3
$\begingroup$

We want to test the effect of dietary supplement on two groups of cows (randomized and controlled for starting weight and age). Group 1 (6 cattle) receives supplement 1 and group 2 (6 cattle) receives supplement 2.

They are housed in the same pen but groups are isolated from each other. Animals are weighted once a month for 3 months, being fed a high energy and high protein ration (+ supplement 1 or 2 depending on their group).

A colleagues states that we should absolutely split the groups and go Group 1a (3 cattle) - group 2a (3 cattle) - Group 1b (3 cattle) - group 2b (3 cattle) to avoid pseudoreplication, since

If the supplements are applied to the group, although measurements are taken individually they should be averaged to the pen (smallest unit upon the supplement is applied). By consequence, you do not have replicates to run the statistical analysis.

In my opinion as the groups are independent and there are no variables that could influence significantly the outcome other than the supplement, using only two groups is still appropriate.
So is the original design (Group1 & Group2, 6 cattle in each) correct here?

$\endgroup$
1
  • $\begingroup$ It's a complicated topic, which depends on the level at which your experimental treatment is being applied. I'll note for the moment that even if your colleague were correct, their suggestion doesn't help a huge amount: you've gone from having 1 experimental unit per treatment to 2. $\endgroup$
    – mkt
    Commented Jun 29, 2023 at 18:48

2 Answers 2

3
$\begingroup$

Seems to me that there are two questions that your experiment might be used to answer. The first is the most obvious: does the supplement affect the weight gains of cows. For that question you are treating 6 cows that share a pen. The second question is slightly different: does putting the supplement into the feed affect the weight gains of a pen of cows. For the second you have only a single pen for each supplement.

Obviously an answer to the first predicts an answer to the second, and vice versa, but they are different questions and it is possible for one to say 'yes' and the other 'no'. If your focus is on the cows then the second question might seem silly, but if you are a farmer who will be adding the supplement to the feed for lots of cows then the second question might be more interesting.

A clinical analog of the distinction would be the difference between does the drug work if a patient takes it?, and would the drug have a positive effect if it was approved for prescription? A 'per protocol' analysis can be used for the first, and an 'intention to treat' analysis might be preferred for the second.

Just as the per protocol analysis takes into account the actual doses of drug taken by a patient, you might need to do something to confirm that all cows in the pen take at least approximately the same amount of the supplement. By "do something" I might mean nothing more than a trivial confirmation that all of the cows eat a well-mixed feed and supplement source, but it is possible that an individual cow might change the amount it eats because it dislikes the taste of supplement.

$\endgroup$
2
$\begingroup$

The answer depends on subject-matter issues specific to feeding cows in pens. As a non-expert, I don't at first glance see that the situation with 6 cows in a pen all getting the same treatment in their feed is any different from 6 patients all getting the same type of pill from a single bottle. As @mkt says in a comment, however, there might be a reason to think of this more like plants in a block receiving the same fertilizer.

You also haven't specified how you are dealing with the 3 measurements per cow, which involve intra-cow (or intra-subgroup) correlations that need to be accounted for. This is a "growth curve" that might be handled by generalized least squares or a mixed model.

A potentially bigger problem is whether your method of isolating the 2 groups within the single pen is itself leading to some unsuspected difference in outcomes unrelated to the supplement. There is no way then to distinguish the effects of the isolation method from the effects of the supplement.

$\endgroup$
1
  • $\begingroup$ I think there are grey areas in pseudoreplication, and this is one, at least based on the information presented. If the feed is supplemented to a general stock for a pen, that seems closer to fertilising a plot of crops than giving pills to individual patients. And we don't treat each plant in a plot as a true replicate, or accept a 1 plot vs. 1 plot comparison as strong evidence. $\endgroup$
    – mkt
    Commented Jun 30, 2023 at 14:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.