# Finding the average of multiple standard deviations with different sample sizes

#### dceverett10

##### New Member
I have run a ton of samples on two specific instruments that are designed to get a specific measurement for my work. I reran each sample on another model of the same instrument. My goal is to find out which instrument is reading the samples with the smallest amount of variation between measurements.

For example on day 1 I ran 3 samples, on day 2 I ran 3 samples, on day 3 I ran 9 samples, on day 4 I ran 6 samples, etc.

I have calculated the standard deviation for each individual day on each instrument. For example I have the standard deviation between the three samples run on day 1 on instrument 1, and also have the standard deviation between the three samples run on day 1 on instrument 2.

Now I would like to combine the standard deviations from each day to get an average to compare the standard deviation from instrument 1 samples to the average standard deviation for instrument 2 samples.

I have basically no experience in statistics. Can anybody point me in the right direction to accomplish this?

Thank you!

#### fed2

##### Active Member
welcome to the world of method qualification/validation.

The variance components are usually estimated by mixed model in this case. You have 3 variance components, i think, day / instrument and residual (repeatability i think). A variance component is basically a standard deviation (squared). maybe someone has some references about that...