Graphs Scatter plots

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

Common Clinical Trial Graphs 200 Scatter Plot 200 Line Plot 201 Bar Chart 202 Box Plot 203 Odds Ratio Plot 203... 

Scatter plots are used widely in clinical trial research, as they are intuitive to read and have many applications. We often look for a drug s effect on some parameter (Y axis) over time (X axis). Also, change-from-baseline scatter plots are useful when you plot the baseline on the X axis and the follow-up value on the Y axis. You will see an example of this graph later in this chapter. 

Note that for box and survival plots, PROC GPLOT is listed as an alternative. Although PROC BOXPLOT and PROC LIFETEST produce excellent graphs by themselves, sometimes it is necessary to make modifications to the output in a way that these procedures cannot handle directly. When modifications are needed, PROC GPLOT is an excellent choice. Also note that PROC REG and PROC UNIVARIATE are listed as options for scatter plots and box plots, respectively, as they can be useful in producing lower-resolution graphics for statistical appendices. 

There are many forms of statistical graphics (a partial list, classified by function, is presented in Table 22.7), and a number of these (such as scatter plots and histograms) can be used for each of a number of possible functions. Most of these plots are based on a Cartesian system (that is, they use a set of rectangular coordinates), and our review of construction and use will focus on these forms of graphs. 

Many types of graphs exist (e.g., bar graphs, contour plots, line graphs, pie charts, scatter plots). 

The central purpose of a graph is to present, summarize, and/or highlight trends in data or sets of data. Graphs of various types (e.g., scatter plots, contour plots, two- and three-dimensional line graphs, and bar graphs) are used for different purposes thus, authors must match their purpose with the appropriate type of graph. 

Dynamic light scattering, coupled with modern computer programs and auxiliary equipment, automatically graphs Zimm plots and computes Mw, Rg, , Cl, and flow rates. New techniques have expanded the method to the semidilute and concentrated regimes (Barth and Sun, 1991). 

Lets take a step back and look at the process. Say that we are plotting a simple scatter plot of some X,Y pairs. The first step is to pick a suitable graph paper, there are a lot of them, different types and scales - someone else has gone through the trouble of working out the rulings, line thickness and such and... 

Figure 4. Decomposition of the ASAXS-intensities measured at different energies of the incident beam according to Eq. (12). The intensities measured at a q-value given in the graph are plotted against the effective real part / ff of the scattering factor (cf. the discussion of Fig. 2). The dashed line shows the fit according to Eq. (12) if is disregarded. Taken from [19].

An alternative method of getting PK data is to take a small extra sample of blood (and urine) at a child s regular scheduled visit when blood is drawn for routine blood work. The time of day of this sample is predetermined by the time of the administration of the medicine. If samples are obtained from many children, a weight-age-corrected, scatter-plot graph can be constructed and a PK profile be calculated. This is the pharmacokinetic screen method. A version of this method is also utilized to gather ethnic data for labeling in adults as well as children, and is called population pharmacokinetics . 

Figure 9 Chromium and nickel concentration scatter plot from heart tissue data. The distribution of concentration values for each element is shown as a bar graph on their respective axes...

The second ChartWizard box lets you specify the type of graph you want. Click on the XY (Scatter) plot your choice will be highlighted. (Do not select the Line plot, because it will automatically assume that all X-values are equidistant. This is convenient when you want to plot, e.g., income or expense as a function of the month of the year, or the region of the country. In scientific applications, however, it makes no sense to treat the X-values merely as labels, and it can yield quite misleading graphs.) Click on Next > to move to the next ChartWizard. 

The Chart Wizard is the usual starting point for graphs in Excel, and a number of different formats are on offer. For calibration graphs always choose the XY (Scatter) plot, which is about halfway down the menu. Do not choose Line which spaces out the points equally. 

In the pharmacokinetic literature, three types of plots are most commonly seen scatter plots, histograms, and bar charts. Good plotting practices for each of these graph types will be presented. Beyond these plots are others, like QQ plots, dot plots, and three-dimensional surface plots. It is beyond the scope of this chapter to cover every conceivable plot, but many of the good plotting practices that will be put forth should carry over into other plot types as well. 

A scatter plot is the simplest type of graph. It simply plots the data points against their values, without adding an connecting lines, bars or other stuff. The first variable is measured along the x-axis and the second along the y-axis. 

Scatter plots are the most common type of graph used to show relationships between a dependent variable (responses) and independent variables (factors). Judiciously selecting and sizing the symbols in scatter plots allows one to communicate trends and the measured values associated error. Frequently, to show the effect of more than one independent variable, different symbol types or colors can be used. Three-dimensional plots, surface plots, and contour plots are becoming more common to illustrate the effect of two or more factors on the dependent variable. Bar charts (and pie charts) are popular for presentations, and histograms are useful to compare the distribution of populations. Ternary plots are used in thermodynamics and to demonstrate explosion limits of different compositions of gases. 

In addition to the well-known scatter-plots, two other graphic tools have been considered in this study Cobweb plots and contribution to the sample mean plots (CSM plots). Cobweb plots have been designed to show multidimensional samples in a two-dimensional graph. Vertical parallel lines separated by equal distances are used to represent the sampled values of several inputs/outputs. Each vertical line is used for a different input/output. Either the raw values or the ranks may be represented. Sampled values are marked in each vertical line and jagged hues connect the values corresponding to the same run. The analysis of cobweb plots enables the characterisation of dependence and conditional dependence. 

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