and also by
8 year. The goals of the analysis were 1) to examine the structure of the varietybyenvironment
9 interaction across farm environments; 2) to determine if more than one recommendation domain
10 existed for these varieties; 3) to determine those variables identifiable before planting which
11 could serve to predict in which recommendation domain a given farm environment would
12 belong; and 4) to determine whether MSAhad it been done in any one or two of the four years
13 of trialsmight have predicted the patterns of S35 adoption actually seen.
14 The yield data for S35 and locals were plotted against environmental index (EI), i.e., site
15 mean, over years and by year. Linear regressions of yield of each variety on EI were done, as
16 were quadratic regressions and quadratic regressions constrained to pass through the origin. The
17 resulting response lines were compared, both visually and statistically.
18 Based on the regressions of the two varieties, tentative recommendation domains based
19 on low or high average site yields were identified. Linear regression of EI on rainfall and date
20 of seedingthe only two nonexperimental variables common to the data sets of all four years
21 of trialswas done to see if recommendation domains could be established on the basis of date
22 of seeding or of average annual rainfall. Analysis of variance was performed, by
7
1 recommendation domain, with domains based on mean date of seeding. Assessment of risk
2 associated with the two varieties was done by calculating and graphing the distribution of lower
3 confidence limits for the mean of each variety in each domain. Finally, mean dates of seeding
4 were calculated, by SODECOTON sector (the smallest SODECOTON administrative division),
5 to determine if average date of seeding corresponded to known patterns of adoption.
6
7 Results and Discussion
8 Linear regression over four years
9 The difficulty with analyzing the results of these varietal trials derives from there being
10 an important varietybyyear interaction. In 1984, S35 yields were far higher than yields of
11 locals, and in lateseeded tests in 1985, S35 yielded over 20% more, although this difference
12 was not statistically significant at a = 0.05. In all other tests, yields of S35 and locals were
13 essentially the same (Table 1). The reason for these differences is that 1984 was a very low
14 rainfall year. On the basis of this fact, S35 had been extended as a "drought tolerant" variety.
15 The 1984 tests, however, were also characterized by generally late seeding dates (Table 1), in
16 part because of late onset of rains in many areas, but also because of logistical difficulties in this
17 first year of tests. The rainfall and dateofseeding factors are confounded in the general "year
18 effect" in combined analysis of variance of these trials.
19 A scatter plot of the data from the 19841987 tests is presented in Figure la; linear
20 regressions from modified stability analysis of S35 and locals yields in the 239 onfarm
21 environments are presented in Figure lb. The predicted responses of the two varieties converges
22 in the range of high Eis; they diverge as EI approaches zero. In the range 0 < EI < 250, the
8
1 predicted yield of locals is less than zero. We know this cannot be the case. First, yields
2 obviously cannot be negative; second, and more to the point for study of MSA, any "true"
3 picture of a response on El must have regression lines that converge at the origin. This axiom
4 derives simply from the nature of the calculation of El as the average of the yields of individual
5 treatments; that is, when El = 0, yield of each variety must also equal zero. The data points
6 themselves obviously converge at the origin (Figure la). Comparing Figures la and lb, another
7 shortcoming of the linear regressions is evident; they do not accurately reflect the divergence
8 and greatest difference between S35 and locals yields in the range 500 < EI < 1500.
9 Before investigating how better to estimate the response of these two varieties across EI,
10 a comment about statistics is appropriate. Note that the mean square deviations from regression
11 are identical for the two varieties. This again is an inescapable statistical artifact of the nature
12 of this analysis; when only two treatments are involved in MSA the calculated regression lines
13 will be "mirror images" of each other, on either side of an "average" response line with a slope
14 of one. This relationship is not so clear with three or more treatments, although the mean of
15 the slopes of all the regression lines will still equal one, but it must never be forgotten that all
16 statistics in this type of regression are highly dependent one on the others and of little intrinsic,
17 absolute value. Similarly, when there are only two treatments in MSA, the sum of the slopes
18 of the two linear regression lines will equal two (since the mean of their slopes equals one).
19 Given that R2 is a simple function of slope, when two regression estimates have equal
20 deviations from regression, i.e., the same "goodness of fit," the one with the greater slope will
21 have a proportionately greater R2 as well. For this reason alone, R2 is of dubious value for
22 comparing the fit of regression estimates of different treatments. If the purpose of MSA were
9
1 to arrive at statistics for regression lines or to do tests on those statistics, such as testing the
2 significance of the difference of the slope from zero, these mathematical anomalies would be
3 important. They are, however, of little concern since the purpose of MSA should not be to
4 generate statistics but to get as accurate a picture as possible of the underlying "structure" of the
5 treatmentbyenvironment interaction to determine if different treatments are specifically adapted
6 to different environments, i.e., if there are different recommendation domains.
7 When there are more than two treatments, the kind of scatter plot in Figure la, with all
8 data points plotted together, is often too cluttered to be of use. A better way to check the fit of
9 a proposed regression estimate is to plot the data and then superimpose the regression line for
10 each treatment separately, as in Figure 2. In Figure 2a it is evident that the simple linear
11 regression prediction overestimates yield of S35 in the range 0 < EI < 500 (as expected) and
12 underestimates yield in the range 500 < El < 2000. In general, though, the estimate is
13 reasonably good, i.e., deviations from predicted yields are more or less symmetrical about the
14 regression line, through the entire range where EI > 1000. An alternative method of checking
15 for goodness of fit is to plot deviations from regression against the environmental index.
16 It would appear, then, that some sort of curved response, bowing upward in the case of
17 S35 and downward for locals, would be a better estimate of the response of yields across EIs
18 than is a straight line. How does one find the best curved response? Two alternatives, the
19 response of yield calculated as a quadratic function of EI, and as a quadratic function of El with
20 the Yintercept restricted to pass through zero, were calculated. The three models were
21 essentially equal; for S35, R2 for the quadratic function was 0.842 and for the constrained
22 quadratic function was 0.839, compared to 0.842 for the linear model. While R2 is of little
10
1 value for comparing regressions of different treatments in MSA, as explained above, it can be
2 valuable for comparing different regression models for a given treatment. Visual comparison
3 of graphs of the three regression lines also showed little advantage of the quadratic functions
4 over the simple linear one.
5 For the purpose of determining potential recommendation domains, the linear regressions
6 in Figure lb, then, are as good as any. Given that we know mathematically that the lines must
7 converge toward the origin at very low Els, we can still posit that S35 yields are greater than
8 yields of locals in lowyielding environments, but that this difference becomes much smaller in
9 highyielding environments. Of particular significance is that the superiority of S35 represents
10 a large difference in proportional terms (50100% increases) in lowyielding environments, but
11 represents only a small proportional difference in highyielding ones.
12
13 Linear regression by year
14 Was it necessary to do four years of testing to arrive at this result? Could the same
15 relationship of S35 and locals yields have been seen using MSA with only one or two years of
16 testing? Had MSA been done on the results of the first year's tests in 1984, the simple linear
17 regressions on El would appear practically the opposite of those over all four years. The 1984
18 data result in regression lines that converge near zero (as expected logically), but that diverge
19 at high Els (Figure 3b). It is not at all apparent from the data points plotted together on El
20 (Figure 3a) that a quadratic response, converging toward El = 0, would have been chosen over
21 a straight line response. In addition, R2 values for the quadratic and constrained quadratic
22 functions are practically no different than that of the linear function. Predicted yields from these
11
1 two estimates indicate, despite a highend convergence, that S35 would be greatly superior to
2 locals across the range 500 < EI < 3000 (Figure 4a), rather than in a more restricted, lower
3 range, as seen in the 198487 data set (Figure la).
4 The key to the difference between the regressions of the 1984 data and of the entire data
5 set is the range and distribution of environments (Els) on which the regression is done. For all
6 four years there is a wide, evenly distributed range of Els from almost zero to 3500, with broad
7 concentrations from 500 to almost 3000 (Figure lb). The range of Els in 1984 is much more
8 weighted toward low values, concentrated from 500 to 1500, but with a relatively high
9 proportion less than 500 and very few above 2000. Taking into account these differences in the
10 distribution of the sample of environments, it can be hypothesized that the primarily linear
11 response of yields across a range of environments weighted toward low and averageyielding
12 Els diverges as El increases, while the response across a range of environments weighted toward
13 average and highyielding Els converges as El increases (Figure 4b). This hypothetical picture
14 of the response appears to fit the plotted data for all four years (Figure la) better than any of
15 the standard regression functions proposed. This sort of segmented response can be estimated
16 using a segmented linear models technique available in some sophisticated statistical software
17 packages. It is possible, of course, that the yield of one treatment, e.g., of the locals in our
18 present example, could intersect the X axis at an EI value well above zero (and therefore equal
19 zero from that point downward to El = 0). When there are only two treatments, the slope of
20 the other treatment would equal two from that point down to EI = 0.
21 Comparing the simple linear responses of S35 and locals on El for 1985, 1986 and 1987
22 to those for 1984 and for 198487, and to the hypothetical twophase response, there is
12
1 considerable evidence of the importance of the range and distribution of environments. In 1985,
2 when environments were evenly and broadly distributed over a range from 500 to 3000, with
3 only one or two either above or below this range, the responses were essentially parallel, with
4 only the slightest convergence toward high Els (Figure 5). With a similar range and distribution
5 of El in 1986, the responses of S35 and locals to environment were practically identical. In
6 1987, when'distribution of El was weighted even more toward the high end of the range, and
7 with only one environment with El < 1000, the response lines were very similar, with a slight
8 crossover in the high range of EI.
9 From comparisons of MSA by year, the hypothesis of different linear responses across
10 different ranges of EI, illustrated in Figure 4b, can be refined. It can be hypothesized, for
11 example, that in a range of lowyielding environments the linear responses of S35 and locals on
12 EI converge toward 0, that in a middle range of environments the slopes of the regression lines
13 are more or less parallel, and that in a high range the lines would converge toward very high
14 Els. This hypothesis is strongly supported by doing MSA on selected, overlapping low,
15 middle, and highEI subsets of the fouryear, 239observation data set (Table 2).
16 It should be clear that the number of tests (or years of tests) needed to get of good picture
17 of the varietybyenvironment interaction will depend on how representative the sample of test
18 environments is of the entire population of environments, across years and locations, for which
19 recommendations are to be made. In this case, in a region where year effects such as rainfall
20 and date of seeding (often highly dependent on the onset of rains) are extremely important
21 determinants of overall mean yields, one or two years of data may not be sufficiently
22 representative.
1 Characterizing environments and determining recommendation domains
2 Using the entire data set, which is the largest and presumably most representative sample
3 of environments, regressions of El on date of seeding were done to see how much of the
4 variability in average yields could be accounted for by date of seeding. For the 19841986 data,
5 El was regressed on rainfall occurring during the 90 days after seeding; these data were
6 unavailable for the 1987 tests. The results of these regressions are presented in Table 3. Over
7 all four years' data, as well as in the subsets for 1984, 1985, and 198485 combined, average
8 yields (EI) were found to be inversely related to number of days planting followed 1 January.
9 This relationship accounted for 17 percent of the variability in yields over all four years, and
10 for almost as much in the 198485 subset. It accounted for only three percent of the variability
11 of yields in 1984, no doubt because such a high proportion of tests that year were seeded late.
12 The relationship between El and rainfall is not consistent from one data set to another
13 (Table 3), and the percentage of variability in yields due to rainfall is much less than that due
14 to date of seeding. Farmers do have some idea of average rainfall over all years; they also
15 know that some regions are generally higher yielding than others. They never know, of course,
16 what the rainfall in any given year will be, but recommendations could conceivably be made to
17 farmers on the basis of knowledge of average rainfall in their area. From the results of
18 regression of El on rainfall, however, such recommendations for S35 versus local varieties
19 would not be warranted.
1 Analysis of results by recommendation domain
2 Farmers can and do, however, make choices among alternative technologies at the time
3 of seeding in function of their knowledge of the effects of date of seeding. The linear
4 regressions of S35 and locals on EI over four years, and the inverse relationship of El and date
5 of seeding, led to the delineation, for this study, of two potential recommendation domains, an
6 earlyseeded one (date of seeding before 26 June) and a lateseeded one (date of seeding after
7 25 June). Analysis of variance and mean separations within each of these domains indicated a
8 mere 10 percent increase in yields from S35 compared to locals in the earlyseeded domain, but
9 a 48 percent increase in the lateseeded domain (Table 4). Combined analysis of variance
10 indicated a significant (a = 0.05) treatmentbydomain interaction. Over all test sites, i.e., for
11 only a single recommendation domain, S35 resulted in only a 21 percent increase in yields; this
12 may seem considerable, but in many cases it may not be enough to offset other characteristics
13 of S35 which farmers find less appealing than for the local varieties (taste, cooking qualities,
14 resistance to bird and other pest damage, etc.).
15 Analysis of risk of low yields showed that in both early and lateseeded domains, the
16 chance of an unacceptably low yield depended almost entirely on the difference between means
17 and very little on differences in the variability in yields on which the means were calculated
18 (Figure 6).
19
20 Ex post verification of proposed recommendation domains
21 How well do the proposed early and lateseeded recommendation domains match the
22 known patterns in the adoption of S35 in the Center North Zone of North Cameroon? In all but
15
1 one of the nine latestseeded SODECOTON sectors (based on average seeding dates of the tests
2 from 1984 to 1987), S35 adoption has been either good or very good (Table 5). Correspondence
3 of late average date of seeding to known acceptability and adoption of S35 was not apparent
4 using just the 1984 subset of tests to calculate the mean seeding date, but was apparent using the
5 1984 and 1985 tests combined.
6
7 Conclusions and Implications for MSA of OnFarm Trials
8 While it is true that this study benefitted much from hindsight, it indicated that when use
9 of modified stability analysis is not overly reliant on stability, regression statistics, or "good"
10 and "poor" environments, it can be of great value in determining specific adaptation to groups
11 of farm environments and in delineating recommendation domains based on characteristics which
12 can be identified before planting. Had MSAwith appropriate environmental characterization
13 been done on the data from the 198487 North Cameroon trials, for example, a recommendation
14 of S35 only for seeding after 20 or 25 June might have led to increased efficiency in extension
15 efforts and perhaps to improved adoption. The same results might even have been obtained by
16 analysis only of the first two years' (198485) data.
17 Although this example was based on MSA with only two treatments, the very simplicity
18 of the datacombined with an exceptionally large number of locations and yearsis useful in
19 illustrating the importance of several key procedures in MSA. The first of these is the plotting
20 of data points on EI before attempting to find the best regression fit. In many cases, a hand
21 drawn approximation of the response will give as good a picture of the treatmentbyEI
22 interaction as will any easily derived regression function.
16
1 This study also highlighted the crucial importance of ensuring that the sample of onfarm
2 trial environments is truly representative of the total population of environments for which
3 recommendations will eventually be made. Representativeness may be relatively easy to judge
4 in some agroecosystems, as with a study recently done in the rainforest zone in Brazil, where
5 the dominant determinant of mean yields was soil fertility, determined by land use type (Singh,
6 1990). In others, however, where important environmental determinants of yield are very
7 unpredictable across locations or across seasons, particular and careful attention must be paid.
8 MSA should not just end at the level of "good" and "poor" environments. Where
9 environmental characteristics can be quantified, their relation to El can be assessed with linear
10 regression. When they cannot, e.g., for land use type, soil texture class, geographical region
11 or zone, etc., correspondence with El can be done by ranking environments from low to high
12 EI and looking for patterns in the ranking of the nonquantifiable variable(s).
13 Once recommendation domains are tentatively identified on the basis of treatmentby
14 environment interactions in the regression portion of MSA, analysis of treatment performance
15 within each domain should be done. In this study, only ANOVA and risk analysis by domain
16 were performed; in cases where socioeconomic trial data have been collected, any number of
17 socioeconomic analyses are possible. In fact, when evaluation criteria other than yield are
18 important to farmers, these criteria should be used for the determination of recommendation
19 domains (Hildebrand and Poey, 1985), as well as for the analyses by domain.
1 Acknowledgements
2 The analyses presented here were done on data extracted from results of trials done by
3 researchers and extension personnel in IRA and SODECOTON in North Cameroon. In
4 particular, they were designed and implemented by the SAFGRAD (1984, 1985) and the Testing
5 and Liaison Unit (1986, 1987) sections of IRA's Agronomic Research Center in Maroua,
6 Cameroon. Funding for much of the work of these onfarm test sections was furnished by
7 USAID, through the SAFGRAD Accelerated Crop Production Officer Project and the National
8 Cereals Research and Extension project. The analyses were done, with permission, while the
9 first author was employed by the International Institute of Tropical Agriculture, and later
10 comprised part of his Ph.D. dissertation at the University of Florida. Appreciation is extended
11 to all concerned in these institutions and projects.
1 References
2
3
4 Freeman, G. H. 1973. Statistical methods for the analysis of genotypeenvironment interaction.
5 Heredity 31:339354.
6
7 Hildebrand, Peter E. 1984. Modified stability analysis of farmer managed onfarm trials.
8 Agron. J. 76:272274.
9
10 Hildebrand, Peter E., and Federico Poey. 1985. Onfarm agronomic trials in farming systems
11 research and extension. Lynne Rienner Publishers, Inc. Boulder, Colorado.
12
13 Hildebrand, Peter E. 1990. Modified stability analysis and onfarm research to breed specific
14 adaptability for ecological diversity. p. 169180. In Manjit S. Kang (ed.) Genotypeby
15 environment interaction and plant breeding. Proc. Symposium on Genotypeby
16 Environmental Interaction and Plant Breeding, 1213 Feb. 1990, Louisiana State
17 University, Baton Rouge.
18
19 Johnson, Jerry J. 1988. Final report of onfarm testing within IRA Maroua 198487. Institute
20 of Agronomic Research, Maroua, Cameroon.
21
22 Russell, J. T. 1991. Yield and yield stability of pure and mixed stands of sorghum [Sorghum
23 bicolor (L.) Moench] varieties in North Cameroon. Ph.D. diss. University of Florida,
24 Gainesville. Diss. Abstr. Int. 5210B:5028.
25
26 Singh, Braj K. 1990. Sustaining crop phosphorus nutrition of highly leached oxisols of the
27 Amazon Basin of Brazil through use of organic amendments. Ph.D. diss. University of
28 Florida, Gainesville. Diss. Abstr. Int. 5201B:0005.
29
30 Testing and Liaison Unit, Maroua. 1986. Annual Report. National Cereals Research and
31 Extension Project, Cameroon.
32
33 Testing and Liaison Unit, Maroua. 1987. Annual Report. National Cereals Research and
34 Extension Project, Cameroon.
35
Table 1.
Summary of onfarm variety test results (from Testing and Liaison Unit, 1986;
Testing and Liaison Unit, 1987; and Johnson, 1988)
Seasonal Mean
Yieldt (ka/ha) Rainfall Seeding
Year Test Group. 535 Local S.E. (mm) Date
1984 North (42 Sites) 1070 598 99 393 3 July
Central (46 Sites) 1573 829 109 359 6 July
1985 EarlySeeded (42 Sites) 1866 1721 Ns 118 504 14 June
LateSeeded (16 Sites) 1416 1156 160 515 28 June
1986 All (38 Sites) 2164 2128 NS 145 621 22 June
1987 All (35 Sites) 1889 1825 Ns 123 604 19 June
t Yields of varieties for a year and test group are significantly
different (*) or not significant (Ns) at the 5% level, by Fisher's
Protected LSD test.
Table 2.
Regressions of yields of S35 and locals on three overlapping segments of the
range of EI, 198487.
EI<1000 500
S35 Locals S35 Locals S35 Locals
Intercept 10 10 144 144 253 253
b 1.31 0.68 1.05 0.95 0.93 1.06
Mean 769 389 1104 722 1992 1733
Regressions of El (S35 and locals) on
198487, 1984, 1985, and 198485.
date of seeding (DOS) and on rainfall*,
a) 198487
Intercept
b
R2
p
b) 1984
c) 1985
Intercept
b
R2
P
Intercept
b
R2
P
d} 198485
Intercept
b
R2
p
DOS
5979
25.4
0.17
0.0001
DOS
3140
11.4
0.03
0.022
DOS
5470
22.6
0.13
0.006
DOS
5209
22.0
0.17
0.0001
Rainfall*
864
1.3
0.07
0.0003
Rainfall
645
1.04
0.03
0.088
Rainfall
2483
1.6
0.09
0.02
Rainfall
1034
0.63
0.01
0.126
t Date of seeding = days after 1 January.
$ Rainfall = mm, 190 days after seeding.
S 1987 excluded from regression of El on rainfall since rainfall data in
this data set was aggregated over the entire year.
Table 3.
Table 4.
Mean grain yields,t 198487 data, over all locations, and by recommendation
domain based on date of seeding.
Over All Locations Seeded Before 26 June Seeded After 25 June
Variety (239 Environments) (138 Environments) (101 Environments)
kg/ha
S35 1670 a 1832 a 1448 a
Locals 1379 b 1672 b 979 b
LSD(~o 85.6 111.2 128.1
t Means within a column followed by different letters are significantly
different at the 5% level, by Fisher's Protected LSD test.
Table 5.
Correspondence of average test date of seeding, by sector, and sectors where S35
had actually been adopted, 198487 data.
N Sector Mean DOS
(Days after 1 Jan.)
10 Bidzar 168.2
10 Lara 169.7
7 Ardaf 169.3
10 Dziguilao 169.8
10 Guidiguis 170.3
11 Karhay I 170.4
13 Gobo 170.4
11 Moutouroua 171.9
14 Mokong 172.0
11 Sorawel 172.9
10 Dana 173.4
9 Mayo Oulo 174.8
14 Zongoya 176.9
10 Karhay II 177.1
8 Kourgui 178.4 **
7 Koza 178.7 **
9 Moulvoudaye 179.1 *
12 Hina 179.7
10 Yoldeo 180.0 *
10 Meme 181.8 **
10 Mindif 183.1 *
8 Dogba 183.1 *
13 Bogo 184.0 *
** Sectors with very good S35 adoption
* Sectors with good S35 adoption
a
5000
4000
3000
2000
1000
0
b
5000
Plot of Sorghum Yields on El, 198487
0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)
S35 + Locals
Linear Regression on El, 198487
Grain Yield (kg/ha)
0 500 1000 1500 2000 2500
El (kg/ha)
3000 3500 4000
 S35 ... Locals o Environments
Figure 1. Yields of S35 and locals plotted (a) and regressed (b) on environmental index
(EI), 19841987 data.
Linear Regression, S35 on El, 198487
Grain Yield (kg/ha)
0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)
S35 observations linear
Linear Regression, Locals on El, 198487
Grain Yield (kg/ha)
1000 '
0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)
+ Locals observations linear
Figure 2. Linear regressions on El of S35 (a) and locals (b) superimposed on plotted data
points, 19841987 data.
S35 and Locals Observations, 1984
Grain Yield (kg/ha)
0 500 1000 1500 2000 2500
El (kg/ha)
S35 + Locals
Linear Regressions, 1984
Grain Yield (kg/ha)
3000 3500
0 500 1000 1500 2000 2500 3000 3500
El (kg/ha)
S35 Locals o Environments
Yields of S35 and locals plotted (a) and regressed (b) on EI, 1984 data.
Figure 3.
Regressions Compared, 1984
Grain Yield (kg/ha)
0 500 1000 1500 2000
El (kg/ha)
2500 3000 3500
 S36 quad.
 Locale quad.
 835 ln.
 Looals lin.
 S35 cons.
 Locals oons.
Hypothetical Response to El, 198487
Grain Yield (kg/ha)
0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)
S35  Locals
Figure 4. Linear, quadratic, and constrained quadratic regressions compared for 1984 data
(a), and a hypothesis concerning the response on EI for all four years (b).
annhl
7
3000
2000
1000
0
1000
Rsquares 335:
Linear: 0.8332 '
Quadratic: 0.8375 
Constrained: 0.8371
><* oo 00 oo coooMeaa SsB of0 9 o0 o o o o
1 1 1 1 1 1
~
S35 and Locals Observations, 1985
Grain Yield (kg/ha)
a
4000
3000
2000
1000
0
]
1
3000 3500
Grain Yield (kg/ha)
4000
3000 S35: b0.98
Locals: b1.02
2000 
1000
0
0 O 00C 0OO m O 00OW0 C m o WC00 0
0 500 1000
1500 2000
El (kg/ha)
2500
3000 3500
 S35  Locals 0 Environments
Yields of S35 and locals plotted (a) and regressed (b) on EI, 1985 data.
3 500 10
.4 +
440 .++ ++ .
+ + +
4
.4t*^^ +
++^+
1 II I I I
Figure 5.
100 1500 2000 2500
El (kg/ha)
+ Locals S35
Linear regressions, 1985
(
Risk, LateSeeded Domain, 198487
400 800 1200 1600
Grain Yield (kg/ha)
Locals, lateseeded  835, lateseeded
2000
Risk, EarlySeeded Domain, 198487
Risk (%)
1200
Grain Yield (kg/ha)
1600
800
2000
Locals, earlyseeded ~ S35, earlyseeded
Figure 6. Means and lower confidence limits for lateseeded (a) and earlyseeded (b)
recommendation domains.
0 *
5 *
/ *
5 ______*0  
IC '* p
