On using an approximate noncentral t-distribution in determining a one-side upper limit for future sample relative...

Area of Science:

• Analytical Chemistry
• Statistical Methods
• Quality Control

Background:

• Reproducibility standard deviations (RSD(R)) are critical for assessing analytical method performance.
• Accurate estimation of RSD(R) upper limits is essential for reliable collaborative studies.
• Existing methods for estimating RSD(R) upper limits may have limitations.

Purpose of the Study:

• To develop a new formula (kappap) for determining one-tailed upper limits of relative standard deviations (RSD(R)).
• To base the new formula on an approximate noncentral t-distribution with Satterthwaite's adjustment.
• To assess the accuracy of the proposed kappap formula.

Main Methods:

• Development of a new formula (kappap) for RSD(R) upper limits.
• Utilizing an approximate noncentral t-distribution and Satterthwaite's adjustment for degrees of freedom.
• Comparison of kappap with Monte Carlo simulations and an existing normal approximation formula (gammap).

Main Results:

• The study introduces the kappap formula for estimating RSD(R) upper limits.
• Accuracy of kappap was evaluated against simulation data and the gammap formula.
• The noncentral t-distribution approach provides a basis for improved RSD(R) estimation.

Conclusions:

• The kappap formula offers a statistically sound method for setting upper limits on reproducibility standard deviations.
• This approach is valuable for future collaborative trials and quality control in analytical science.
• The developed formula demonstrates potential for more accurate reproducibility assessments.