Lead-time bias

Guidelines are to sample from a moving stream of powder and to sample the whole of the stream for many equal periods of time. This ensures that all parts of the powder are equally accessible and this maximizes accuracy.f The sample thief does not meet these criteria and therefore should not be used. Despite being popular, it suffers from many disadvantages, which lead to bias and error. Most other methods are immediately ruled out as suitable if these guidelines are followed. 

The main consequences are twice. First, it results in contrast degradations as a function of the differential dispersion. This feature can be calibrated in order to correct this bias. The only limit concerns the degradation of the signal to noise ratio associated with the fringe modulation decay. The second drawback is an error on the phase closure acquisition. It results from the superposition of the phasor corresponding to the spectral channels. The wrapping and the nonlinearity of this process lead to a phase shift that is not compensated in the phase closure process. This effect depends on the three differential dispersions and on the spectral distribution. These effects have been demonstrated for the first time in the ISTROG experiment (Huss et al., 2001) at IRCOM as shown in Fig. 14. 

Ruggedness testing evaluates how small changes in the method conditions affect the measurement result, e.g. small changes in temperature, pH, flow rate, composition of mobile phase, etc. The aim is to identify and, if necessary, better control method conditions that might otherwise lead to variation in measurement results, when measurements are carried out at different times or in different laboratories. It can also be used to improve precision and bias. 

If a large number of readings of the same quantity are taken, then the mean (average) value is likely to be close to the true value if there is no systematic bias (i.e., no systematic errors). Clearly, if we repeat a particular measurement several times, the random error associated with each measurement will mean that the value is sometimes above and sometimes below the true result, in a random way. Thus, these errors will cancel out, and the average or mean value should be a better estimate of the true value than is any single result. However, we still need to know how good an estimate our mean value is of the true result. Statistical methods lead to the concept of standard error (or standard deviation) around the mean value. 

The formation of pores during anodization of an initially flat silicon electrode in HF affects the I-V characteristics. While this effect is small for p-type and highly doped n-type samples, it becomes dramatic for moderate and low doped n-type substrates anodized in the dark. In the latter case a reproducible I-V curve in the common sense does not exist. If, for example, a constant potential is applied to the electrode the current density usually increases monotonically with anodization time (Thl, Th2]. Therefore the I-V characteristic, as shown in Fig. 8.9, is sensitive to scan speed. The reverse is true for application of a certain current density. In this case the potential jumps to values close to the breakdown bias for the flat electrode and decreases to much lower values for prolonged anodization. These transient effects are caused by formation of pores in the initially flat surface. The lowering of the breakdown bias at the pore tips leads to local breakdown either by tunneling or by avalanche multiplication. The prior case will be discussed in this section while the next section focuses on the latter. 

The statistical test procedures that we use unfortunately are not perfect and from time to time we will be fooled by the data and draw incorrect conclusions. For example, we know that 17 heads and 3 tails can (and will) occur with 20 flips of a fair coin (the probability from Chapter 3 is 0.0011) however, that outcome would give a significant p-value and we would conclude incorrectly that the coin was not fair. Conversely we could construct a coin that was biased 60 per cent/40 per cent in favour of heads and in 20 flips see say 13 heads and 7 tails. That outcome would lead to a non-significant p-value (p = 0.224) and we would fail to pick up the bias. These two potential mistakes are termed type I and type II errors. 

We now check whether Eq. (1), with S /3 = e2/ and modified as above to account for finite propagation time, can explain our data. The unknown parameters are the resistance Rq and the effective environment noise temperature Tq. We checked that the impedance of the samples was frequency independent up to 1.2 GHz within 5%. Fig. 2 shows the best fits to the theory, Eq. (1), for all our data. The four curves lead to Ro = 42 12, in agreement with the fact that the electromagnetic environment (amplifier, bias tee, coaxial cable, sample holder) was identical for the two samples. We have measured the impedance Zenv seen by the sample. Due to impedance mismatch between the amplifier and the cable, there are standing waves along the cable. This causes Zenv to be complex with a phase that varies with frequency. We measured that the modulus Zenv varies between 30 12 and 70 12 within the detection bandwidth, in reasonable agreement with f o = 42 12 extracted from the fits. 

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