Why conduct experiments?
Download
Report
Transcript Why conduct experiments?
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
49
49
46
44
35
35
42
43
45
45
42
42
45
45
41
39
32
32
49
46
44
40
39
39
39
41
45
45
44
42
42
42
39
39
33
33
48
44
40
40
39
39
39
38
38
43
43
40
39
39
39
39
39
37
48
44
44
42
39
39
39
38
38
44
44
40
39
40
41
41
41
43
44
44
42
40
39
39
39
38
38
44
44
44
43
43
43
41
41
43
37
37
38
38
38
40
40
40
40
44
45
44
44
44
44
37
37
38
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
49
49
46
44
35
35
42
43
45
45
42
42
45
45
41
39
32
32
49
46
44
40
39
39
39
41
45
45
44
42
42
42
39
39
33
33
48
44
40
40
39
39
39
38
38
43
43
40
39
39
39
39
39
37
48
44
44
42
39
39
39
38
38
44
44
40
39
40
41
41
41
43
44
44
42
40
39
39
39
38
38
44
44
44
43
43
43
41
41
43
37
37
38
38
38
40
40
40
40
44
45
44
44
44
44
37
37
38
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
8.0
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
5
10
15
20
25
30
35
number of replicates
40
45
50
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