Question

The following three columns of data represent observations (number of aphids killed per m²) following three pesticide treatments (A-C), with each treatment being “replicated” five times.

A	B	C
5.1	5.7	6.5
8.2	6.3	8.1
8.3	7.7	8.9
9.5	9.8	10.2
12.1	11.2	13.6

Analyse the strength of evidence for a treatment effect (A-C) if:

i. the experiment was completely randomised (i.e. rows have no meaning)

and alternatively if:

ii. the experiment was in randomised spatial blocks, with observations from the same block being in the same row (i.e. 5.1, 5.7, 6.5 block 1; 8.2, 6.3, 8.1 block 2…). In this case the rows have meaning.

Why do you come to different conclusions about the effects of pesticide dependent on the method applied? In each instance, please provide a statement of the null hypotheses and alternates, the fitted equation, a qualitative summary of whether the model assumptions are met, and a conclusion.

Answer 1

	Mean	n	Std. Dev
	8.6400	5	2.5274	A
	8.1400	5	2.3266	B
	9.4600	5	2.6745	C
	5.7667	3	0.7024	Block 1
	7.5333	3	1.0693	Block 2
	8.3000	3	0.6000	Block 3
	9.8333	3	0.3512	Block 4
	12.3000	3	1.2124	Block 5
	8.7467	15	2.3943	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatments	4.441	2	2.2207	6.49	.0212
Blocks	73.077	4	18.2693	53.37	8.27E-06
Error	2.739	8	0.3423
Total	80.257	14

The model assumptions are met.

The p-value is 0.0212.

Since the p-value (0.0212) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is the effects of pesticide dependent on the method applied.