Provide Information Regarding Statistics & Econometrics : Post Hock Tests on RCBD Lecture

Post Hoc Tests on RCBD

Lecture – 09

Example:

Three fertilisers are allocated to four categories of plants: local, regional, and imported. The fourth night's growth in millimetres is reported as follows:

Plant	Fertilizer 1	Fertilizer 2	Fertilizer 3
Local	65	63	71
Regional	67	66	72
Imported	68	70	75
Hybrid	62	57	69

Test the relevance of three fertilisers' effects on four plant categories, as well as the significance of the four categories' growth rates. Create an acceptable statistical model for the above experiment. Use the post-hoc test if you notice anything significant.

Solution:

The experiment consists of three treatments (i.e., Fertiliser 1, Fertiliser 2, and Fertiliser 3) and types of plants considered as blocks. The yield is the growth of the plants. The yield depends on the type of fertilisers and the type of plants. So, this experiment is represented by the following linear statistical model.

Yij = μ + βi + Tj + ϵij i = 1, 2, 3, 4. j = 1, 2, 3.

Where:

μ: The mean growth of the plants

βi : effect of the type of plants.

Tj: Fertiliser effect.

Plant	Fertilizer 1	Fertilizer 2	Fertilizer 3	Ti.	Ti. ^2
Local	65	63	71	199	39601
Regional	67	66	72	205	42025
Imported	68	70	75	213	45369
Hybrid	62	57	69	188	35344
T.j	262	256	287	805	162339
T.j ^2	68644	65536	82369	216549

SV	d.f	SS	MS	F	F table
Block	3	135.17	45.057	14.356	8.94
Treatment	2	110.92	55.46	17. 671	19.33
Error	6	18.83	3.1384
Total	11	264.92

The findings of the study show that the effect of three fertilisers on the growth of the four types of plants is insignificant, while the growth of the four types of plants is significant at the 5% level.

The post hoc tests are applicable to the types of plant growth.