# Is this a repeated measures experiment?

We conducted an experiment on hens with seven treatments (medicines) replicated three times. Every treatment was implemented on a flock of fifteen young hens and three of these treated hens were slaughtered after 7, 14, 21, 28, and 35 days and measurements were observed. I wonder whether

• these data should be analyzed as repeated measure (split plot nomenclature)
• if Treatment$\times$Time interaction is significant then orthogonal polynomial contrast (i.e., linear, quadratic, and cubic etc.) should be used.

Or there is another better approach to analyze this kind of data? I'd appreciate if someone can share/tell a similar worked example. Thanks

• Were the hens selected at random for slaughter? – fgregg Jun 24 '11 at 13:47
• Hens were selected at random. – MYaseen208 Jun 24 '11 at 14:14

If the hens were assigned the treatment at random, and then chosen for slaughter at random, then you can think of any three slaughtered hens as a random sample from a notional population of hens treated at time $t$ and observed at some $t+n$. However, @Nick Sabbe is right that if there are herd effects, then these may confound your treatment effect. With only one group per treatment, if there are herd effects, you will have a hard time knowing whether group differences are really due to treatment.

I would consider analyzing the data as follows, assuming that your outcome can be fit into a linear model directly or through some link function.

\begin{align} &\text{Outcome}_{ij} = \beta_{0j} + \beta_{1j}t + \beta_{2j}t^2 + \beta_{3j}t^3 + \ldots + \varepsilon_i\\ &\beta_{0j} = \gamma_{00} + u_{0j} \\ &\beta_{1j} = \gamma_{10} + u_{1j} \\ &\beta_{2j} = \gamma_{20} + u_{2j} \\ &\beta_{3j} = \gamma_{30} + u_{3j} \\ &\ldots \end{align}

Where $i$ indices a particular bird, and $j$ a treatment group, $\gamma$'s describe the development of the a bird with an "average" treatment, and the $u$'s are treatment group specific deviations (either due to shared treatment or some other group property like a herd effect). You can represent the $u$'s as a random effect or as dummy variables. If you use dummy variables you can choose another contrast baseline besides the "average" treatment. Orthogonal polynomials would make your results easier to interpret.

• Thanks for nice explanation. Would you like to share an example preferably analyzed in R. – MYaseen208 Jun 25 '11 at 3:25

I think your situation is a lot more complicated than a simple (!) repeated measurements.

Since you are removing some hens from each herd, the herd is effectively changing. Imagine the difference when you (by chance) pick the three sickest hens first to be removed, as opposed to letting them in: this could very well be of influence on the remaining hens in the herd (you don't specify whether the disease is transferable, but even then: it could influence the 'social structure' of each herd).

It might be that a transition model (which allows the results of previous measurements to be used as regressors for the next measurement) corrects for this, but I have no real experience with this.