How to use inverse prediction statistics when taking an average of the measured Y response?

Question

HI there,

I have run some experiments where I have formed a calibration curve of Y responses to known X concentrations. I have also run 4 replicates of unknown X concentrations and have associated measured Y values. I want to obtain the confidence intervals for estimating the mean concentration from these 4 replicates, interpolating from the calibration curve. I am aware of the inverse prediction function in jmp to find the confidence intervals, but that only takes into consideration one measured Y value at a time. I am unsure how to approach the problem if I then want to include the errors associated with the mean measured Y values from the unknowns rather than just 1 value assuming no measurement error.

Any help would be greatly appreciated.

Many thanks,

Andrew

Mark_Bailey · Answer

Without replicates, the RMSE estimate from the standard curve fit is model-dependent and based on a small number of degrees of freedom (number of observations (8) - number of parameters (4) = 4). If the model is good (practically no bias) then this RMSE is pretty good but small DF will lead to wider confidence interval.

(BTW, if you have four parameters then you only need four concentrations. The trick is where to place them? JMP Nonlinear Design can help! Then you can also determine the best replication, too.)

Andy152 · Answer

Hi Mark,

Thanks for the response. The standard curve curve was made up of single measurements at 8 different concentrations. It was just the unknowns where the 4 replicates were conducted. As different numbers of replicates were conducted for the standard concentrations and the unknowns, does that prevent the treatment of unknown mean that you proposed?

Regards,

Andrew

Mark_Bailey · Answer

I assume that you determined the standard curve with four replicates at each known concentration. Therefore, the RMSE for the Y variable from the fitted curve is estimated from the replicate errors assuming no lack of fit. Entering the mean response for each unknown will produce a confidence interval that uses the RMSE from individuals as you desired.