# Number Of Biological Replicates vs Number Of Technical Replicates

#### biotechno

##### New Member
Hi everyone,

We receive a diferente group of samples from the same group from time to time.

When we receive a bigger number of Biological Replicates from the same group, we dont need so many Technical replicates - would you agree?

If the Number of Biological Replicates is big enough, it might not even make sence to do any Technical Replicates to evaluate the group - would you agree?

How many Technical Replicates would you sugest vs Biological Replicates?

We try never to use less than 6 Biological Replicates. But when we have 20, or 50 or 100 Biological Replicates, how we decide how many technical Replicates would make sense, if any?

Thank you all of your time!

#### fed2

##### Active Member
Interesting i have oft pondered this issue. depend on the relative size of the variance between technical replicates, and that between biological replicates. Basically your right though. Also bioreps usually >>>>>>>>> variance than tech reps. so usually keep tech reps to minimum.

The basic stats on the issue is:

Y_{i,j} = X_{i} + Eps_{i,j} : ith animal, jth tech rep, X_i the 'true' value for ith animal.

So mean over tech reps for ith animal:
Y mean_{i} = X_{i} + Eps_mean_i

and take variance
SD( Y_mean_{i} ) = SD between bio reps + tech stdev /sqrt(# tech reps)

and so you see with this square root thing 'diminishing returns' on increasing the tech reps. Thats basically saying you don't benefit from reweighing the same rat 1000 times.

if you want to turn it into a cost optimization, consider the constraint
Total cost = Bio reps * bio rep cost + techreps*tech cost;

If that all seems like too much math, and to most it does, consider the 'rule of 3' for tech reps.

good luck.

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#### biotechno

##### New Member
Thank you very much for your answer!

We will study it with great interest

#### fed2

##### Active Member
I went through the motions on minimize Variance = biovariance/# bio reps + tech variance / ( (#tech reps)(#bio reps) )
subject to
Cost = Bio reps * bio rep cost + techreps*tech cost;

I thin it works out to
# tech reps = sqrt( Bio cost * Tech variance / Tech Cost * Bio Var )
So bigger bio cost or tech variance leads to more tech reps.

In words: The number of tech reps depends on how much the ratio of the tech variance to bio variance exceeds teh ratio of their costs.

How does that sound?

Im sure that formula is out there, but its hard to google up.

In practice though, the tech variance and tech cost are always much smaller, so choose the minimum 'plausible' number. Usually 3, 2 maybe. 1 makes people uneasy for obvious reasons.