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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:

enter image description here

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.

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Based on the image you uploaded, I don't think you have a nested structure. You seem to have all combinations of Photoperiod, Temperature and Time, which would make this a full factorial experiment. That makes this very simple to analyze - you just need a basic linear model with lm(Y ~ Photoperiod * Temperature * Time). If I were you, though, I would probably only analyse the interactions you had specific hypotheses for instead of all the terms in that model (to avoid chasing noise).

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    $\begingroup$ Thank you user5151349! Actually I was about doing the basic linear model you tell me, but I realized that there is no independence between Time levels because there were physically in the same climate chamber; i.e., I had 4 climate chambers (25ºC 16L8D, 25ºC 10L14D, 6ºC 16L8D, 6ºC 10L14D) and the some of the individuals inside where removed at t=50, others at t=70, others at t=90 and the last ones at t=150. That is why I though I had a kind of split-plot design, but not exactly. Am I wrong? Thank you again in advance $\endgroup$ – mjrs Jun 28 '16 at 15:22
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    $\begingroup$ This relates to a long debate on pseudoreplication, and climate chambers tend to be a somewhat grey area. While it is important to think about, there are limits at which its application becomes technically correct but practically insignificant (Thought experiment: are multiple plots in the same field pseudoreplicated? Same forest? Same region? Where's the boundary?). To cut a long story short, what you are proposing makes sense, but 1) I think it is common to treat this as a full factorial anyway, and 2) I would be very surprised if you got a different answer. $\endgroup$ – mkt - Reinstate Monica Jun 29 '16 at 7:46
  • $\begingroup$ But if you do want to go down this road, I would check out lmer in package lme4 . $\endgroup$ – mkt - Reinstate Monica Jun 29 '16 at 7:46
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    $\begingroup$ 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. $\endgroup$ – EdM Jun 29 '16 at 13:21
  • $\begingroup$ Good point, @EdM, I should have been clearer about that. $\endgroup$ – mkt - Reinstate Monica Jun 29 '16 at 13:24

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