Unbalanced repeated measure design for the given data?

Question

I have 3 factors factor1 (treatment) with 2 levels (control, stress) factor2 (Variates) with 12 Levels (Var1, Var2,....Var12) factor3 (Time) with 12 levels (Week1, Week2,..., Week12)

The treatment has 3 replicates for control and 6 replicates for stress. Would it be unbalanced Design? What design would you suggest in this case?

looking forward for your positive response! Thanks in advance! Regrads, Jacki

Answer 1

Judging by your description- Yes, your design is unbalanced. But you haven't specified what happens with the factor2? or when you say variates - you mean to say that you include co-variates in the model as in ANCOVA. As you say, repeated measures, I am assuming each of the 3 replicates in control and 6 replicates in stress have 12 measurements across the time points.

It is very hard to suggest a design unless you tell us:

1. What do you want to infer from the experiement, i-e- parameter(s) of interest.
2. Any major reason for 3 and 6 replicates in the different treatment levels of factor1.
3. Any other experiment specific detail (may or may not be technical).

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Update:

Jackie, given the limited details, a wild guess of your design (pictorially) will be:

_______Control________________Stress___________

______V1 V2 ... V12___|_____V1 V2 ... V12________

____W1 | . | . |

____W2 | . | . |

____..... | . | . |

.

.

____W12| . | . |

In this table Vs represent varieties and Ws represent weeks. I wanted to ask if all the varieties were present in control and stress, respectively. Control groups include plants not treated with NO3 and stress group were treated with NO3. "." represent the reading of chlorophyll.

If the above design is true, then your design is a simple Split Plot Design with Control as the whole plot treatment and you can treat v1, v2 .. v12 as blocks or "biological replicates" (the choice depends on your specific field and if you want to answer questions related to varieties). And time would be the repeated measure. The correlation between the time points can be modeled using various models, one of the popular choices is AR(1) (SAS also gives you a bunch of options in PROC GLIMIX).

If you want to answer questions related to how treatment (control and stress) interact with time, you can look at the interaction term in the ANOVA analysis.

Please let me know if this answers your question? or there are more details need to be added. I would be particularly interested to know the use of Variety variable, specifically, is it just a block or do you actually want to answer questions related to variety of plants.