Randomised complete block deisgn 2 x 2 factorial

[#1]

Hi there,

I am new to JMP so am hoping you can help!

My experiment was a randomised complete block 2 x 2 factorial design with two levels of supplementary additives. A total of 480 individuals were blocked into pens of 5 (pen acts as the experimental unit, not individual), and pens within a replicate were alloacted to one of the 4 dietary treatments. I had 24 replicates in total, but the experiment was conducted over two batches, the first 240 individuals (12 reps) in february and the second batch of 240 indivudals (12 reps) in April. I therefore need to account block for rep and account for batch.

I just want to check i am doing the ANOVA correctly, in the 'construct model effects' box i have my two factors, their interaction, Batch and rep, is this correct? However, when i do this batch looses its DF (as in the picture) so im not sure what to do?

I also need to add a covariate for start weight for some of the analysis, does this also go in the 'construct model effects' box or should continous covariates go in another box?

Thanks!

[#2]

Hi Tegan,

If I understand correctly - and there is every chance that I do not! -

• A rep is 4 pens of 5 animals.
• Within each rep the 4 pens have 1 of 4 different treatments according to the 2 x 2 factorial.
• You have 24 reps in total,
• in two batches of 12.
• So 96 pens in total,
• which means 96 rows of data.

I'm not sure why rep needs to be included as an effect. Rep seems to me to be an artificial construct here.

Is there any reason to expect a systematic difference between reps. I.e. some reason why all pens within a rep would experience some effect that would change their overall response relative to another rep? Is each rep all within a different building? Or was each rep started at a different time point? Or each rep is from a different parent stock (dont know if that is possible in nutrition trials but I'm jsut tyring to think of possible examples!)?

If there is no reason for a systematic effect of rep then I dont think it needs to be in the model.

If it should be in the model then I would think it should be in there as a random effect.

Similarly "batch" should be a random effect.

One reason for using random effects is that they consume less degrees of freedom.

I hope that helps. Let me know if I have got something wrong in my understanding or if you have questions.

Phil

[#3]

Just to add that I think the reason you are seeing lost degrees of freedom in your ANOVA is because you have both rep and batch as fixed effects. And these 2 effects are aliased. It is not possible to separate their effects. If you wanted to estimated both then I would think that they should be both as random effects with rep nested within batch.

[#4]

Hi Phil,
Thanks for your reply.
Yes that is correct, so I have 96 rows of data.
So rep needs to be included because the individuals were allocated according to their weight so the pens were balanced within rep, so for example, the 4 pens in rep 1 that are on different treatments are balanced for their weight, and the same for rep 2 etc. So essentially rep 1 might have a higher average weight than rep 2. They are also balanced for sex and litter origin too within replicate.
So it sounds as if I need to include them as random effects and rep nested within batch. Please see image attached - what does it mean when it comes up with an error message saying there is no intercept? (the scribbled out bits are just my two factors and their interaction).
Thanks,
Tegan
[cid:image001.png@01D4BFA0.3B980C80]

[#5]

That makes sense.
I can't see the image. I don't think you have attached it properly (unfortunately you can't just paste images).

[#6]

Hi Phil,

Apologies hopefully you can see it now

Tegan

[#7]

Okay, I think I see what has happened there. Specifying nested effects is not trivial!

I think what you have there is Batch nested within Rep - Batch[Rep]. Whereas you want Rep nested within Batch - Rep[Batch]. I think you should also have Batch as an effect. And both Rep[Batch] and Batch should be random effects.

There is an example of a nested random effects model in the JMP Documentation here. It is from a very different industry and appliction but it should make sense.

Phil

[#8 · Accepted solution]

Just to complete the answer this is how you can then use the report to interpret that analysis.

• The top 3 parts of the report should be fairly familiar. You can see the significance of your fixed treatment effects. This is the important bit because these are the effects that are of interest. Most of the rest of the report is just telling you about the random effects that you recognise are sources of variance but don’t really care about.
• Random effect predictions is giving you estimates of the effect of the difference for each rep
• The REML variance components will tell you how variance is attributed to your random effects (Rep and Batch in this case).
• There are more effect details lower down.
• You can also see the estimated means of the response for each level of your random effects (Rep and Batch in this case).