The expanded uncertainty can be found at two different levels of sophistication. The simpler approach uses simply a preset k value (most often 2) and the actual coverage probability is not discussed. This approach is presented in the first video lecture.
Finding the expanded uncertainty (simpler approach)
http://www.uttv.ee/naita?id=17644
https://www.youtube.com/watch?v=KomDnLRArDs
The second approach is more sophisticated. It is an approximation approach based on the assumption that the distribution function of the output quantity can be approximated by a Student distribution with the effective number of degrees of freedom found by the so-called Welch-Satterthwaite method. This enables then to use the Student coefficient corresponding to a desired level of confidence (coverage probability) as the coverage factor. This approach is explained in the second video lecture.
Finding the expanded uncertainty (the Welch-Satterthwaite method)
http://www.uttv.ee/naita?id=17916
https://www.youtube.com/watch?v=CylWJjG_8ck
The XLS file containing the combined standard uncertainty and expanded uncertainty calculation and the XLS file containing the expanded uncertainty calculation using coverage factor found using the effective number of degrees of freedom form the Welch-Satterthwaite approach can be downloaded from here:
 | uncertainty_of_photometric_nh4_determination_kragten_solved.xls | 53 KB |
| uncertainty_of_photometric_nh4_determination_kragten_solved_df.xls | 48 KB |
