# Unbalanced repeated measure design for the given data?

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?

• I think it would be excellent if you could give more detail (see suncoolsu's answer). Furthermore, with design, do you mean how to analyze the data? – Henrik Oct 13 '10 at 8:59

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).

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.

• Hi all, Thanks for you answers! 1) I want check the effect of treatment(control, stress) with time (week1, week2,...,week12) and with varieties (var1,var2,...,var12). 2) difference b/w replicates is because of source available 3)Some description of data is given below: All Citrus plants were grown in pots with same soil and all condition same. Then only' Stress' labelled plants were treated with chemical 'NO3' and other plants 'Control' were untreated. Chlorophyll content (Data given) was recorded at day 1 and then each week for exactly the same plants. – jacki Oct 13 '10 at 11:27
• @Jacki, Your experimental design looks like a special case of Split plot design, but to decide the special case, I need extra details. Can you please represent your design inform of a picture (see my update) ? Currently, I don't see how you use the varieties? Is the difference between varieties of interest or not? – suncoolsu Oct 13 '10 at 15:11
• Thanks for you detailed answer and help! The design you made is fine. Yes I am also interested to see the differences between varieties. Do you know how to do in SPSS? – jacki Oct 13 '10 at 22:40
• @Jacki, you would do this in SPSS using the mixed model options. I am sorry, but this is the end of my knowledge in SPSS (not a regular user :-( ). I can point out some good reference for R or SAS, in case you are interested. – suncoolsu Oct 14 '10 at 0:17
• Also, please modify your question above so that we can see the full detail. The comment space is too small for such discussions. – suncoolsu Oct 14 '10 at 0:39