What happen if k is more than 2?
- Thread starter neoth
- Start date
The guidance from these authoritative documents would seem to suggest that you just fudge it. If DoF is >10, then k=2 it shall be.
Consider this except from the GUM (section G.6.6):
"""
For many practical measurements in a broad range of fields, the following conditions prevail:
- the uncertainty of uc
is reasonably small because its effective degrees of freedom veff has a significant magnitude, say greater than 10.
Under these circumstances, the probability distribution characterized by the measurement result and its combined standard uncertainty can be assumed to be normal because of the Central Limit Theorem; and uc can be taken as a reasonably reliable estimate of the standard deviation of that normal distribution because of the significant size of veff. Then, based on the discussion given in this annex, including that emphasizing the approximate nature of the uncertainty evaluation process and the impracticality of trying to distinguish between intervals having levels of confidence that differ by one or two percent, one may do the following:
- adopt k = 2 and assume that U = 2uc defines an interval having a level of confidence of approximately 95 percent.
"""
Further, consider this excerpt from NCLSI LM8 (section 7):
"Where three or more independent sources of error contribute to the combined uncertainty by comparable amounts, and the number n of repeated observations exceeds 10, k=2 may be assumed with negligible error."
Consider this except from the GUM (section G.6.6):
"""
For many practical measurements in a broad range of fields, the following conditions prevail:
- the uncertainty of uc
is reasonably small because its effective degrees of freedom veff has a significant magnitude, say greater than 10.Under these circumstances, the probability distribution characterized by the measurement result and its combined standard uncertainty can be assumed to be normal because of the Central Limit Theorem; and uc
can be taken as a reasonably reliable estimate of the standard deviation of that normal distribution because of the significant size of veff. Then, based on the discussion given in this annex, including that emphasizing the approximate nature of the uncertainty evaluation process and the impracticality of trying to distinguish between intervals having levels of confidence that differ by one or two percent, one may do the following:- adopt k = 2 and assume that U = 2uc
defines an interval having a level of confidence of approximately 95 percent."""
Further, consider this excerpt from NCLSI LM8 (section 7):
"Where three or more independent sources of error contribute to the combined uncertainty by comparable amounts, and the number n of repeated observations exceeds 10, k=2 may be assumed with negligible error."