Measured quantities

The error analysis requires assumptions about the type of uncertainty to attribute to the individual measurements. Unfortunately, none of the individual measurement uncertainties are based upon a statistical analysis. Rather, the measurement uncertainties are based upon engineering judgment, classified as Type B [41, 42] by the International Organization for Standardization (ISO).

Table 5 summarizes the various measurement uncertainties for this experiment. Since the uncertainty in each measured quantity must be quantified, an error model must be chosen. Here, a Gaussian distribution is used for convenience. The uncertainties in Table 5 are characterized by the ±2 σ interval, corresponding to a coverage of approximately 95 %.

Table 5: Standard uncertainties for the measured quantities of voltage V, current I, current measurement time t, specimen length L, specimen diameter D, and bulk resistance R_B.

Measured Quantity	Uncertainty Source	±2σ
V	−1−	±0.054 V
I	−1−	±0.0006 A
t	-1-	±0.120 s
L	−2−	±3 mm
D	−3−	±2 %
RB	−4−	±2.0 Ω
−1− Equipment specifications. −2− Tolerance reported in ASTM C 1202. −3− Tolerance reported in ASTM C 470. −4− Typical nearest neighbor differences at minimum.

The choice of the 2σ interval is based upon engineering judgment. If a reputable electronics manufacturer specifies that a voltmeter has an accuracy of 0.054 volts, it is assumed that 2 σ  =  0.054 V represents the expectation that the voltmeter will be in error by more than ±0.054 volts only 5 % of the time. This is a conservative estimate since one would expect such a device to be "out of spec" far less than 5 % of the time. In Table 5, the 2σ intervals for the equipment specifications are the accuracies specified by the manufacturer.

Two of the remaining uncertainties in Table 5 are for dimensional measurements. Unfortunately, statistical measurements of the corresponding dimensions of each specimen were not performed. Therefore, the uncertainty in the length and diameter of each specimen is based upon the tolerances specified in the corresponding ASTM specification, with the assumption that the specified tolerance represents a 2σ interval.

The final quantity in Table 5 is the bulk resistance measured by IS. Here, the 2σ interval is a "best guess" based solely on general observations. The minimum in the value of −Z" is not an exact quantity. The curvature at the minimum dictates the accuracy of the determined quantity. The 2σ interval represents an overall characterization of the interval between adjacent values of Z ' at the minimum of −Z". Many of the adjacent values were considerably less than this quantity, but none was greater.