# ANOVA 3 factors: 2 fixed factors, 1 factor nested within crossed fixed factors

I have a dilema of the suitability of the analysis with my design. I have 3 fixed factors: - Photoperiod (2 levels: 16L8D; 10L14D) - Temperature (2 levels: 6ºC; 25ºC) - Time (4 levels: 50;70;90;150 days)

Photoperiod and Temperature are crossed, and Time is nested within the crossed factors. See this image:

I have tried the following ANOVA nested model: (Y: dependent variable; df: dataframe)

aov(Y ~ (Photoperiod * Temperature) + Error((Photoperiod * Temperature)/Time), data=df)


And I get that results:

Call:
aov(formula = Y ~ (Photoperiod * Temperature) +
Error((Photoperiod * Temperature)/Time), data=df)

Grand Mean: 4.492955

Stratum 1: Photoperiod

Terms:
Photoperiod
Sum of Squares  197.7843
Deg. of Freedom        1

1 out of 2 effects not estimable
Estimated effects are balanced

Stratum 2: Temperature

Terms:
Temperature
Sum of Squares   3795.089
Deg. of Freedom         1

1 out of 2 effects not estimable
Estimated effects are balanced

Stratum 3: Photoperiod:Temperature

Terms:
Photoperiod:Temperature
Sum of Squares           197.7843
Deg. of Freedom                 1

Estimated effects are balanced

Stratum 4: Photoperiod:Temperature:Time

Terms:
Residuals
Sum of Squares   626.4977
Deg. of Freedom         2

Residual standard error: 17.69884

Stratum 5: Within

Terms:
Residuals
Sum of Squares   30658.85
Deg. of Freedom       182

Residual standard error: 12.97903


I don't know if this approach is right, and how can I get p-values from those results.

• If there is only 1 climate chamber per photoperiod/temperature combination, there is no way in any event to untangle any specific climate-chamber influence from its associated photoperiod and temperature combination. So it's not clear what is to be gained from anything other than a factorial analysis. Also, the OP should note that calling summary(aov(...)) provides more information than the default aov() output on the console. – EdM Jun 29 '16 at 13:21