Experimental nonrandom sampling

Statistical experimental design is characterized by the three basic principles Replication, Randomization and Blocking (block division, planned grouping). Latin square design is especially useful to separate nonrandom variations from random effects which interfere with the former. An example may be the identification of (slightly) different samples, e.g. sorts of wine, by various testers and at several days. To separate the day-to-day and/or tester-to-tester (laboratory-to-laboratory) variations from that of the wine sorts, an m x m Latin square design may be used. In case of m = 3 all three wine samples (a, b, c) are tested be three testers at three days, e.g. in the way represented in Table 5.8 ... 

To optimize resolution in lifetime-based assays, a comparison of relative estimates is always favorable. If the FLIM experiment is carried out in an environment where temperature cannot be tightly controlled, it is also convenient to cycle between different samples during the same experimental session, in order to average out thermal and other instrumental drifts. When applicable, this practice may be useful to suppress any nonrandom variation in the detection. 

In general, structure solution from powder XRD data has a good chance of success only if the experimental powder XRD pattern contains reliable information on the intrinsic relative intensities of the diffraction maxima, which requires that there is no preferred orientation in the powder sample. Preferred orientation arises when the crystallites in the powder sample have a nonrandom distribution of orientations, and this effect can be particularly severe when the crystal morphology is strongly anisotropic (e.g. long needles or flat plates). When a powder sample exhibits preferred orientation, the measured relative peak intensities differ from the intrinsic relative diffraction intensities, limiting the prospects for determining reliable structural information from the powder XRD pattern. In order to circumvent this... 

Peak intensities. If the material exhibits preferred orientation (i.e. a nonrandom distribution of orientations of the crystallites within a powder), the relative intensities of peaks in the powder XRD pattern will deviate from the intrinsic relative intensities that are characteristic of the crystal structure, and hence the powder XRD patterns recorded for two samples of the same material but exhibiting different degrees of preferred orientation may appear substantially different. This issue is particularly pertinent in comparing an experimental powder XRD pattern with a simulated powder XRD pattern for a known crystal structure, as there are implicitly no effects due to preferred orientation in the latter case. 

Biological replication and appropriate controls are essential to ChIP experiments to assess reproducibility because of the nonrandom shearability of DNA and off-target effects of enrichment. A minimum of two replicates are recommended for both experimental and control samples. Control samples consist of two types a library consisting of formaldehyde-treated and -sheared DNA without antibody (input control) and a library where nonspecific, nonnuclear antibody is used for enrichment to the cross-linked DNA (mock library). Peaks in mapped reads from the enrichment library can be compared to peaks found from mapped reads control libraries to separate real and falsepositive peaks (Figure 4A). 

Figure 15-31 shows the effect of sample size on the standard deviation for a nonrandom mixture. L is a constant for a given mixture or state of mixedness. It can be determined experimentally if the value of 0 is known at one value of N. The condition of L = 0 corresponds to random mix ... 

---