Number bias

For the 1500 buret readings sampled, the expected frequency F, is 150 in each class, with the assumption of no number bias. The calculated value of is 23,952/150 = 160, a value that at 9 degrees of freedom (the number of classes minus 1) lies far above the 99.9 percentile probability level and indicates pronounced number bias. The bias in this case is for small numbers and against large ones (a common type of bias for this type of reading). Another indication of number bias is obtained by comparing the observed standard deviation s = V23,952/9 = 52 with that calculated from the binomial distribution (Section 27-3) s = Vnp(l — p), which for n = 1500, p = 0.1, and 1 — p = 0.9 gives s = 2 for 10 equal classes of probability 0.1. 

Number bias varies considerably from observer to observer. The commonest bias is for the digits 0 and 5, but prevalent also is bias toward even numbers and against odd ones, and for low numbers and against high ones. Such number bias imposes a limitation on the accuracy of readings by an individual. 

A universal source of personal error is prejudice, or bias. Most of us, no matter how honest, have a natural tendency to estimate scale readings in a direction that improves the precision in a set of results. Alternatively, we may have a preconceived notion of the true value for the measurement. We then subconsciously cause the results to fall close to this value. Number bias is another source of personal error that varies considerably from person to person. The most frequent number bias encountered in estimating the position of a needle on a scale involves a preference for the digits 0 and 5. Also common is a prejudice favoring small digits over large and even numbers over odd. 

Systematic errors arise not only from procedures or apparatus they can also arise from human bias. Some chemists suffer from astigmatism or colour-blindness (the latter is more common amongst men than women) which might introduce errors into their readings of instruments and other observations. Many authors have reported various types of number bias, for example a tendency to favour even over odd numbers, or 0 and 5 over other digits, in the reporting of results. It is thus apparent that systematic errors of several kinds are a constant, and often hidden, risk for the analyst, so the most careful steps to minimize them must be considered. 

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

Another important feature of the Tanimoto coefficient when used with bitstring data is that small molecules, which tend to have fewer bits set, will have only a small number of bits in common and so can tend to give inherently low similarity values. This can be important when selecting dissimilar compounds, as a bias towards small molecules can result. 

Uncontrolled Variables and Randomization. A number of further variables, such as ambient conditions (temperature, pressure, etc), can be identified but not controlled, or are only ha2ily identified or not identified at all but affect the results of the experiment. To ensure that such uncontrolled variables do not bias the results, randomisation is introduced in various ways into the experiment to the extent that this is practical. 

This is a formidable analysis problem. The number and impact of uncertainties makes normal pant-performance analysis difficult. Despite their limitations, however, the measurements must be used to understand the internal process. The measurements have hmited quahty, and they are sparse, suboptimal, and biased. The statistical distributions are unknown. Treatment methods may add bias to the conclusions. The result is the potential for many interpretations to describe the measurements equaUv well. 

Let us now cool the interface down to a temperature T(driving force for solidification. This will bias the energies of the A and B molecules in the way shown in Fig. 6.5. Then the number of molecules jumping from liquid to solid per second is... 

When rods are required they are placed in wooden trays in a formolising bath. If the requirement is for a disc or blank such as used by the button trade the extrudate is cut up by an automatic guillotine and the blanks are immersed in the formalin solution. For manufacture of sheets the rods are placed in moulds and pressed into sheets before formolising. Many attractive patterns may be made by pressing different coloured rods into grooves set on the bias to the rods, thus forming new multi-coloured rods. This operation may be repeated a number of times in order to produce complex patterns. 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

An improvement of this method—the so-called biased sampling [55] (or inversely restrieted sampling)—suggests to look ahead at least one step in order to overcome the attrition. Consider a SAW of i steps on a -coordination number lattice. To add the / + 1st step one first checks which of the = q — neighboring sites are empty. If k qQ > k>0) sites are empty one takes one of these with equal probability 1 /A if A = 0 the walk is terminated and one starts from the beginning. This reduces the attrition dramatically. Now each A-step walk has a probability PAr( i ) = Ylf=i so that dense configurations are clearly more probable. To compensate for this bias, each chain does not count as 1 in the sample but with a weight... 

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