I regularly see confusion between repeated measurements and replicated measurements in experimental designs. They are very different, and so are the analyses that result from them.
Yes, repeated measurements and replicated measurements are both multiple response measurements taken with the same combination of parameters! But repeated measurements are taken during the same series of experiments or consecutive series, while replicated measurements are taken during identical but different series of experiments, often randomized.
Replicates
In Design of Experiments, a replicate is an independent execution of the same experimental treatment, performed under identical factor settings but including all sources of experimental variability.
This implies:
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The system is fully reinitialized
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New material, batch, operator, or time point
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Independence between runs
What replicates estimate
Example
Two experimental runs performed on different days with the same factor levels are considered replicates.
Which analysis?
In this situation, you want to estimate pure error.
Pure Error is the variability observed between true replicates at identical factor settings. Pure error isestimated from replicated design points using the lack-of-fit decomposition.
Note that the RMSE represents the total residual variability, including both pure error and model lack of fit.
If you have replicates, you can access to the Lack of fit section in your Standard Least Square report from usual setting of Fit Model Platform
Repetitions
A repetition (or repeated measurement) refers to multiple measurements taken within the same experimental run, without reinitializing the process.
This typically involves:
What repetitions estimate
Example
Measuring the same sample three times using the same instrument corresponds to repetitions, not replicates.
Which analysis?
When the design includes repetitions:
REML (Restricted Maximum Likelihood) is recommended to estimate variance components.
The REML personality is selected when the Fit Model platform model is launched and when a factor is defined as random.
The definition of a random effect is done by the attribute option
And the report will have an additional section related to REML. This will explain the % of variation explained by the random effects.
Conclusion
In summary, replicates provide an estimate of the pure experimental error, whereas repetitions reflect only measurement variability and should be accounted for using random effects models.
