Metrohm viva 1.1 (ProLab) - Manual (Page 74)

2.3 Formula editor
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viva 1.1 (for process analysis)
Sign('CV.AverageTemp') = Sign of the value of the common variable
CV.AverageTemp
2.3.4.5.10 Quantiles of the Student's t-distribution
Dialog window: Formula editor ▶ Operators/Functions
Syntax
t
s
= Tinv(Probability, Degrees of freedom)
Calculates the quantiles of the Student's t-distribution for two-sided inter-
vals.
The result describes the half interval length as a multiple of the standard
deviation of a sampling totality with given degrees of freedom within
which, with the indicated probability, the mean value of the distribution
lies, when the interval is centered on the mean value of the sampling
totality.
Parameters
Probability
Number type, value range: 0 - 1. Direct entry as number or as formula
providing a number. If the type or value is non-permitted, then the result
will become invalid. This is to indicate the probability of the unknown
mean value of the t-distributed result falling within the two-sided interval.
Degrees of freedom
Number type, value range: 1 - n. Direct entry as number or as formula
providing a number. If the type of value is non-permitted, then the result
will become invalid. The number of independent samplings for calculat-
ing the standard deviation, reduced by the number of adjusted parame-
ters for the model to which the standard deviation refers, must be speci-
fied as degrees of freedom (Degrees of freedom = Number of samplings –
Number of parameters).
Examples
Tinv(0.95; 9) = 2.26: With a 10-fold determination (e.g., of a titer) half
the interval length corresponds to 2.26 times the standard deviation.
Calculation of the confidence interval for a mean value of sam-
pling: A variance-homogenous sampling with a range n for a normally
distributed quantity with an expected value µ has the mean value x
m
, the
standard deviation s and the degrees of freedom v = n – 1. The half inter-
val length t
s
· s/ √n then indicates how high, within the given probability,
the maximum absolute difference is between the mean value x
m
and the
expected value µ. Here the confidence interval is the full interval length,
centered to the mean value: µ = x
m
± t
s
· s/ √n.
Titer determination: 0.991, 1.021, 0.995, 1.003, 1.007, 0.993, 0.998,
1.015, 1.003, 0.985