1. Experimental Design in Agriculture CROP 590, Winter, 2015

2. Why conduct experiments?...
To explore new technologies, new crops, and new areas of production
To develop a basic understanding of the factors that control production
To develop new technologies that are superior to existing technologies
To study the effect of changes in the factors of production and to identify optimal levels
To demonstrate new knowledge to growers and get feedback from end-users about the acceptability of new technologies
Exploratory => physiological study => e.g., breeding => agronomy => extension

3. What is a designed experiment?
Treatments are imposed (manipulated) by investigator using standard protocols
May infer that the response was due to the treatments
Potential pitfalls
As we artificially manipulate nature, results may not generalize to real life situations
As we increase the spatial and temporal scale of experiments (to make them more realistic), it becomes more difficult to adhere to principles of good experimental design

4. What is an observational study?
Treatments are defined on the basis of existing groups or circumstances
Uses
Early stages of study – developing hypotheses
Scale of study is too large to artificially apply treatments (e.g. ecosystems)
Application of treatments of interest is not ethical
May determine associations between treatments and responses, but cannot assume that there is a cause and effect relationship between them
Testing predictions in new settings may further support our model, but inference will never be as strong as for a designed (manipulative) experiment
Ethical issues – example – effect of wildfire on wildlife populations
This class almost exclusively covers designed experiments rather than analysis of observational studies

5. Some Types of Field Experiments (Oriented toward Applied Research)
Agronomy Trials
Fertilizer studies
Time, rate and density of planting
Tillage studies
Factors are often interactive so it is good to include combinations of multiple levels of two or more factors
Plot size is larger due to machinery and border effects
Integrated Pest Management
Weeds, diseases, insects, nematodes, slugs
Complex interactions betweens pests and host plants
Mobility and short generation time of pests often create challenges in measuring treatment response

6. Types of Field Experiments (Continued)
Plant Breeding Trials
Often include a large number of treatments (genotypes)
Initial assessments may be subjective or qualitative using small plots
Replicated yield trials with check varieties including a long term check to measure progress
Pasture Experiments
Initially you can use clipping to simulate grazing
Ultimately, response measured by grazing animals so plots must be large
The pasture, not the animal, is the experimental unit

7. Types of Field Experiments (Continued)
Experiments with Perennial Crops
Same crop on same plot for two or more years
Effects of treatments may accumulate
Treatments cannot be randomly assigned each year so it is not possible to use years as a replication
Large plots will permit the introduction of new treatments
Intercropping Experiments
Two or more crops are grown together for a significant part of the growing season to increase total yield and/or yield stability
Treatments must include crops by themselves as well as several intercrop combinations
Several ratios and planting configurations are used so number of treatments may be large
Must be conducted for several years to assess stability of system
Common practice in the tropics; Stability with respect to variable climatic conditions or pest and disease pressures

8. Types of Field Experiments (Continued)
Rotation Experiments
Determine effects of cropping sequence on target crop, pest or pathogen, or environmental quality
Treatments are applied over multiple cropping seasons or years, but impact is determined in the final season
Farming Systems Research
To move new agricultural technologies to the farm
A number of farms in the target area are identified
Often two large plots are laid out - old versus new
Should be located close enough for side by side comparisons
May include “best bet” combinations of several new technologies
Recent emphasis on farmer participation in both development and assessment of new technologies

9. The Scientific Method
Formulation of an H ypothesis
P lanning an experiment to objectively test the hypothesis
Careful observation and collection of D ata from the experiment
I nterpretation of the experimental results

10. Steps in ExperimentationH
Definition of the problem
Statement of objectives P
Selection of treatments
Selection of experimental material
Selection of experimental design
Selection of the unit for observation and the number of replications
Control of the effects of the adjacent units on each other
Consideration of data to be collected
Outlining statistical analysis and summarization of results D
Conducting the experiment I
Analyzing data and interpreting results
Preparation of a complete, readable, and correct report

11. The Well-Planned Experiment
Simplicity
don’t attempt to do too much
write out the objectives, listed in order of priority
Degree of precision
appropriate design
sufficient replication
Absence of systematic error
Range of validity of conclusions
well-defined reference population
repeat the experiment in time and space
a factorial set of treatments also increases the range
Calculation of degree of uncertainty

12. Hypothesis Testing H0:  = ɵ HA:   ɵ or H0: 1= 2 HA: 1 2
If the observed (i.e., calculated) test statistic is greater than the critical value, reject H0
If the observed test statistic is less than the critical value, fail to reject H0
The concept of a rejection region (e.g.  = 0.05) is not favored by some statisticians
It may be more informative to:
Report the p-value for the observed test statistic
Report confidence intervals for treatment means
Some statisticians do not favor the designation of an alternative hypothesis
Could also have one tailed tests.

13. Hypothesis testing
It is necessary to define a rejection region to determine the power of a test
Decision
Accept H0
Reject H0
false positive? false negative?
Classical hypothesis test P(data|H0); (probability of observing the data, or data more extreme, if null hypothesis is true)
Bayesian probability looks at P(H0|data)
Reality
Correct 
Type I error 
Type II error
1 - 
Power
H0 is true
1 = 2
HA is true
1  2

14. Power of the test Power is greater whenHO HA
1 – 
1 –  
/2
Power is greater when
differences among treaments are large
alpha is large
standard errors are small

15. Review - Corrected Sum of Squares
Definition formula
Computational formula
common in older textbooks
correction factor
uncorrected
sum of squares

16. Compare to critical t for n-1 df for a given  (0.05 in this graph)
Review of t tests
To test the hypothesis that the mean of a single population is equal to some value:
where
df = n-1
Because t is a random variable from a continuous distribution, a particular value of t has no probability associated with it. We have to look at ranges of values to determine the area under a curve.
df = 6
df = 3
df = 
Compare to critical t for n-1 df for a given  (0.05 in this graph)

17. Review of t tests
To compare the mean of two populations with equal variances and equal sample sizes:
where
df = 2(n-1)
The pooled s2 should be a weighted average of the two samples

18. Review of t tests
To compare the mean of two populations with equal variances and unequal sample sizes:
where
df = (n1-1) + (n2-1)
The pooled s2 should be a weighted average of the two samples

19. Review of t tests
When observations are paired, it may be beneficial to use a paired t test
for example, feeding rations given to animals from the same litter
t2 = F in a Completely Randomized Design (CRD) when there are only two treatment levels
Paired t2 = F in a RBD (Randomized Complete Block Design) with two treatment levels

20. Measures of Variation s (standard deviation)
CV (coefficient of variation)
se (standard error of a mean)
L (Confidence Interval for a mean)
(standard error of a difference between means)
LSD (Least Significant Difference between means)
L(Confidence Interval for a difference between means)