## Nested ANOVA with covariates

### Nested ANOVA with covariates

I have a data set in which I recorded cricket calling songs of four
populations that are divided into two zones, allopatric zone and
sympatric zone. In addition to calling song characters, I also noted
age and temperature to adjust for calling song characters. My goal of
these analyses is to see whether calling song characters differ
between two zones after adjusting age and temperature.

The followings are the structure of my data set:
dependent variables: pro, cro, pdo, cfo, pno, ...
fixed factors: zone(1,2) and pop(1,2,3,4) (pop is nested within zone)
covariates: age and temperature

So I ran the following syntax:

GLM
pro cro pdo cfo pno  BY pop zone  WITH age temperature
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/CRITERIA = ALPHA(.05)
/DESIGN = age temperature pop zone pop(zone).

My questions to everybody is:
1. Is this syntax right?

2. How do I test interactions between covariates and factors? Should I
include "age*zone" and "age*temperature" in the design? Or any other
combinations?

3. The results of the above GLM showed that age did not affect any of
calling song characters, but temperature affected several calling song
characters. Then can I exclude age from the analysis?

4. How do I test assumptions of analysis of covariance including
homogeniety of slopes?

I have a data set in which I recorded cricket calling songs of 13
populations that were divided into two zones, allopatric zone and
sympatric zone. In addition to calling song characters, I also noted
temperature to adjust for calling song characters. My goal of
these analyses is to see whether calling song characters differ
between two zones after adjusting temperature.

The followings are the structure of my data set:

dependent variables: PRO, CRO, PDO, CFO (calling song characters)
fixed factors: ZONE, POP (POP is nested within zone)
covariates: TEMPERATURE

So I ran nested analyses of variance with TEMPERATURE as covariate. My
question is whether I should include the interaction term
(ZONE*TEMPERATURE) for the analyses.

Specific Question 1:
It turns out that the interaction term was not significant in three
dependent variables: CRO, PDO, CFO. Even though the interaction term
was not significant, it did influence the significane of other terms
such as ZONE or ZONE(POP). Then should I report the results of nested
ANOVA without the interaction term? That is, the analysis was done
without the interaction term from the beginning.

Specific Question 2:
The interaction term (ZONE*TEMPERATURE) was significant in PRO (P =
0.025). This means that ZONE or TEMPERATURE were important for PRO
regardless of significance of ZONE or TEMPERATURE separately. Is this
understanding right?

Thanks for the help in advance.