Experimental Design in Agriculture CROP 590, Winter, 2015

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

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

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

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

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

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

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

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

Steps in Experimentation H 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

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

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.

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

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

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

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)

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

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

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

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)