It greatly depends on what your research question is and what the difference between the repeated measures are.

If the 3 reps are technical re-measurements of the same part of a stable sample (instrumental error) then the implications are very different compared with 3 different sub-samplings (sampling error) or 3 technical re-measurements of an unstable sample (time dependent changes).

In some cases averaging together is relevant for estimating between-individuals trends followed by assessment of the degree of within-individual variation.

Method exist that handle multi-level replicates, incorporating within and between individual variation (and other sources of variation. Look into multi-level modelling as one option.

You do replicate measurements simply to improve the accuracy of the read-out per animal. If you do inferential statistics, then only independent values must be used. Values you obtained from replicate mesurements fror the same animal are not independent. If some recordings from an animal are relatively large, the other recordings of the same animal will likely be large, too. Thus, knowing one (or some) of the value from one particular animal gives us some information about other values in your dataset (which are about this same animal). For this reason, these values are not independent. Inferential analyses assume that each value adds the same amount of information, what is not true when the values are not indepentent. When nnon-independent data is used, the analyses over-estimate the amount of information that is actually in the data.

To put it simply: in inferential analyses, the number of values should match the number of animals (that are treated independently). You can achieve this by using the averages of the replicate mesurements per animal.

There are more complicated designs possible with replications on different levels. E.g. you can only treat a batch of animals together, or the animals are litter mates, or the experiment was conducted in batches, possibly by different people. All these factors cause that the individual measurements are not really independent (what applies to measurements from a specific animal applies also to measurements from a specific batch, from a specific litter, from a specific experimenter etc.). One usually uses hierarchical or mixed models to correctly account for this (more or less complex) structure of independence.

If you don't account of non-independence in your data/analysis, you are analysing pseudo-replicates. You can start a google-search with these words to get more information.

Eve Corrie

3 has no statistical validity whatsoever - throw away the 2 outliers and you're left with a perfect measurement. You may as well take 1 measurement only if you can't do 8+ measurements (the pharma industry may argue 6).

Minor comment on James Renwick Beattie comment above:

If the 3 reps are technical re-measurements of the same part of a stable sample (instrumental error) then the implications are very different compared with 3 different sub-samplings (sampling error) or 3 technical re-measurements of an unstable sample (time dependent changes).

• 3 replicate consecutive measurements (intra-assay precision) measure instrumental variation plus any changes of the material during the measurement. The latter is not usually considered but can be significant. In most cases it's just as easy to take 10 consecutive measurements as it is to take 3. This will certainly indicate if there are changes to the test sample during the measurement itself
• 3 sub-samplings will have the same 2 precision markers above plus the heterogeneity or otherwise of the material or subject

It is the usual case that the instrumental variation is the smallest (by 1 or 2 orders of magnitude usually). Techniques give high accuracy and precision on tiny amounts of sample and this is a plus as well as a minus.

Hi Eve,

If I may...(and perhaps to put the valid arguments that have been put forward in a much simpler context).

As long as you are not performing a type of experiment called "repeated measure analysis," what would be required of you is to take the average of the "3 separate recordings" for every animal you have tested. Then you will subject those calculated averages (of all the animals you have used in the experiment) to the appropriate statistical test (T-TEST or ANOVA or whatever fits the number of factors you have, with respect to your experimental design).

Collecting multiple recordings from one experimental animal is (to a large extent) aimed at ensuring that your record per instance of measurement per animal is a "precise recording." (That could be interpreted as, your recording instrument is as accurate in its measurement as possible, and/or that your experimental sample is not changing arbitrarily).

If on the other hand, "if" your layout during your design of the experiment follows "repeated measure analysis," kindly ignore all of what I just said. But if I did understand your question correctly, then you would be violating certain assumptions prerequisite to use of the model you intend to apply in your analysis, if you go on to use the repeat recordings for each animal.

I hope this helps.

Sincerely,

Dami

I agree with the point stressed by Jochen Wilhelm: independent measurements! Other question is the analysis of replications on different levels, e.g. measurements in several time; a batch of animals; etc.

Thank you all for your detailed answers! I can't pretend to have understood every word, but it's cleared a lot up for me regarding reporting INDEPENDENT measurements only! Thanks to these clarifications I'll certainly only be using the average for each animal.

You will have very easy and definite answer if you are able to clarify why the three measurements were taken for each animal? Is it to find how the measurement varies according to different time points or you wanted to have a precise/stable measurement?