Strip Plot (Split Block) RCBD Design

Appropriate when the interaction is important between the two factors,

Appropriate when the two factors are applied in the large plots; one treatment applied in horizontal position and other in vertical position

Factor A and Factor B is randomized independent of the other factor: Both randomized in each block

ERROR divided into three components: Error a, Error b, Error ab

~ Number of treatments determined in the Factor A: treatments randomized in one direction

~ Number of treatments determined in the Factor B: treatments randomized in the other direction than Factor A

~ Above process repeated in the other blocks: number of levels of Factor A and number of levels of Factor B, and the replications should be determined. [Square plots are recommended (to reduce variability within the blocks)]


WE HAVE:

a =  levels of Factor A

b = levels of Factor B

r = number of replications

GT = Grand Total

Mean = GT/abr


DEGREES OF FREEDOM:

Block = r-1

Factor A = a-1,         Factor B = b-1,

Error (a) = (a-1)(r-1)    Error (b) = (b-1)(r-1)

A x B = (a-1)(b-1)

Error (ab) = (a-1) (b-1) (r-1)

Total = (abr - 1)


SQUARES:

Correction Factor = GT*GT / abr

Total R Square / ab

Total A Square / br

Total B square / ar

Total AB square / r

Total AR square / b

Total BR square / a

Total ABR square


SUMS OF SQUARE:

Total SS = Toatal ABR Square  - CF

RSS = Total R square/ab - CF

ASS = Total A square/br - CF

BSS = Total B square/ar - CF

ESS (a) = Total AR square/b - Total A square/br - Total R suqare/ab + CF

ESS (b) = Total BR square/a - Total B square/ar - Total R square/ ab + CF

ESS (ab) = Total ABR suqare - (AB sq + AR sq + BR sq) + (A sq +B sq + R sq) - CF


MEAN SQUARE:

dividing sum of squares with respective  df 

~ MS


F COMPUTED

factor A = Mean Squ (A) / EMS (a)

factor B = Mean Squ (B) / EMS (b)

A x B = Mean Sq (AB) / EMS (ab)


POOLED MSE = SS a + SS b + SS ab / df (Error a + Error b + Error ab)

Pooled CV = Sq root Pooled MSE / Mean


CV of A, B and AxB from respective MSE 


LSD: only if levels are significant

Sq Root [(2 * MSE) / no other levels of other factor * no. replications]



Resources:

Arnouts, Heidi, et al. “Design and Analysis of Industrial Strip-Plot Experiments.” Quality and Reliability Engineering International, 2018, p. n/a-n/a, www.academia.edu/14930782/Design_and_analysis_of_industrial_strip_plot_experiments. Accessed 18 Oct. 2020.

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