Multiplier Selection
Numerical factors applied to combined standard uncertainty scale interval bounds to achieve a specified level of confidence. Metrology standards utilize coverage factor expansion to convert standard uncertainties into expanded uncertainties representing defined statistical intervals. A factor of two corresponds to an approximate ninety-five percent confidence level under a Gaussian probability distribution.
Gaussian Interval
Normal distribution assumptions govern standard coverage factor calculations when degrees of freedom are large. Applying coverage factor expansion under normal conditions uses fixed multipliers derived from standard normal probability tables. When measurement results follow normal distributions without significant systematic biases, a multiplier of two covers approximately ninety-five point four five percent of the distribution.
Student Distribution
Small sample sizes and estimated variances alter the underlying probability density function of measurement data. Calculating coverage factor expansion for limited repeated measurements requires using Student t-distribution tables based on calculated effective degrees of freedom. Effective degrees of freedom are evaluated using the Welch-Satterthwaite formula.
As effective degrees of freedom decrease, the required expansion factor increases significantly to maintain ninety-five percent confidence.
Tail Inflation
Asymmetric distributions and non-Gaussian influence factors alter tail probabilities in measurement models. Non-linear measurement equations expand uncertainty bounds non-uniformly. Calibration certificates state the chosen expansion factor and resulting confidence interval clearly.
