1. Experimental Error Variation between plots treated alike is always present Modern experimental design should: nprovide a measure of experimental error variance nreduce experimental error as much as possible

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Example: central Missouri farm Aerial photograph, soil pH and 3-year average grain yields Source: http://muextension.missouri.edu/explore/envqual/wq0450.htmhttp://muextension.missouri.edu/explore/envqual/wq0450.htm

11. 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!

12. 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

13. Control of Experimental Error Accuracy = without bias  average is on the bull’s-eye  achieved through randomization Precision = repeatability  measurements are close together  achieved through replication Bull’s eye represents the true value of the parameter you wish to estimate Both accuracy and precision are needed!

14. To eliminate bias To ensure independence among observations Required for valid significance tests and interval estimates OldNewOldNewOldNewOldNew In each pair of plots, although replicated, the new variety is consistently assigned to the plot with the higher fertility level. Low High Randomization

15. Replication The repetition of a treatment in an experiment AA A B B B CC C D D D

16. 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 Sample variance Number of replications Standard error of a mean Broadens the base for making inferences Smaller differences can be detected

17. Effect of number of replicates

18. 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

19. 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

20. 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 

21. 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

22. Effects of competition In general, experimental materials should be evaluated under conditions that represent the target production environment 

23. 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

24. 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

25. 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

26. 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 1/10 th 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

27. In doing an ANOVA, it is best to carry the full number of figures obtained from the uncorrected sum of squares n Do not round closer than this until reporting final results If, for example, the original data contain one decimal, the sum of squares will contain two places 2.2 * 2.2 = 4.84 Rounding in ANOVA

28. Terminology experiment treatment factor levels variable experimental unit (plot) replications sampling unit block experimental error  planned inquiry  procedure whose effect will be measured  class of related treatments  states of a factor  measurable characteristic of a plot  unit to which a treatment is applied  experimental units that receive the same treatment  part of experimental unit that is measured  group of homogeneous experimental units  variation among experimental units that are treated alike

29. Barley Yield Trial Experiment Hypothesis Treatment Factor Levels Variable Experimental Unit Replication Block Sampling Unit Error