Question

In an experiment to determine the effects of conventional and reduced tillage agriculture on crop yield for oats, 3 varieties of oats and two levels of fertilization (0.5 and 1 kg/ acre) were examined using conventional and reduce tillage techniques. Twenty 20 x 60m plots were each partitioned into 6 -10 x 20m subplots and subplots assigned at random to receive a combination of oat variety and fertilizer treatment. Ten of these plots were subjected to conventional tillage practices and 10 were subjected to reduced tillage practices. Each subplot was harvested at seasons' end and crop yield is expressed in bushels/acre. Examine the data provided in the data file oats.csv. Report hypothesis tests for all possible effects.

Data provided in the data file oats.csv. :

	tr	fert1v1	fert1v2	fert1v3	fert2v1	fert2v2	fert2v3
1	1	55.59555	62.28367	54.02856	52.3082	66.11916	47.28625
2	1	54.83042	66.4528	58.34965	51.20269	70.35817	59.59235
3	1	47.17417	53.11721	48.0996	42.20308	56.72854	49.01972
4	1	49.92158	59.02375	51.37804	47.1327	63.70916	51.65932
5	1	63.2877	69.37552	67.33111	60.75426	76.44359	64.48788
6	1	43.26808	51.84271	43.80456	43.46588	58.33783	41.24954
7	1	53.43448	61.23901	56.50824	55.53189	66.73144	54.54501
8	1	52.09698	59.69132	56.43002	46.99428	67.06747	57.05954
9	1	53.23395	59.83314	57.81001	54.74937	64.69777	57.40591
10	1	43.52501	48.36869	43.50235	40.54583	53.5147	45.39921
11	2	49.76705	52.92597	51.92696	48.5611	58.35346	48.73186
12	2	57.11089	60.52846	55.08849	52.75431	63.08562	58.9274
13	2	57.08448	69.46167	59.38628	59.41141	77.39677	59.74098
14	2	55.65932	64.41633	55.02598	55.76469	72.4667	56.30465
15	2	67.73778	72.19191	67.87371	67.11457	77.51533	64.34463
16	2	63.81949	66.31592	59.74957	63.24728	70.01633	61.11576
17	2	59.57243	63.58954	59.51328	60.33233	68.53625	59.57449
18	2	53.61506	60.7735	56.80479	47.1538	64.1669	59.46785
19	2	61.84216	67.61936	64.58683	57.77677	75.37341	63.0163
20	2	60.88292	67.25251	60.19583	58.40519	72.17987	57.51454

Answer 1

Let CT be the Conventional Tillage and RT be the Reduced Tillage.

Now a thorough examination of the yield data of Oat given above gives the following insights:

Tillage Practice	Max of fert1v1	Max of fert1v2	Max of fert1v3	Max of fert2v1	Max of fert2v2	Max of fert2v3	Max Yield	Mean Yield
CT	63.2877	69.37552	67.33111	60.75426	76.44359	64.48788	76.44359	66.94668
RT	67.73778	72.19191	67.87371	67.11457	77.51533	64.34463	77.51533	69.46299

It can be inferred from the above findings that there is no significant difference between CT and RT practices as the average yield per acre are almost same, 67 and 69 bushels per acre. The difference may be attributed to treatment effect or inherent fertility variation.

Let's formulate the relevant hypotheses to test and validate the above inference at say, 5% level of significance.

H₀: CT = RT, CT_fert1v1 = RT_fert1v1, CT_fert1v2 = RT_fert1v2, CT_fert1v3 = RT_fert1v3, CT_fert2v1 = RT_fert2v1, CT_fert2v2 = RT_fert2v2, CT_fert2v3 = RT_fert2v3, CT_fert1v1 = CT_fert1v2 = CT_fert1v3 = CT_fert2v1 = CT_fert2v2 = CT_fert2v3, RT_fert1v1 = RT_fert1v2 = RT_fert1v3 = RT_fert2v1 = RT_fert2v2 = RT_fert2v3

Against,

H1: CT < RT