Case Study 15: A factorial experiment to study the effect of seeding

rate and nitrogen side-dressing on yields of two dry bean

(Phaseolus vulgaris L.) cultivars
Ncebo S. Zulu and Albert T. Modi

Department of Crop Science, School of Agricultural Sciences and Agribusiness, University of

KwaZulu-Natal, Pietermaritzburg, Private Bag X01, Scottsville 3209, South Africa

Contents

Summary
Glossary
Background
Objectives
Questions to be addressed
Study design
Source material
Data management
Statistical modelling
Reporting
Findings, implications and lessons learned
Study questions
Related reading
Acknowledgements

Summary

Two dry bean cultivars (Umtata – a single-time flowering variety, and Kranskop – a
continuously flowering variety) reported to be suitable for growing under conditions prevalent
in the area around Pietermaritzburg are studied. A randomised block factorial experiment was
planned and carried out at Ukulinga Research Farm of the University of KwaZulu Natal to
compare growth and yield of the two cultivars at different seeding rates and with and without
nitrogen side-dressing. The design, layout and sampling of the experimental plots are described.

Total biomass and grain yield after three months of growth are analysed. Total biomass was
higher in the Kranskop than the Umtata cultivar but grain yield was lower. Seeds were planted
at a 75 cm between-row spacing and at three different within-row spacings: 5 cm, 10 cm and 15
cm apart. Biomass and grain yield increased in a linear manner with decreasing spacing.
Application of nitrogen fertiliser had no effect. There were no significant interactions involving
cultivar, level of spacing or fertiliser application.

Plant height and number of leaves were measured weekly over a four-week period after the start
of emergence. Analysing weekly data together results in a split-plot in time model. The
difference between this and the conventional split-plot experiment is described and methods of
analysis outlined. Kranskop plants grew higher than those for Umtata over the four-week
period.

The difference in cultivar type (continuous versus single flowering) is considered to be the
primary reason for differences in plant growth and yield. Planting later in the season than is
normal practice may also have had a bearing on the way the two cultivars performed.

Glossary
Some terms with which the reader may not be familiar:

Biomass: Total plant yield inclusive of usable and non-usable portions and exclusive of roots.

Harvest index: Ratio of economically important grain yield to the total plant biomass yield.

LAN: Limestone Ammonium Nitrate, a fertiliser containing 28% of nitrogen (N).

Determinate cultivar: a cultivar that produces flowers once.

Indeterminate cultivar: a cultivar that flowers continuously.

Background
Dry bean (Phaseolus vulgaris L.) is a food crop of high economic importance with high protein
content and grown in all habitable continents (Beninger and Hosfield 2003). It has probably been
domesticated from a wild form having a long slender vine which is found in Mexico and Central
America (Beninger and Hosfield 2003). Dry bean is an annual crop which thrives in warm
climates. It grows optimally at temperatures of 18oC to 24oC and requires a minimum of 400 to
500 mm of rain during the growing season. It prefers an optimum soil pH of 5.8 to 6.5, is very
sensitive to acidic soils (pH<5) and will not grow well in soils that are compacted, too alkaline
or poorly drained (Dry bean Production in South Africa 2002).

The choice of cultivars to be grown in a particular area is also important to be sure that the
cultivar produces beans of an appropriate size and colour, which can be both genetic and
associated with growth and yield performance (Dry Bean Production in South Africa 2002). For
successful production, high-quality (certified) seed with a high germination percentage (80% or
higher) must be used. Low quality seed can cause a poor and an uneven field stand, resulting in
uneven maturity and loss in yield. The growth habit of a dry bean cultivar also needs to be well
understood. Some cultivars are determinate (i.e. they produce flowers once) or indeterminate
(i.e. they flower continuously over a period of time).

The probability of fully effective inoculation and high rates of nitrogen fixation is rather low.
Accordingly, many growers apply nitrogen to reduce the risk of inoculation failure. Soil tests
are recommended to determine whether other nutrients are at appropriate levels. Preliminary
research was conducted by the Department of Plant Sciences at the University of Saskatchewan
on nitrogen fertilisation. Results from their research in 1999 indicated that inoculation had little
effect. However, addition of fertiliser nitrogen increased dry bean yield.

The density at which seed is sown influences dry bean yield. Studies with other row crops have
shown that crop competitiveness can be increased by reducing row spacing and increasing plant
density (Goulden 1976). Growers are nowadays interested in narrow row dry bean production
that allows them to use the same seeding and harvesting equipment that they use for cereals.
Narrow row dry bean production, however, may preclude or greatly inhibit inter-row cultivation
to control weeds. The aim of the current study was to determine the effect of varying the density
at which dry bean seeds were planted, with or without nitrogen fertiliser, on dry bean growth,
yield and seed quality.

Objectives
This study sets out with three objectives:

To compare growth, yield and seed quality of two dry bean cultivars: Umtata (a
determinate variety) and Kranskop (an indeterminate variety) when grown under
conditions prevalent in the area around Pietermaritzburg.
To determine the effect of application of nitrogen fertiliser on growth, yield and seed
quality of Umtata and Kranskop dry bean cultivars when grown under these conditions.
To determine the effect of different densities of plant spacing on growth, yield and seed
quality of Umtata and Kranskop dry bean cultivars when grown under these conditions.
Questions to be addressed

In this case study we shall discuss:

How to design, lay out and sample plots

in a randomised block factorial
experiment that allows each of the
objectives to be investigated
simultaneously.
How to analyse the results of a
randomised factorial experiment.

We shall also describe the meaning and use of

contrasts to investigate the patterns expressed
by variations in yield resulting from the three
levels of spacing used in the experiment.

Plant growth was measured weekly. Analysis

of weekly values together results in a split-plot in time model. We shall discuss the difference
between a conventional split-plot experiment and a split-plot in time experiment.

Finally we shall give some tips for presenting results from factorial experiments.

Study design

A randomised complete block design with four blocks was used to lay out a factorial
experiment at Ukulinga Research Farm, University of KwaZulu-Natal, Pietermaritzburg. Details
of the field plan and treatments are presented on the next page. Two cultivars (Umtata – a
determinate variety and Kranskop – an indeterminate variety) were used for the
experiment.These cultivars are genetically different and are two of the most popular varieties
shown to be suitable for the environment around Pietermaritzburg.
The seeds were planted at three seeding rates: 5 cm, 10 cm and 15
cm apart. Two levels of fertiliser (0 and 60 kg/ha N) were applied
with the application of 60 kg/ha supplied as Limestone
Ammonium Nitrate (LAN) two weeks after planting.

Plots were square (3 m long and 3 m wide) with a spacing of 50

cm between plots. Five rows were planted 75 cm apart within each
plot. These spacings, both within and between rows, were within
the spacings commonly used for commercial dry bean production
in South Africa, namely, 50 cm to 75 cm between and 5 cm to 15
cm within rows.

The factorial arrangement for the treatments randomised within

blocks is shown alongside in black. The first number (0, 1, 2)
represents seed spacing, the second (0, 1) fertiliser level and third
cultivar (0=Umtata, 1=Kranskop). Plot numbers are indicated in
red.

Seeds were hand sown over a period of two days from the last day
of February to the first day of March 2007. This was somewhat
later in the season than when dry beans are conventionally planted.
Two of the four blocks were planted on each day so that any
differences that may have occurred between days of planting were confounded with block.

Measurements were made from plants in the three inner rows. The outer two rows and the ends
of the inner rows were ignored, their purpose being to protect the inner plants from influences
of adjacent plots. One week after first emergence five plants in each of the three inner rows
were selected at random for weekly measurement of height and number of leaves over a period
of four weeks. They were tagged for ease of
identification at each week of measurement.

This method did lead to some bias since only

a proportion of the shoots had emerged when
the 15 plants were selected. During the four
weeks of measurement of height and number
of leaves these will have likely remained
amongst the tallest. This was unavoidable
but the primary interest was to compare
trends in growth between the two cultivars.

Total biomass yield, grain yield and harvest

index were calculated from harvesting all
inner plants at 3 months.

The skeleton analysis of variance for biomass and grain yield demonstrates that there are more
than sufficient degrees of freedom for the residual term.

Source material
The data are stored in CS15Data1 and CS15Data2. CS15Data1 contains weekly mean values of
plant height (cm) and number of leaves per plant measured on five plants selected at random.
CS15Data2 contains yields recorded at three months after sowing, namely total biomass and
grain yield (recorded in kg per plot) and harvest index (%). It also contains emergence (%)
values at two weeks. Corresponding documentation files are CS15Doc1 and CS15Doc2,
respectively.

When opening the two data files one will notice that the order in which plot numbers is
presented differs in the two files (see below). This is discussed under Data Management.

Data management
Note how the data are organised in CS15Data1 and CS15Data2. Open these files. The first
column contains the plot number. This is followed by the number of the block in which the plot
resides and then each of the factors: level of spacing, whether or not fertiliser was applied, and
the cultivar. CS15Data1 also contains week number. These columns are followed by columns
containing the values recorded for each of the variables. Both files have been entered into
GenStat, tidied up and stored as Excel files. Note how many decimal places are recorded for
biomass and grain yield in CS15Data2 and height and number of leaves in CS15Data1. Values
have been derived from raw measurements. Thus they have been recorded with a suitable
number of decimal places consistent with the likely precision of measurement. Harvest index is
derived from grain yield and biomass and so shows more decimal places.

The numbers of decimal places in CS15Data1 are not fixed (* is the default in GenStat and also
Excel). This means that data are presented up to the last non-zero digit. Thus, the average height
of plants in plot number 8 is presented as 12, rather than 12.0. This is not a particularly useful
way to present the data for it makes it more difficult to check by eye that the data have been
entered correctly in the spread sheet. It would have been better for all height values to have been
presented with one decimal place. GenStat has a useful Spread → Column →
Attributes/Format... command (the same can be achieved by right clicking a column heading)
that allows the numbers of decimal places to be changed and also the width of the column.
Thus, by using this command for the variable Biomass in CS15Data2 all values can be made to
have the same number of places, namely two.

CS15Data1 is presented in plot number order. The data in CS15Data2 have been sorted into
factor level order. Some researchers feel that data have to be presented in treatment order for
statistical analysis. This is not true, certainly in the case of GenStat. This program can handle
data presented in any order. It is much better to leave the data in the order that they have been
entered, as in CS15Data1, for this means that the data in the spread sheet can at any time be
compared with the values written in the experimental recording sheet.

Statistical modelling

Plant yield (biomass)

Analysis of variance of 3-month

biomass is obtained via Stats →
Analysis of variance..., then choosing
General Treatment Structure (in
Randomized Blocks) for the design and entering Cultivar*Spacing*Fertiliser for the treatment
structure. It is useful to click Options and tick the cv% box to include the coefficient of
variation term in addition to other values automatically displayed.

From the analysis of variance for biomass it can be seen that there are significant differences
between cultivars (P<0.001) and among spacings (P<0.01) but that addition of fertiliser had no
significant effect. There are no significant interactions.

A coefficient of variation of 15.4% is displayed at the end of the GenStat output. This is not an
unreasonable level of error variation for this type of experiment.

It is interesting to see how the analysis of variance command is expressed in the GenStat Input
log.

At any time the user can alter the above text, select the five lines and click Run → Submit
Selection. Sometimes this may be more efficient way of doing things than filling in the dialog
box again.

The levels of the spacing factor

(namely 5 cm, 10 cm and 15 cm)
are equally spaced. We can
therefore include a contrast within
the analysis of variance to test for
linear or quadratic relationships. We
do this by clicking the Contrasts...
box in the dialog box shown
alongside and entering Spacing for
the 'Contrast Factor'.

This causes an additional two lines

to be included in the analysis of variance. They show that biomass is linearly related to level of
spacing (P<0.001) and that this accounts for virtually all the variation caused by differences in
spacing, with hardly any left in the Deviations mean square.
The table of means shows that biomass yield was
lower for Umtata (Cultivar C0) than for Kranskop
(Cultivar C1). This is possibly related to the different
growth habits of the two cultivars. Umtata has a
determinate growth habit (flowers once) whereas
Kranskop has an indeterminate growth habit (flowers
continuously). It can be calculated from the values
below that mean biomass yield per plot decreased
linearly with increased spacing by an average of 0.27
kg per plot per 5 cm increase in spacing.

It is worth clicking Options... in the analysis of variance dialog box and then Residual Plots to
examine the distributions of residuals. The shapes of both the histogram and the normal and
half-normal plots of residuals (which should lie on a 45 o line through the origin) indicate some
non-normality amongst the residuals. The scatter plot of residuals suggests a possible slight
increase in variation with increasing value. However, there are no extreme residual values
displayed and it is difficult to think of a reason for these patterns. Analysis of variance is a
robust procedure and can often deal satisfactorily with departures from normality, and we shall
assume that it does in this case.

Plant yield (grain

yield)

We can likewise analyse grain

yield and harvest index. From
the analysis of variance for
grain yield we can see that
there is a significant
difference between cultivars
(P<0.001) and a significant
but smaller difference among
spacing levels (P<0.05).
Again there are no significant
interactions. If we were to
include a contrast term for spacing we would find that the linear component is again significant
(P<0.001). The relationship with cultivar, however, was opposite to that for biomass (see
below).
The reason for Umtata having a higher grain yield may be that being determinate it is able to
utilise its energy better and not waste it in growing in a vegetative way. Kranskop, on the other
hand, may continue to grow in a vegetative way, even after reaching flowering stage, resulting
in competition between leaves and seeds for nutrients and water.

Plant yield (harvest index)

There is a significant difference in harvest index between cultivars (P<0.001). Umtata (C0) had
a higher harvest index than Kranskop (C1). As already mentioned this may be due to differences
in growth habit. Spacing had no significant effect on harvest index.
Plant height

Plant height was measured weekly over four weeks from 15 plants selected at random.
Although emergence by week 2 was just 50% it had reached 100% by week 4. There were no
significant differences in
rates of emergence among
cultivars or levels of spacing.

To analyse all the weekly

data together we need to
create a dialog box for a
Split-Plot Design via Stats
→ Analysis of Variance...
with week playing the role
both as a factor and a sub-
plot.

However, this method does

not fulfill the requirements
for a regular split-plot design since, as a subplot, week, being a repeated measure, is a regular
measurement in time and so cannot be considered as a random component.

One way to get around this is to think of the analysis in terms of a 'split-plot in time' model.
This design is different from that of a conventional split-plot design and needs a degree of
caution in the interpretation of the analysis of variance. A simple approach that can sometimes
be applied is to replace the degrees of the residual for the sub-plot part of the analysis by the
main plot residual degrees of freedom and to recalculate the F-probabilities for week and its
interactions with other factors.
The analysis of variance is shown
here. We have used the contrast button
in the dialog box to add linear and
quadratic components for spacing.

Consider the main plot component of

the analysis (Block.Plot stratum).
Notice first the size of the residual
mean square compared with that of the
sub-plot stratum (6.52 times larger). A
common mistake when dealing with
these types of data is to analyse them
as a randomised block including week
as a factor in the same stratum as the
others. When this is done the residual
mean square becomes a composite of
the two residual means squares to the
right, resulting in faulty conclusions
about the statistical significance of
main plot treatment effects.

The analysis of variance shows

significant differences in mean plant
height between cultivars (P<0.001)
and also a significant linear effect of spacing (P<0.05). Note, however, that we may look at
these results differently after we have examined other assumptions of analysis of variance.
Plant yield (plant
height)
Now consider the sub-plot
component of the analysis of
variance. The printed F-
probabilities are shown in grey,
but these are based on 108
degrees of freedom, which, as
described earlier, are applicable
to a split-plot, not a split-plot in
time design.

For a split-plot in time analysis

we apply the conservative
method of recalculating the F-
values by using the same 33
degrees of freedom shown in
the main plot stratum also for
the subplot stratum.

Thus, the F-values in yellow

have been recalculated with 33
degrees of freedom for the
denominator. These
probabilities can be seen to be
slightly higher than the original
values, although in this example the significance levels remain as P<0.01 and P<0.05,
respectively, and so are not changed.

With the knowledge that significant

interactions have been highlighted
between week and cultivar and between
week and spacing we can now study two-
way tables of means. The first thing that
one should notice is that there is a rapid
increase in height over the 4-week period.
It is likely that the variation in plant
height has increased too, and, if so, this
could invalidate the combined analysis of
variance for the four weeks. We should
have carried out an exploratory analysis
first!! – see Study question 3.

However, let us proc eed assuming all is well. (Alternative solutions will be discussed later.)
It can be seen that Umtata (C0) is shorter than Kranskop (C1) and that the linear (though
not the proportional) difference in height between the two cultivars has gradually increase d
over time. Similarly, the relative decrease in plant height with increased spacing also
increases over time.
The full GenStat output provides two standard errors for differences between means. One is
for comparison between subplots across main plots and
one for comparison between subplots within the same
main plot. Thus, for week x spacing the standard errors
are 1.510 for comparisons across main plots and 1.010
(as used for the calculation of the L.S.D. on the
previous page) for comparisons within a main plot.

GenStat also calculates, as shown here, a composite

number of degrees of freedom (namely 69.35) from
the main plot and subplot residual degrees of freedom. However, as we are dealing with a
split-plot in time analysis, not a conventional split -plot, the composite value becomes 33
anyway.

The problem that we have been ignoring (investigated in Study question 3) is that the
residual variance increases with increases in plant height from week 1 to 4; so this rather
invalidates the analysis that we have been carrying out. So what can we do? Study
question 4 provides one solution by calculating linear and quadratic components for week
which can then be analysed separately using the simpler randomised block model. This
approach for dealing with repeated measurements (i.e. expressing variations over time in
terms of one or two linear functions of the repeated measure) is also described
in Biometrics Unit, ILRI (2005) for the analysis of body weight and packed cell volume
measured over time in a pilot vaccine experiment in cattle.

The standard errors featuring in this table have been abstracted from the GenStat output
and placed below the means. Multiplying them by 2 gives approximate least significant
differences (LSDs) (P<0.05) for comparisons within each week. Thus, the L.S.D. for spacing
is 2 x 1.010 = 2.02. It can be seen that a significant difference in spacing (P<0.05) begins
to occur in the third week.

Reporting
We shall here describe how to present results of analysis of the data for yield per plot.

When there are no significant interactions mean results can be readily presented in the form
of a simple table of overall means. The following table lists the two factors that had an
effect on yield down the left hand side and presents the variables of interest across the top.
Notice that for each variable a standard error (S.E.D.) is included to compare the
differences between two means. Mean values are presented with a suitable number of
significant figures and S.E.D.s have either the same number of significant decimal places or,
where these are inadequate, one more. Presenting the results in this way makes it easy for
the reader to judge both the biological and statistical significance of the mean differences
between cultivars and spacings. Note that it is not necessary to introduce indications of
statistically significant effects within the table (e.g. superscript letters). Note also how the
title fully describes the contents of the table.

Table: Differences in mean 3-month yields per plot (size 9m 2) of Umtata (determinate) and Kranskop (indeterminate) dry
bean cultivars sown at different spacings in late February/early March at Ukulinga Research Farm, University of KwaZulu -
Natal, Pietermaritzburg.
a
R atio of grain yield to biomass bStandard error of
diffe rence betwe en two m eans

Alternatively, results can be presented as

figures. These column charts display the
yields of the two cultivars in terms of total
biomass and grain yield side by side. The
first figure demonstrates visually how
Umtata provided a higher grain yield than
Kranskop despite producing a lower total
biomass. Note that S.E.D.s have been
included within the title.

The second figure shows the effect of reducing the spacing between plants on biomass and
grain yield.

Results presented in scientific publications

should not be duplicated. The author needs
to decide which form of presentation is
better – as a table or a figure.

Findings, implications and lessons learned

The study has shown that:

Application of nitrogen fertiliser had no effec t on dry bean yield under the conditions
that prevailed in Pietermaritzburg.
Decreasing the spacing between plants caused an increase in plant height and yield
in terms of both total biomass and grain yield, irrespective of the cultivar.
The determinate dry bean type, Umtata, yielded more grain yield than the
indeterminate type, Kranskop, which in contrast produced the higher total biomass.
 It is hypothesised that the poorer grain yield of Kranskop may be due to the late
planting date which restricted the period of indeterminate growth.

Regarding statistical methods we have gained a better understanding of:

the design and analysis of factorial experiments;

plot design and methods of sampling;
the use of contrasts in assessing the significance of the linear e ffect of a factor with
more than two equally spaced levels (e.g. the spacing factor);
the meaning of split-plot in time and approaches to the analysis of repeated
measures;
the value in studying distributions of residuals to be sure that methods of analysis of
variance are valid;
methods of presentation of results from factorial experiments for scientific reports.

Study questions
1. Define the term 'contrast'. Describe the circumstances when a contrast can be useful
in an analysis of variance.
2. Plants were randomly selected for the recording of plant height and leaf number
when only a proportion of plants had emerged. Think of an alternative method that
might reduce possible bias and provide a more accurate estimate of average plant
height across the whole plot.
3. Use the Spread → Restrict/Filter command in GenStat to select data for plant
height in CS15Data1 for each week in turn. Analyse each week separately using the
design for a randomised block and comment on the changes in residual variance.
Explain how you feel statistical analysis should proceed and give your reasons.
4. Again using the data for plant height calculate linear and quadratic contrasts for
week. To do this calculate the linear transformation (-3xweek1 -1xweek2 +1xweek3
+3xweek4) and the quadratic transformation (-1xweek1 +1xweek2 +1xweek3 -
1xweek4). Note that in order to do this calculation you will first need to unstack the
data. Perform an analysis of variance of these two variables and comment on the
results of the analysis.
5. Repeat Question 3 using number of leaves instead of plant height.
6. Repeat Question 4 using number of leaves instead of plant height.

7. Analyse the data for percentage emergence in CS15Data2 and verify that there are
no significant effects on emergence for any of the factors. Sometimes the arc sign
transformation is used for the analysis of percentage data. Explain why this is not
necessary here. Had there been a difference in emergence rate bet ween Umtata and
Kranskop suggest how you might deal with this in the analysis of yield.
8. Write a report to summarise in fewer than 50 words the results displayed in the table
shown under Reporting.
9. Total grain yield was higher in this experiment for Umtata than for Kranskop. This
was opposite to the difference in total biomass. Taking into consideration the
determinate and indeterminate natures of the two cultivars suggest reasons for this.
10. Discuss how the poorer harvest index of Kranskop compared with Umtata may be
related to the late planting date. Taking into account the conclusions that have been
drawn in this experiment design a follow-up experiment at a more suitable planting
time that can yield more information on the suitability of different cultivars in the
Pietermaritzburg environment.
Related reading
Beninger C W, Hosfield, G L 2003. Antioxidant activity of extracts, condensed tannin
fractions, and pure flavonoids fromPhaseolus vulgaris L. seed coat color genotypes.
Journal of Agricultural and Food Chemistry. 51: 787-788. Abstract

Biometrics Unit, ILRI 2005. Basic biometric techniques in experimental design and
analysis. International Livestock Research Institute, Nairobi, Kenya, 63 pp. Full text

Drybean Production in South Africa 2002. ARC-Grain Crops Institute (ARC-GCI),

Potchefstroom, South Africa

Goulden D S. 1976. Effect of plant population and row spacing on yield and components
of yield in navy beans (Phaseolus vulgaris). N.S.J. Exp. Agric. 4:177-180. Abstract

Acknowledgements
We acknowledge advice given by the late Mr Harvey Dicks on the statistical analysis. Dr
John Rowlands made some amendments to the version prepared by the authors to
emphasise various aspects of the design and statistical analysis of factorial experiments to
allow the case study to be used as a teaching aid.