Prediction interval for unequal replicates

[statclean]

Dear experts,

I am trying to develop an algorithm for calibration studies (analytical chemistry). The algorithm could be used for estimation of calibration parameters, limit of detection & quantitation etc. For this I have to construct a prediction interval for the calibration curve. Now the only problem which I am facing is how to deal with unequal number of replicates (i.e. unequal number of Y responses) for each X value. For the estimation of calibration curve I am using the mean of Y responses weighted by the number of replicates at each X value. If I treat each Y replicates as individual points then the prediction interval can be estimated using this formula:
PI = YPred ± t*Se*SQRT(1+1/N+(x-xbar)²/Sxx)
Similarly for replicates (equal number) at each X value, the formula changes to:
PI = YPred ± t*Se*SQRT(1/m+1/N+(x-xbar)²/Sxx)
This formula seems suitable only for equal numbder of replicates. I need your help in deciding how to use the above formula for the estimation of prediction interval for unequal number of replicates.

Thanks in advance.

 

[Valkarie]

The formula you have mentioned is for equal number of replicates and cannot be used for unequal number of replicates. To deal with unequal number of replicates, you can use a weighted least squares analysis. This approach takes the variance of each replicate into account and assigns different weights to each measurement. The weights are inversely proportional to the variance of each replicate. This approach can be used to construct the prediction interval for an unequal number of replicates. Additionally, you can also use bootstrapping methods to estimate the prediction interval. Bootstrapping involves resampling with replacement from the original data to create a distribution of simulated datasets, which can then be used to generate the prediction interval.