Suppose an experiment is going to be performed in space to test the influence of two factors on the luminous flux (lumens) of projection lamps:
A: Filling pressure (1000, 1100, 1200) psi
B: Cleaning gas (N_{2}, ArN_{2})
The total number of experimental combinations is the product of the two factors' levels: \( 3 \times 2 = 6\). It was decided to take 2 replicates per cell, hence the total number of observations is \( 6 \times 2 = 12\).


Filling pressure (A) (psi) 


1000 
1100 
1200 
SUM 
Cleaning
gas (B) 
N_{2} 
88
89 
91
91 
87
88 
534 
Cell sum 
177 
182 
175 

ArN_{2} 
92
94 
87
90 
95
93 
551 
Cell sum 
186 
177 
188 


SUM 
363 
359 
363 
1085 
\( \text{(*) Significant variable} \)
\( F_{0.05, \ 2, \ 6} = 5.14 \) \( \; \; \; F_{0.05, \ 1, \ 6} = 5.99 \)
SOURCE 
SS 
DF 
MS 
F 

Filling pressure (A) 
2.67 
2 
1.34 
0.85 
Cleaning gas (B) 
24.08 
1 
24.08 
15.21* 
Interaction AB 
44.67 
2 
22.34 
14.11* 
Error 
9.5 
6 
1.58 

TOTAL 
80.92 
11 


\( F = 0.85\) is to be compared with \( F_{0.05, \ 2, \ 6} = 5.14 \). Since \( 0.85 \lt 5.14 \), A is not significant i.e. it does not affect the luminous flux significantly.
\( F = 15.21 \) is to be compared with \( F_{0.05, \ 1, \ 6} = 5.99 \). Since \( 15.21 \gt 5.99 \), B significantly affects the luminous flux.
\( F = 14.11 \) is to be compared with \( F_{0.05, \ 2, \ 6} = 5.14 \). Since \( 14.11 \gt 5.14 \), the interaction effect is statistically significant.
When the interaction term is statistically significant, it’s necessary to investigate the effect of its factors that individually appeared to be non significant. In this case the effect of A should be investigated further. For this example the assumptions of normality and constant variance held. Since the order of the experiments isn’t given it’s not possible to test the independence of the residuals.
Using Excel
Under Data, Data Analysis, select ANOVA: TwoFactor With Replication.
Enter the table (from B2 to E23 as the input range). Fill in 2 in Rows per sample and hit OK.
The conclusion is the same as the analysis previously done.