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.