Interaction plots

Fig. 2.17. Azimuthal angles p, (a) and energies (b) for orientational structures of adsorbed molecules on a square lattice with quadrupole-quadrupole interactions plotted versus the inclination angle 6 reckoned from the surface normal direction. Sublattices j of the structures described are labelled by the numbers 1,2,3, and the boundaries of the orientational phases under consideration are designated by the letters A, B, C, D, E, F, G. Regular and bold lines refer to the limiting cases AUt = 0 and Al/4 kBT(AU4 < 0).

Figures 3 and 4 display what are known as, interaction plots , where the mean of triplicate analyses is plotted with respect to CRM and analytical protocol. Where all methods extract a similar amount of the element, the lines representing CRMs will be parallel. In cases where the lines cross, there is an interaction between the mineralogy of the CRM and the analytical protocols. For Cr, this latter effect is clearly demonstrated, whereas for As, the methods consistently extract proportionally similar amounts.

The details, beyond the model, are not presented, however, the key conclusions are for some of the elements there is no statistical difference between the standard Aqua Regia digestions analytical protocols and a significant difference for some elements with the EPA 3050B digestion. These differences are shown in the interaction plots of Figure 4. 

Line chart Pictogram Pie chart Contour plot Stereogram Color map Histogram Means plot Sliding reference distribution Notched box plot Factor space/response Interaction plot Contour plot Predicted response plot Confidence region plot Confidence limits Graph paper Power curves Nomographs Sample-size curves Trilinear coordinates... 

Figure 14 Interaction plot for AM, acetic acid-methanol...

Figure 15 Interaction plot for MC, methanol-citric acid...

Figure 2.3 Interaction plot for a 2 design (the response is given as yield(%), see text for details).

Figure 2. Interaction plot of the design factor Weld Type with the noise factor Part Width (mm) with performance measure on the vertical axis. The slope with respect to Part Width is flatter when the Weld Type is at its low level, implying that the low setting of Weld Type will reduce transmitted variation.

The experiment provides estimates of the parameters au, au, i,..., au which can be substituted into (2) and the dj can then be chosen so as to make the noise factor regression slopes as close to 0 as possible. If there is a single design factor that interacts with a noise factor, then interaction plots such as Figure 2 expose the full... 

An interactive plotting program for Eq. (2) is available online which allows the entry of different sets of the parameters A, B, and C and then displays up to five plots simultaneously, together with the parameters for each plot. The values of / and p> at any value of ip on each plot can be inspected by moving the cursor to the location, followed by clicking and holding the left mouse button at that location.174175... 

Figure 6a shows interaction plot between (kj) and (Ka). Through the chart, it is possible to realize that the effect of (ki) in the response (acrylic acid concentration in the steady state) is different at different levels of (Ka), The maximum acrylic acid concentration is... 

Score and loading plots are interconnected so that any descriptor change in the loading plot is reflected by changes in the position of compounds in the score plot. Pairwise comparison can be made directly with interactive plots as developed in the Golpe program, and the relative contributions to the property imder study is shown in the related descriptors space. 

T. Williams and C. Kelly, GNUPLOTt An Interactive Plotting Program. E-mail pixarlinfo-gnuplot ucbvax.berkley.edu. 

Unfortunately, there are no post-hoc comparison tests to explain significant interaction effects identified for two-way ANOVAs or ANCOVAs. In this case, chemical education researchers usually create an interaction plot (Figure 1). In interaction plots, the mean score for each subgroup is placed on the vertical axis, and one of the independent variables is placed on the horizontal axis at equal intervals. Data points from each subgroup of the other independent variable are connected with lines. If there were no interaction between the two variables, these lines would be parallel. These plots provide the researcher with a visual means of identifying the effects of one independent variable on the other. 

Figure 1. Interaction plots for significant interactions (a) Interaction between animation treatment and gender (Reproducedfrom reference 21. Copyright 2006 ACS Division of Chemical Education, Inc.), (b) Interaction between molecule type and visual treatment (These data are from reference 18. Copyright 2001 ACS Division of Chemical Education, Inc.)...

Figure 28 Free energy of interaction plotted as a function of distance for different pH values, Amino acid glutamic add, (Taken from Ref, 107, with permission.)...

Fig. 2.4. Proton relaxation of HBr and HCl through scalar interaction. Plot used to obtain halogen relaxation time and scalar spin coupling constant [cf. Eq. (1.26)]. Tjp is the relaxation time in the rotating frame and where is the...

The density values that have been reported are given in Table 3. The density of a material depends on how closely the ions can pack together and, hence, on the size and shape of the ions and ion—ion interactions. Plots of glass transition versus density showed no significant correlation. 

Fig. 15.5 Evaluation results (a) interval plot and (b) interactions plot...

The temis on the left-hand side correspond to neutral species, and hence are available from measurements, and those on the right-hand side pertain to the ion-dipole and ion-quadrupole interactions. Plots of the left-hand side against extrapolated to infinitely large ion size, although not linear (due to the br term), then yield 2 H (Na, W S) as the ordinate intercept. 

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