A symmetric distribution, characterized by its degrees of freedom, that describes the scatter of a mean estimated from a small sample when the population standard deviation is unknown. Its tails are heavier than the normal's, so fewer degrees of freedom demand a larger coverage factor for the same coverage probability: about 2.65 for 95.45 % with 5 degrees of freedom against 2.00 with infinite degrees of freedom. By 30 degrees of freedom the factor has fallen to about 2.09, close enough to 2 that many labs simply use the normal.
Only four repeats, so pull k from the t-distribution table, not the normal.
Also heard as
- t-distribution
- Student's t
Related terms
Degrees of freedom
A count of the independent information behind an uncertainty estimate, showing how reliable that estimate is.
Coverage factor
The multiplier applied to combined standard uncertainty to obtain expanded uncertainty, usually k = 2.
Welch-Satterthwaite formula
The equation that estimates effective degrees of freedom for a combined uncertainty, used to pick the coverage factor.
Normal distribution
The bell-shaped distribution assumed for most certificate values and averaged readings, set by mean and standard deviation.