Split-split plot by time with unbalance treatment nested within time

[henganl2]

Hello everyone, 

I have questions about the model setting for the split-split plot design. 

My data set includes 4 treatment combinations (main-plot), 3 cultivars (sub-plot), and we collect the data at 3 growth stages  (sub-sub plot). Each treatment has 2 or 3 replicates.  

The treatment combinations were:

I want to run an ANOVA test to see the effect of treatments on the collected data (Obs). 

and here is my questions: 

1) What is the proper way to code the treatment? 

one way is to separate inoculation (Treat_I) and fungicide treatment (Treat_F) and code as two factors 

the problem is,  the fungicide treatment only applied at stage 3, I try to code this treatment as NA at Stage 1 and 2, 

will this cause problems during analysis?  

another way is to code them as one factor that has 4 combinations (Treat), but it may not be the correct way too. 

2) Should I nested the treatment within Stage?  

Here is some sample data and my model:

Data sample; 
Plot_ID$ Cultivars$ Rep$ Treat$ Treat_I$ Treat_F$ Treat_F_2$ Stage$ Obs
cards;
18QM1011 LD13 1 Inoc/no Inoc . no V4_R1 24.24
18QM1033 Williams 1 NIC/yes NIC . yes V4_R1 120.6
18QM2022 LD12 2 Inoc/no Inoc . no V4_R1 54.74
18QM3011 LD12 3 Inoc/yes Inoc . yes V4_R1 88.46
18QM3033 LD12 3 Inoc/no Inoc . no V4_R1 43.5
18QM1012 Williams 1 Inoc/no Inoc . no V4_R1 79.82
18QM1041 LD13 1 NIC/no NIC . no V4_R1 42.52
18QM2023 Williams 2 Inoc/no Inoc . no V4_R1 242.96
18QM3012 LD13 3 Inoc/yes Inoc . yes V4_R1 70.4
18QM3041 Williams 3 NIC/no NIC . no V4_R1 95.26
18QM1013 LD12 1 Inoc/no Inoc . no V4_R1 37.4
18QM1042 Williams 1 NIC/no NIC . no V4_R1 133.5
18QM2031 LD13 2 NIC/no NIC . no V4_R1 45.04
18QM3013 Williams 3 Inoc/yes Inoc . yes V4_R1 135
18QM3042 LD13 3 NIC/no NIC . no V4_R1 43.82
18QM1021 LD12 1 Inoc/yes Inoc . yes V4_R1 332.98
18QM1043 LD12 1 NIC/no NIC . no V4_R1 63.9
18QM2032 LD12 2 NIC/no NIC . no V4_R1 16.9
18QM3021 Williams 3 NIC/yes NIC . yes V4_R1 93.84
18QM3043 LD12 3 NIC/no NIC . no V4_R1 41.34
18QM1022 LD13 1 Inoc/yes Inoc . yes V4_R1 40.66
18QM2011 LD13 2 Inoc/yes Inoc . yes V4_R1 78.38
18QM2033 Williams 2 NIC/no NIC . no V4_R1 66.14
18QM3022 LD13 3 NIC/yes NIC . yes V4_R1 97.86
18QM1023 Williams 1 Inoc/yes Inoc . yes V4_R1 254.92
18QM2012 LD12 2 Inoc/yes Inoc . yes V4_R1 37.42
18QM2041 LD13 2 NIC/yes NIC . yes V4_R1 42.92
18QM3023 LD12 3 NIC/yes NIC . yes V4_R1 104.9
18QM1031 LD13 1 NIC/yes NIC . yes V4_R1 97.34
18QM2013 Williams 2 Inoc/yes Inoc . yes V4_R1 202.26
18QM2042 Williams 2 NIC/yes NIC . yes V4_R1 122.58
18QM3031 Williams 3 Inoc/no Inoc . no V4_R1 187.28
18QM1032 LD12 1 NIC/yes NIC . yes V4_R1 55.52
18QM2021 LD13 2 Inoc/no Inoc . no V4_R1 56.42
18QM2043 LD12 2 NIC/yes NIC . yes V4_R1 62.4
18QM3032 LD13 3 Inoc/no Inoc . no V4_R1 114.36
18QM1022 LD13 1 Inoc/yes Inoc . yes R2_R3 106.68
18QM2011 LD13 2 Inoc/yes Inoc . yes R2_R3 313.62
18QM2033 Williams 2 NIC/no NIC . no R2_R3 166.98
18QM3022 LD13 3 NIC/yes NIC . yes R2_R3 392.5
18QM1023 Williams 1 Inoc/yes Inoc . yes R2_R3 56.72
18QM2012 LD12 2 Inoc/yes Inoc . yes R2_R3 123.76
18QM3023 LD12 3 NIC/yes NIC . yes R2_R3 184.68
18QM1031 LD13 1 NIC/yes NIC . yes R2_R3 265.96
18QM2013 Williams 2 Inoc/yes Inoc . yes R2_R3 480.54
18QM2042 Williams 2 NIC/yes NIC . yes R2_R3 741.88
18QM3031 Williams 3 Inoc/no Inoc . no R2_R3 79.52
18QM1032 LD12 1 NIC/yes NIC . yes R2_R3 86.04
18QM2021 LD13 2 Inoc/no Inoc . no R2_R3 236.32
18QM2043 LD12 2 NIC/yes NIC . yes R2_R3 90.46
18QM3032 LD13 3 Inoc/no Inoc . no R2_R3 251.68
18QM1033 Williams 1 NIC/yes NIC . yes R2_R3 35.24
18QM2022 LD12 2 Inoc/no Inoc . no R2_R3 174.82
18QM3011 LD12 3 Inoc/yes Inoc . yes R2_R3 324.54
18QM3033 LD12 3 Inoc/no Inoc . no R2_R3 136.52
18QM1012 Williams 1 Inoc/no Inoc . no R2_R3 27.36
18QM1041 LD13 1 NIC/no NIC . no R2_R3 86.8
18QM2023 Williams 2 Inoc/no Inoc . no R2_R3 201.6
18QM3012 LD13 3 Inoc/yes Inoc . yes R2_R3 267.86
18QM3041 Williams 3 NIC/no NIC . no R2_R3 305.4
18QM1013 LD12 1 Inoc/no Inoc . no R2_R3 29.46
18QM1042 Williams 1 NIC/no NIC . no R2_R3 89.2
18QM2031 LD13 2 NIC/no NIC . no R2_R3 71.1
18QM3013 Williams 3 Inoc/yes Inoc . yes R2_R3 426.38
18QM3042 LD13 3 NIC/no NIC . no R2_R3 193.2
18QM1021 LD12 1 Inoc/yes Inoc . yes R2_R3 51.4
18QM1043 LD12 1 NIC/no NIC . no R2_R3 78.86
18QM2032 LD12 2 NIC/no NIC . no R2_R3 160.92
18QM3021 Williams 3 NIC/yes NIC . yes R2_R3 269.04
18QM3043 LD12 3 NIC/no NIC . no R2_R3 225.86
18QM1012 Williams 1 Inoc/no Inoc no no R5 523.32
18QM1042 Williams 1 NIC/no NIC no no R5 327.4
18QM3021 Williams 3 NIC/yes NIC yes yes R5 252.5
18QM1013 LD12 1 Inoc/no Inoc no no R5 157.36
18QM1043 LD12 1 NIC/no NIC no no R5 281.04
18QM3022 LD13 3 NIC/yes NIC yes yes R5 75.54
18QM1021 LD12 1 Inoc/yes Inoc yes yes R5 212.98
18QM2013 Williams 2 Inoc/yes Inoc yes yes R5 289.54
18QM3023 LD12 3 NIC/yes NIC yes yes R5 178.8
18QM1022 LD13 1 Inoc/yes Inoc yes yes R5 245.74
18QM2021 LD13 2 Inoc/no Inoc no no R5 314.52
18QM3031 Williams 3 Inoc/no Inoc no no R5 67.96
18QM1031 LD13 1 NIC/yes NIC yes yes R5 65
18QM2031 LD13 2 NIC/no NIC no no R5 287.78
18QM3032 LD13 3 Inoc/no Inoc no no R5 266.26
18QM1032 LD12 1 NIC/yes NIC yes yes R5 581.22
18QM3011 LD12 3 Inoc/yes Inoc yes yes R5 180.02
18QM3033 LD12 3 Inoc/no Inoc no no R5 265.14
18QM1033 Williams 1 NIC/yes NIC yes yes R5 332.46
18QM3012 LD13 3 Inoc/yes Inoc yes yes R5 93.02
18QM3041 Williams 3 NIC/no NIC no no R5 242
18QM1041 LD13 1 NIC/no NIC no no R5 278.92
18QM3013 Williams 3 Inoc/yes Inoc yes yes R5 139.82
18QM3043 LD12 3 NIC/no NIC no no R5 60.46
;;;
proc mixed data=sample method=REML;
class Plot_ID Seed Rep Treat Treat_I Treat_F Stage;
model Obs = Rep Seed
                Treat_I Treat_I*Seed
                Treat_F Treat_F*Seed
                Stage Stage*Treat_I Stage*Treat_F Stage*Treat_I*Treat_F;
random Rep Rep*Seed Rep*Treat_I Rep*Treat_F Rep*Treat_I*Treat_F;
run;quit;

Could anyone give me some suggestions? Thanks!! 

[sld]

Based on the sample data you provided, I've tried to sleuth out your design. For what it's worth, I attach my code.

I do not intend these comments to be critical (because we all start without knowing anything) but there appears to be many design concepts that you are unfamiliar with. If you have access to a statistical consultant at your institution, my strong recommendation is that you work with them to improve your understanding of experimental design and to develop an appropriate statistical model for your experiment.

If you have absolutely no access to statistical expertise, let us know and we'll see what we can do. But keep in mind that the answer to your question is truly and well beyond what we can readily address in this forum.

I hope this helps move you forward.