Hi All

I am a master’s student and I have a statistical question.  I have an
experiment evaluating the effects of intertidal elevation (fixed; 3 levels)
(iz) and seaweed canopy cover (fixed; 2 levels) (c_nc) on species richness
(richness). Quadrats are randomly distributed across 5 sites (random factor)
(site)with 4 replicates in each elevation and canopy treatment combination
per site; therefore, I am using a nested model.  The model is described by
Underwood in his Experiments in Ecology textbook (1997, page 367) and is:


 df
            Mean square denominator

Intertidal Zone                                                    2
            S(I*C)

Canopy Cover                                                    1
            S(I*C)

Intertidal zone * Canopy cover                             2
S(I*C)

Site (Intertidal zone * Canopy Cover)                   24
Error

Error                                                                 90



The usual procedure is to run this “main effects” model and, when there is a
significant interaction term, to run simple effects at each level of A)
intertidal zone and B) canopy cover using this model (as an example for each
level of intertidal elevation):


 df
            Mean square denominator

Canopy Cover                                                    1
            S(C)

Site(Canopy)                                                      8
            Error

Error                                                                90

Essentially, my data shows significance in the main model for Intertidal
zone (p = 0.0019), Canopy cover (p= 0.0034) and for the nested site term (p<
0.0001), but there is no significance in the interaction term (p=
0.6978).  Regardless
of this non-significant interaction term, I still ran simple effects, for
each intertidal elevation separately, and found significance in the canopy
treatment at two of the intertidal elevations (p = 0.0013 and p = 0.0003),
with no significant difference occurring in the third elevation (p= 0.4842).
Does anyone know why I may be getting a non-significant interaction term
even when canopy effects depend on the level of elevation being considered?
My main effects model in r is:

mod <- aov (richness ~ c_nc + iz + c_nc*iz + Error((iz*c_nc)/site), data =
data)

And the simple effects model at each intertidal elevation separately is:

mod <- aov (richness ~ c_nc + Error((c_nc)/site), data = data)

And here is an example of the data in R:

    site  iz  c_nc   quad        richness

1    1    1    C      AD-C        4

2    1    1    C      AX-C        4

3    1    1    C      AJ-C        5

4    1    1    C      AY-C        6

5    1    2    C      AW-C        7

6    1    2    C      AH-C        4

Thanks so much for the help!

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