Experimental Error

Variation between plots treated alike is always present

Modern experimental design should: provide a measure of experimental error variance reduce experimental error as much as possible

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

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

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

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

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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

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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

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

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

Example: central Missouri farm

Aerial photograph, soil pH and 3-year average grain yields

Source: http://muextension.missouri.edu/explore/envqual/wq0450.htm

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!

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

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 valueof the parameter you wish to estimate

Both accuracy and precision are needed!

To eliminate bias To ensure independence among observations Required for valid significance tests and interval estimates

Old New Old New Old New Old New

In each pair of plots, although replicated, the new variety is consistently assigned to the plot with the higher fertility level.

Low High

Randomization

Replication The repetition of a treatment in an experiment

A A

A

B

B

B

CC

C

D

D

D

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

Effect of number of replicates

Effect of replication on variance

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0 5 10 15 20 25 30 35 40 45 50

number of replicates

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ean

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

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

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

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

Effects of competition In general, experimental materials should be evaluated

under conditions that represent the target production environment

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

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

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

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 1/10th 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

In doing an ANOVA, it is best to carry the full number of figures obtained from the uncorrected sum of squares

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

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

Barley Yield Trial

ExperimentHypothesisTreatmentFactorLevelsVariableExperimental UnitReplicationBlockSampling UnitError