Why use the CV? Its a function of the standard error which in the simplest case is SD/n^0.5

So going from 10 to 5 replicates changes the efficiency by a factor of root 2.

You can do more formal analyses using the accuracy in parameter estimation approach (this lets you set the assurance that the width of a CI is less than or equal to some value). For a more detailed analysis in more complex cases you could use a simulation approach.

But if you can estimate the SD then you can just see how many replicates gets the standard error to an acceptable value for your desired margin of error e.g., roughly 2 SEs should be smaller than your min detectable change for 95% confidence.

es, the coefficient of variation (CV) can be a useful tool to estimate the number of measurement replicates needed to better detect changes over time, particularly in experimental or observational studies where variability in measurements is a concern. The CV provides a normalized measure of variability relative to the mean, making it a valuable metric for planning replication in studies.

Hellow, THank you so much I kind thought long abou the answer from Thom Baguley, whic was very helpful, but I still strugle with some things.

I’m working on the design of a longitudinal echocardiographic study in pediatrics, and I’d be very grateful for your input on a few statistical challenges I’m trying to resolve.

Let’s say I’ve already measured the within-subject standard deviation (SD) and intraclass correlation coefficient (ICC) for a given parameter (e.g., LV wall thickness or mitral inflow velocity), and I’ve optimized my protocols. I’ve decided that using, say, 10 repeated measurements per subject gives me the most realistic level of precision for that parameter.

Now, my main question is: -> How do I determine the number of patients I need to detect a true change over time, especially in children where within-group variability is inherently high due to age-related differences?

But here’s the catch:

• Within-subject variance may change over time. Some children have higher SD at baseline than at follow-up (or the opposite).
• The intrinsic variability of the parameter itself may evolve over time (e.g., during growth or puberty).
• Standard mixed-effects models often assume equal variance (homoscedasticity) over time — which could lead to misinterpretation.
• Using medians across replicates might reduce outliers, but could also mask true biological trends.

So I'm wondering:

• Is there a way to model or calculate the required sample size while accounting for the number of repeated measurements and the parameter’s intrinsic variability?
• If I’m measuring 25 different parameters, each with different CV or SD, could I optimize by adjusting replicates instead of just increasing n?
• And finally — could center-specific variability (equipment, staff, protocols) be factored in? Ideally, each center could measure its own reproducibility, and plug that into a formula that combines intrinsic variability and number of replicates per parameter.

Has anyone tackled something like this — or come across a modeling strategy, framework that would help?

Many thanks in advance for any thoughts or resources!