# Inquiry about means comparision of factorial experiments

#### hazemalashwal

##### New Member
urgent and important dear, friends I need clarification about comparison between interaction of treatments. If I've factorial experiment (2*3) with three rep. and the design was RCBD, and I've the following data input:
R I T H
1 1 1 171.3
1 1 2 143.6
1 1 3 143.8
1 2 1 168.4
1 2 2 144.7
1 2 3 161.1
2 1 1 184.6
2 1 2 174.2
2 1 3 135.4
2 2 1 166.2
2 2 2 175
2 2 3 143.4
3 1 1 188.8
3 1 2 173.6
3 1 3 141.2
3 2 1 166.4
3 2 2 144.6
3 2 3 152.6

Then, when I analyze it by two-way ANOVA (in randomized blocks), the F-value was not significant of interactions (I*T), but when I looked to LSD I found that there is a significant differences:
***** Analysis of variance *****

Variate: H

Source of variation......d.f........s.s....... m.s......v.r......F pr.

R stratum...................2........189.9.....94.9.....0.68

R.*Units* stratum I.....1.........64.6.......64.6.....0.46...0.512 T..............................2.........2361.5...1180.7..8.43...0.007 I.T............................2.........600.6.....300.3...2.14...0.168
Residual ...................10........1400.0....140.0

Total.........................17......4616.6

but when I made the analysis of interactions only as a non factorial experiment by one-way ANOVA with the following data input:
R T H
1 1 171.3
1 2 143.6
1 3 143.8
1 4 168.4
1 5 144.7
1 6 161.1
2 1 184.6
2 2 174.2
2 3 135.4
2 4 166.2
2 5 175 2
6 143.4 3
1 188.8 3
2 173.6 3
3 141.2 3
4 166.4 3
5 144.6 3
6 152.6

The result of analysis showed that the F-value was significant:
***** Analysis of variance *****

Variate: H

Source of variation......d.f.......s.s...........m.s.......v.r.......F pr.

R stratum...................2........189.9.......94.9......0.60

R.*Units* stratum T.....2.........2361.5....1180.7...7.43....0.007 Residual....................13........2065.2....158.9

Total........................17........4616.6

Why? And What happened, what's wrong? What's the correct? please, I hope to find urgent answer, and thankyou in advance

Hazem Al-Ashwal