Experimental Error
Variation between plots treated alike is always present
 Modern experimental design should:
provide a measure of experimental error variance
reduce experimental error as much as possible
Natural sources of error in field experiments
 Plant variability
– type of plant, larger variation among larger plants
– competition, variation among closely spaced plants is smaller
– plot to plot variation because of plot location (border effects)
 Seasonal variability
– climatic differences from year to year
– rodent, insect, and disease damage varies
– conduct tests for several years before drawing firm conclusions
 Soil variability
– differences in texture, depth, moisture-holding capacity, drainage,
available nutrients
– since these differences persist from year to year, the pattern of
variability can be mapped with a uniformity trial
Choice of Experimental Site
 Site should be representative
 Grower fields may be better suited to applied research
 Suit the experiment to the characteristics of the site
– make a sketch map of the site including differences in
topography
– minimize the effect of the site sources of variability
– consider previous crop history
– if the site will be used for several years and if resources
are available, a uniformity test may be useful
Greenhouse effects
 Greenhouse and growth chambers are highly
controlled, but in practice may be quite variable
 Not representative of field conditions
– light
– growth media
– unique insect pests and diseases
 Experiments can be conducted in the off-season
Uniformity Trials
 The area is planted
uniformly to a single crop
 The trial is partitioned into
small units and harvested
individually
 Adjustments are made to
distinguish patterns in the
data from random noise
 Areas of equal yield are
delineated
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Interpretation
 Determine suitability of the site
for the experiment
– uniformity critical for fertility trials
 Make decisions concerning
management of site over time
– cover crops
 Group plots into blocks to
reduce error variance within
blocks
– blocks do not have to be
rectangular
 Determine size, shape and
orientation of the plots
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Uniformity trials?
 costs
 time constraints
 land limitations
 pressure to publish or perish
 may already have knowledge of field
characteristics, previous cropping history
 new technological tools may achieve the same
or better result
Precision Agriculture
Techniques, technologies, and management strategies that
address within-field variability of parameters that affect crop
growth.
soil type
soil organic matter
plant nutrient levels
topography
water availability
weeds
insects
Tools of Precision Agriculture
 GPS and GIS – constant reference to
geographic coordinates
 Remote Sensing – infrared maps
 Equipment such as combines that can
continuously monitor yield at harvest
 Crop Modeling
 Spatial analyses
Example: central Missouri farm
Aerial photograph, soil pH and 3-year average grain yields
Source: http://muextension.missouri.edu/explore/envqual/wq0450.htm
Spatial Analyses
 Utilize patterns in the data to adjust for heterogeneity in
an experiment
 Example: ASReml
http://www.vsni.co.uk/software/asreml
Not a substitute for good experimental design and technique!
Strategies to Control Experimental Error
 Select appropriate experimental units
 Increase the size of the experiment to gain more
degrees of freedom
– more replicates or more treatments
– caution – error variance will increase as more heterogeneous
material is used - may be self-defeating
 Select appropriate treatments
– factorial combinations result in hidden replications and therefore
will increase n
 Blocking
 Refine the experimental technique
 Measure a concomitant variable
– covariance analysis can sometimes reduce error variance
Control of Experimental Error
Bull’s eye represents the true value
of the parameter you wish to estimate
Accuracy = without bias
 average is on the bull’s-eye
 achieved through randomization
Precision = repeatability
 measurements are close together
 achieved through replication
Both accuracy and precision are needed!
Randomization
 To eliminate bias
 To ensure independence among observations
 Required for valid significance tests and interval estimates
Low
Old
High
New
Old
New
Old
New
Old
New
In each pair of plots, although replicated, the new variety is
consistently assigned to the plot with the higher fertility level.
Replication
 The repetition of a treatment in an experiment
A B D A
C D B C
B A D C
Replication
 Each treatment is applied independently to two or more
experimental units
 Variation among plots treated alike can be measured
 Increases precision - as n increases, error decreases
Standard error
of a mean
Sample variance
Number of replications
 Broadens the base for making inferences
 Smaller differences can be detected
Effect of number of replicates
Variance of the mean
Effect of replication on variance
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number of replicates
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What determines the number of replications?
 Pattern and magnitude of variability in the soils
 Number of treatments
 Size of the difference to be detected
 Required significance level
 Amount of resources that can be devoted to the
experiment
 Limitations in cost, labor, time, and so on
The Field Plot
 The experimental unit: the vehicle for evaluating
the response of the material to the treatment
 Shapes
– Rectangular is most common - run the long dimension parallel to
any gradient
– Fan-shaped may be useful when studying densities
– Shape may be determined by the machinery or irrigation
Plot Shape and Orientation
 Long narrow plots are preferred
– usually more economical for field operations
– all plots are exposed to the same conditions
 If there is a gradient - the longest plot dimension should
be in the direction of the greatest variability


Border Effects
 Plants along the edges of plots often perform differently
than those in the center of the plot
 Border rows on the edge of a field or end of a plot have an
advantage – less competition for resources
 Plants on the perimeter of the plot can be influenced by
plant height or competition from adjacent plots
 Machinery can drag the effects of one treatment into the
next plot
 Fertilizer or irrigation can move from one plot to the next
 Impact of border effect is greater with very small plots
Effects of competition
 In general, experimental materials should be evaluated
under conditions that represent the target production
environment


Minimizing Border Effects
 Leave alleys between plots to minimize drag
 Remove plot edges and measure yield only on
center portion
 Plant border plots surrounding the experiment
Types of variables
 Continuous
– can take on any value within a range (height, yield, etc.)
– measurements are approximate
– often normally distributed
 Discrete
– only certain values are possible (e.g., counts, scores)
– not normally distributed, but means may be
 Categorical
–
–
–
–
qualitative; no natural order
often called classification variables
generally interested in frequencies of individuals in each class
binomial and multinomial distributions are common
Rounding and Reporting Numbers
To reduce measurement error:
 Standardize the way that you collect data and try to be as
consistent as possible
 Actual measurements are better than subjective readings
 Minimize the necessity to recopy original data
 Avoid “rekeying” data for electronic data processing
– Most software has ways of “importing” data files so that you don’t
have to manually enter the data again
 When collecting data - examine out-of-line figures
immediately and recheck
Significant Digits
 Round means to the decimal place corresponding to
1/10th of the standard error (ASA recommendation)
 Take measurements to the same, or greater level of
precision
 Maintain precision in calculations
If the standard error of a mean is 6.96 grams, then
6.96/10 = 0.696  round means to the nearest 1/10th gram
for example, 74.263  74.3
But if the standard error of a mean is 25.6 grams, then
25.6/10 = 2.56  round means to the closest gram
for example, 74.263  74
Rounding in ANOVA
 In doing an ANOVA, it is best to carry the full number of
figures obtained from the uncorrected sum of squares
If, for example, the original data contain one
decimal, the sum of squares will contain two
places
2.2 * 2.2 = 4.84

Do not round closer than this until reporting final results
Terminology
 experiment

planned inquiry
 treatment

procedure whose effect will be measured
 factor

class of related treatments
 levels

states of a factor
 variable

measurable characteristic of a plot
 experimental unit (plot)

unit to which a treatment is applied
 replications

experimental units that receive the same
treatment
 sampling unit

part of experimental unit that is measured
 block

group of homogeneous experimental units
 experimental error

variation among experimental units that
are treated alike
Barley Yield Trial
Experiment
Hypothesis
Treatment
Factor
Levels
Variable
Experimental Unit
Replication
Block
Sampling Unit
Error