Relationship between mean yield, coefficient of variation, mean square error and plot size in wheat field experiments

Coefficient of variation:

• Relative measure of variation

• = (standard deviation/mean)*100 = (s/x)*100

• = (square root of the variance/mean)*100 = s2/x

• MSE = s2

• Index of the reliability of the experiment (Gomez & Gomez)

• Used to describe the amount of variation in a population (Cochran)

• Used to evaluate results from different experiments involving the same units of measure (Steel et al)

Relationship between mean yield, coefficient of variation, mean square error and plot size in wheat field experiments

Coefficient of variation:

• Relative measure of variation

• = (standard deviation/mean)*100 = (s/x)*100

• = (square root of the variance/mean)*100 = s2/x

• MSE = s2

• Index of the reliability of the experiment (Gomez & Gomez)

• Used to describe the amount of variation in a population (Cochran)

• Used to evaluate results from different experiments involving the same units of measure (Steel et al)

MATERIALS and METHODS

362 Wheat field experiments

200 Fertilizer, weed management and tillage

142 Variety Trials

Information Collected from each Trial:RepsNumber of treatmentsPlot sizeCVDegrees of freedom (error term)MSEMean YieldSED

MATERIALS and METHODS

362 Wheat field experiments

200 Fertilizer, weed management and tillage

142 Variety Trials

Information Collected from each Trial:RepsNumber of treatmentsPlot sizeCVDegrees of freedom (error term)MSEMean YieldSED

Plot Size: 16’ x 30’ or 4.88 x .9.1m = 44m2

Fertilizer/Weed/TillagePlot Size: 16’ x 30’ or 4.88 x .9.1m = 44m2

Fertilizer/Weed/Tillage

Plot Size: 4’ x 4’ = 1.48m2 Variety TrialsPlot Size: 4’ x 4’ = 1.48m2 Variety Trials

Fertilizer, Weed, and/or Tillage Experiments

Mean Min Max Std. Dev

# of replications 3.83 2.00 6.00 0.77

# of treatments 11.1 4.00 49.0 8.10

Mean yield (kg/ha) 2802 379 5915 1222

MSE (kg2/ha2) 113782 8256 480822 97743

CV, % 13.3 3.09 61.8 7.51

Plot size, m2 37.2 8.4 96.0 24.3

Standard error (kg/ha) 231 64.2 558 98.7

Fertilizer, Weed, and/or Tillage Experiments

Mean Min Max Std. Dev

# of replications 3.83 2.00 6.00 0.77

# of treatments 11.1 4.00 49.0 8.10

Mean yield (kg/ha) 2802 379 5915 1222

MSE (kg2/ha2) 113782 8256 480822 97743

CV, % 13.3 3.09 61.8 7.51

Plot size, m2 37.2 8.4 96.0 24.3

Standard error (kg/ha) 231 64.2 558 98.7

Variety Trials

Mean Min Max Std. Dev

# of replications 3.34 2.00 6.00 0.92

# of treatments 14.8 4.00 60.0 11.7

Mean yield (kg/ha) 2841 967 5196 924

MSE (kg2/ha2) 140179 40576 342290 78607

CV, % 13.7 5.17 30.9 5.29

Plot size, m2 3.49 0.31 19.1 3.13

Standard error (kg/ha) 290 138 532 107

Variety Trials

Mean Min Max Std. Dev

# of replications 3.34 2.00 6.00 0.92

# of treatments 14.8 4.00 60.0 11.7

Mean yield (kg/ha) 2841 967 5196 924

MSE (kg2/ha2) 140179 40576 342290 78607

CV, % 13.7 5.17 30.9 5.29

Plot size, m2 3.49 0.31 19.1 3.13

Standard error (kg/ha) 290 138 532 107

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Plot size, m2

Mean yield, kg ha-1 Mean yield, kg ha-1

y = 49.92 + 0.02x r2 = 0.084 y = 11.68 - 0.0014x+ 12135(1/x) r2 = 0.42

y = 115.03 - 0.01x r2 = 0.01y = 9.66 + 0.03x r2 = 0.16

FIGURE 1. Relationship between mean yield, mean square error (MSE), coefficient of variation (CV) and plot size from 220 fertilizer, weed management and tillage trials.

FIGURE 1. Relationship between mean yield, mean square error (MSE), coefficient of variation (CV) and plot size from 220 fertilizer, weed management and tillage trials.

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y = 94.29 + 0.01x r2 = 0.0081 y = 11.35 - 0.0014x + 16934(1/x) r2 = 0.44

Mean yield, kg ha-1 Mean yield, kg ha-1

y = 130.93 - 4.25x r2 = 0.019y = 6.91 + 0.04x r2 = 0.43

Plot size, m2

FIGURE 2. Relationship between mean yield, mean square error (MSE), coefficient of variation (CV) and plot size from 142 variety trials.FIGURE 2. Relationship between mean yield, mean square error (MSE), coefficient of variation (CV) and plot size from 142 variety trials.

1. CV useful for comparing the experimental variation of trials containing variables with common units

2. Smaller plot sizes employed in plant breeding trials (average of 3.59m2) compared to fertilizer/weed/tillage trials (average of 37.2m2) reduced the variability encountered in the estimation of the mean.

3. Smaller plot size employed in the variety trials is considered to be advantageous in field plot work since it is consistent with the resolution where detectable differences in soil test parameters exist and that should be treated independently

Replication

Randomization

1. CV useful for comparing the experimental variation of trials containing variables with common units

2. Smaller plot sizes employed in plant breeding trials (average of 3.59m2) compared to fertilizer/weed/tillage trials (average of 37.2m2) reduced the variability encountered in the estimation of the mean.

3. Smaller plot size employed in the variety trials is considered to be advantageous in field plot work since it is consistent with the resolution where detectable differences in soil test parameters exist and that should be treated independently

Replication

Randomization