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!