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Does Nitrogen fertiliser have a larger effect on yield then Phosphorus fertiliser?

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The independent variable were the differing levels of combined P and N fertiliser:

1) 3N, 5P

2) 5N, 3P

3) 0N, 5P

4) 5N, 0P

And two controls were used one positive and one negative:

5) 5N, 5P

6) 0N, 0P

The dependent variable was the resultant yield.

Six blocks were used and so 6 replicates. With 6 treatments overall, including the two controls. The design is a randomised complete block design (RCBD).

The Mutalau research station was the trial site.

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Table 2, Skeleton ANOVA

| Source | df
| Blocks | 6-1=5
| Treatment | 6-1=5
Factor N= 3-1=2
Factor P= 3-1=2
Interaction NP=4
| Residual | 35-5-9= 21
| Total | 36-1=35

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Interaction effect hypothesis test

H₀: there is no interaction between the treatment factors

H₁: there is an interaction between the treatment factors

If there is not sufficient evidence to reject the null hypothesis, the main effect hypothesis will be:

For δ (nitrogen)

H₀: the means are all the same

H₁: the means are not all the same

For τ (Phosphorus)

H₀: the means are all the same

H₁: the means are not all the same

all tests will be conducted at a significance level of 5%, or α = 0.05

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For the uniformity trial, no fertiliser was added to any of the 36 plots. The resulting Crop was harvested 2 days later.

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Figure 1 Heatmap of the uniformity trial

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As the fertility gradient decreases from left to right, the blocks will be placed perpendicularly to the gradient, with the left column being block 1, and the last column being block 6.

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Figure 2, Colour coded treatment number with corresponding levels.

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Yₐₑₓ = μ + βₑ + τₐ + αₓ + (ατ) ₓₐ + εₐₑ

Y is the individual observation when treatment factor ₓ (Nitrogen) is at either 0, 3 or 5 , and when the treatment factor ₐ (Phosphorus) is at either 0, 3 or 5, within block ₑ, which is either in 1, 2, 3, 4, 5 or 6.

μ is the overall mean

βₑ is the blocking effect,

αₓ is the treatment factor effect of Nitrogen

τₐ is the treatment factor effect of phosphorous

(ατ) ₓₐ is the interaction effect of nitrogen and phosphorous at the combination level of ₓₐ.

εₐₑₓ is the residual effect