AGRO 3503, Unit I-3. Basic statistics used in agronomic field research.
I. Introduction.
Much of the progress in higher crop yields has been attributed to field research.
Ideas are usually developed and preliminary testing stages occur in laboratory,
growth chamber and greenhouse studies, but until these ideas are tested in actual
field conditions, the reliability and efficiency of new innovations remain unsure.
The need for field validation of ideas is due to the complex nature of the crop
environment and unpredictable nature and effect of the weather, pests and soil. The
effects of uncontrolled events on research treatments is known as variability.
II. Sources of variability.
1. soil: texture, organic matter, cation exchange capacity, depth, drainage, etc
2. weather: sunlight, wind, temperature, moisture, storms, etc
3. insect and disease pests
4. previous soil management activities
5. field equipment precision
6. human error and others
III. Old time research philosophy:
# 1. Formulate a hypothesis based on theories, cause and effects, etc.
#2 . Test the hypothesis.
#3. Always include a ‘control’ whenever feasible.
For example, a simple variety trial of Bt corn may have the hypothesis that there
exists a variety, or group of varieties, that will consistently and significantly yield
higher than the others.
IV. The 3 R’s of experiments:
1. Randomize the treatments.
2. Replicate the treatments.
3. Repeatability (that is, the experiment should be designed and reported in such
a way that others can repeat the study or that it is repeated for several growing
seasons to test year to year weather variability).
V. Experimental design.
A. The experimental design is the way that the treatments will be assigned in the field
and how the results will be analyzed statistically for accurate evaluations.
B. Basic model: Y = Xn + error
Y = the independent variable (the one or ones measured, such as yield and test wt)
Xn = the treatments (for example, variety and planting date)
C. Examples of some experimental designs commonly used in field studies:
In the examples below, consider that the yields of three rice varieties (V1, V2, V3)
are tested at two planting dates (early, E, and late, L). Total treatments: 6.
1. Randomized Complete Block (RCB): all treatments are randomly assigned in
a replication ‘block’.
Field
layout, RCB with 4 replications per treatment
NOTE: each row = a block or rep.
|
V1, E |
V2, L |
V1, L |
V3, E |
V2, E |
V3, L |
|
V3, L |
V2, E |
V1, L |
V2, L |
V1, E |
V3, E |
|
V2, E |
V1, L |
V1, E |
V3, E |
V3, L |
V2, L |
|
V3, L |
V1, E |
V 3, E |
V1, L |
V2, E |
V2, L |
2. Split-plot: main block plot is assigned to one treatment, such as planting date,
then split into a second treatment, such as variety. This gives more statistical
sensitivity in the analysis to the split treatment, ie., variety, and may be more
efficient to construct in the field due to labor, field or equipment limits.
Field layout, split-plot with four replications per treatment,
Main plot treatment = planting date, split treatment = variety
|
V2, E |
V1, E |
V3, E |
V1, L |
V3, L |
V2, L |
|
V1, L |
V3, L |
V2, L |
V2, E |
V1, E |
V3, E |
|
V1, L |
V3, L |
V2, L |
V3, E |
V2, E |
V1, E |
|
V1, E |
V3, E |
V2, E |
V1, L |
V2, L |
V3, L |
3. Latin Square: a square equal to the number of total treatments. All treatments
assigned to each row and column. The number of replications = number of
treatments. A very sensitive design.
Field layout, Latin square design (six reps.)
|
V3, L |
V1, E |
V1, L |
V2, E |
V2, L |
V3, E |
|
V3, E |
V3, L |
V1, E |
V1, L |
V2, E |
V2, L |
|
V2, L |
V3, E |
V3, L |
V1, E |
V1, L |
V2, E |
|
V2, E |
V2, L |
V3, E |
V3, L |
V1, E |
V1, L |
|
V1, L |
V2, E |
V2, L |
V3, E |
V3, L |
V1, E |
|
V1, E |
V1, L |
V2, E |
V2, L |
V3, E |
V3, L |
Notice that all treatments are found in any given row or column.
4. Factorial design. This usually describes studies with different rates of
treatments and may be arranged in the field using any of the designs
previously mentioned. The total number of treatments of a factorial
study is found by multiplying the different levels of treatments. For
example: a study testing the effects of 3 fungicides (X, Y and Z), at
three rates (high, medium, low), and two timings (early and late) would
have: 3 X 3 X 2 = 12 different treatments in the field, or 12 treatments
per rep. This could be arranged as a RCB, split-plot, or even a split-split-plot!
VI. Sources of error in field research:
1. soil
2. climate
3. localized areas of pest damage
4. border rows
5. human
6. instrument error
7. size of plots
8. not enough reps
9. many others unexpected!
VII. Contributions of statistics to experiments and research.
1. help in interpreting the results
2. help to compare treatments
3. help in planning and designing a valid study (the expected statistical analyses
of any study should be planned ahead of implementation!)
4. data inferences, these lead to planning future studies
5. help measure overall variability of the results.
Remember, any good study should end with two results:
1. answer questions
2. lead to new questions that need answers!
VIII. Common statistic calculations:
1. mean = average
2. median = middle of the data
3. standard deviation = measure of the variability of a mean
4. standard error = measure of the variability about a mean taking into
consideration the number of treatments and reps.
5. C.V. = coefficient of variation = overall measure of the variability of
results in reference to the treatments.
6. correlation coefficient = relative relationship among two different treatments.
7. R2 value = coefficient of determination = relative accuracy of the statistical
model
8. probability limits = tests for significant treatment differences.
IX. Commonly used tests.
A. Mean comparisons:
1. L.S.D. = ‘Least Significant Difference’ = limit of differences between any
two treatments before statistically significant (not very sensitive test).
2. Multiple range tests = similar to L.S.D. but looks more at grouping the data.
3. t tests = more sensitive test between any two given treatments.
B. ANOVA models = ‘Analysis of Variance’ = very sensitive tests to see overall if
treatments were different. Good test to start with to test the hypothesis.
C. Regression models = tests of treatment response. Used a lot in rate studies.
D. Response surfaces = multiple regression tests that look multi-dimensionally at
several rate applied treatments. Good to find the ‘best’ combination of treatments
if possible, ie., rate and timing of fungicides.
X. General traits of good field research:
1. 3+ reps
2. 3+ seasons
3. different locations, soils
4. randomized
5. contain ‘border’ rows to eliminate the edge effect on yields
6. weather data is collected
7. good records and observations are kept
8. designed around valid statistical principals
9. able to be repeated by another investigator
Even the best of plans can go bad due to unforeseen events. For example, the wheat variety trials at the U of A Southeast Research and Extension Center were completely lost in the 200 – 2001 season due to unusually high rainfall which caused flooding that kept the plots under water for several weeks, killing all the plants!