Should replicates within blocks be averaged prior to ANOVA in CRBD?
For example, consider a factorial experiment with CRBD, with the two factors A (Levels 1 and 2) and B (Levels 1 and 2), and 4 Blocks (1 to 4), each including 10 replicates (plants), therefore with a total of 160 plants.
Should the dataset include 160 or 16 records?
For example, consider a factorial experiment with CRBD, with two factors A (Levels 1 and 2) and B (Levels 1 and 2), and 4 Blocks (1 to 4), each including 10 replicates (plants), therefore with a total of 160 plants.
Should the dataset include 160 or 16 records?
Dear Giovanni,
If your original experimental design included the replications you can not average the replications. Doing that, appart of modifying your orginal design, you are eliminating from the design the variability due to replications, i.e., the experimental error, that could greatly affects the results of your analyses as the only source of variability would be that due to blocks.
Dear Juan,
thanks for your answer. Therefore, to average the replicates prior to analysis should decrease the power of F test. Is it correct?
Ciao Giovanni,
it is incorrect to use the sub samples as replications. Increase the degrees of freedom of the error and the probability of obtaining significant differences between treatments that are not.
Dear Giovanni,
Do not average your values. Having 160 records is way better than having 16. your effort of collecting 160 records would go in vain if you average it. the more data you feed, the better it becomes.
Thanks Pietro and Zohara.
Pietro, I'm not sure if replicates within block can be considered sub-samples. Actually they are different subjects. Also, if sub-samples exist (e.g., two contemporary measures on the same subject), perhaps nested factors should be considered. Is it correct?
i do not think the average will help but rather working with what you have
In general, I wouldn't average samples within a block unless the variability of the replicates is exceedingly large or a goal is to minimize variability and optimize a response. Then you'll have a multiobjective optimization.
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