Box plot

Figure 4. Monomer density profile Pn,(y) normalized such that p ,(y) = 1 if the monomers were distributed homogeneously in the simulation box plotted vs. y at various values of s/ksT from e/ksT = 0.1 (circles to s/kfiT = 0.019 (erosses). Data are for a symmetrical AB polymer mixture with Na = Nb = N = 32, the interface occurring at y = 0. From Miiller et al." ...

FIGURE 3.7 MeHg concentration (ng/g dry weight) in sediment from 5 sites in the Florida Everglades. Box plots represent 5 replicate samples taken at 4 different times over 4 years. 

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

Box plots, also known as box and whisker plots, are commonly used to display univariate statistics for a given variable across another variable. The statistics typically displayed in a box plot are the minimum, first quartile, median, third quartile, and maximum values. Mean values are often included in box plots as well. The following is a sample box plot of a clinical response measure showing how three different drug therapies compare to one another. 

Box plot PROC BOXPLOT, PROC GPLOT, or PROC UNIVARIATE... 

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. 

The following is an example of a box plot of seizure data by treatment at each of three visits. This first example is created with the traditional PROC GPLOT. This box plot has boxes that span the interquartile range and whiskers that extend to the maximum and minimum values. Also, a connecting line joins the median values for each treatment. 

Here is the SAS program that creates this box plot. 

Program 6.4 Creating a Box Plot Using PROC GPLOT... 

BOXJTOO MEANS TO CREATE BOX PLOTS WITH BOXES (25TH AND 75TH PERCENTILES - THE INTERQUARTILE RANGE) JOINED (J) AT THE MEDIANS WITH WHISKERS EXTENDING TO THE MINIMUM AND MAXIMUM VALUES (00) AND TOPPED/BOTTOMED (T) WITH A DASH. 

CREATE BOX PLOT. VISIT IS ON THE X AXIS, SEIZURES ARE ON THE y AXIS, AND THE VALUES ARE PLOTTED BY TREATMENT. proc gplot... 

Mean values could be added to the preceding plot by calculating the means for each treatment by visit and then merging them back with the seizures data. Then, a PLOT2 statement could be used in PROC GPLOT to overlay the mean values. The following is an example of a box plot modified in these ways. 

Here is the SAS program that creates this box plot. The initial input DATA step is omitted because it is the same as in Program 6.4, and the changes necessary to produce this plot are highlighted. 

There are other ways to create box plots in SAS. If you want a quick box plot, you can use PROC UNIVARIATE with the PLOT option. A more elegant option is to use PROC BOXPLOT, which was introduced in SAS 8. PROC BOXPLOT is explained in detail in the SAS/STAT User s Guide. The following is a sample of the same box plot as in the previous example, but created with PROC BOXPLOT. 

Program 6.6 Creating a Box Plot with Means Using PROC BOXPLOT... 

Note that PROC BOXPLOT uses SAS/GRAPH statements such as GOPTIONS and SYMBOL statements. There is a vast array of display options in the PROC BOXPLOT PLOT statement not used here. You may want to investigate those options if you decide to enhance the box plot further. 

Here is the SAS program that creates the preceding graph. It is a bit complex, because SAS/GRAPH does not provide horizontal box plots and this is typically what is desired for odds ratio plots. So, this sample program relies extensively on the Annotate facility to produce the plot. Notes follow the program. 

A-allele. Upper extreme of the linear scale has been omitted, (b) Discrimination between genotypes with Invader. In the box plot the black bars represent medians, whiskers interquartile range and circles outliers. 

Fig. 2. Percent quartz in C horizon (dashed trend line) and weight percent Al (filled boxes) in C horizon soils along the W-E transect (truncated box plot boxes include 50% of data, extent of lines include 80% of data solid line is the median). Geochemical data shown by the box plots were grouped into 10 areas (vertical dashed lines, numbers at top of plot) defined by commonalities of physiographic features.

Fig. 3. Percent feldspar in C horizon (dashed trend line) and weight percent Na in C horizon soils along the W-E transect (filled boxes). Plot specifics as in Figure 2. 

Fig-1- Box plot for Hg concentrations (ppb, dry weight) in fungal fruiting bodies, by order. 

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... 

The relative accuracy of estimation is illustrated in Figure 3 by the box plots obtained from the individual data sets. On the basis of Figure 3, the accuracy of the estimates decreases with the data variability. 

Figure 3 Box plots of Wo, b, and c values estimated after fitting Eq. (2) to individual (simulated, 6-fold replicated) errant data sets and their deviation from the actual parameter values. Upper graphs refer to data with SD = 2 and lower graphs refer to data with SD = 4. The actual W0 value was always 100.

Fig.l. Trends on the VHMS alteration box plot showing alteration related to (a) hydrothermal activity and (b) diagenesis. 

A histogram is used to describe the variability of results. For this purpose the range of possible values for the results is divided in a number of groups. Each group should have the same range. When the measurements are complete, count the number of observations in each group and draw a box-plot of the frequencies vs. the groups. 

Box Plot This plot is useful when analyzing the pattern of the data. It displays several important features of data such as central tendency, variability, departure from symmetry, and presence of outliers. 

Another graphical description of the data is used when comparing the results of several trials is the box plot (also called box-and-whisker plot). A box represents the range of the middle 50% of the data, and whiskers extend to the maximum and minimum values. A line is drawn at the median value. A glance a this plot allows one to assess the symmetry and spread of the data. Figure 5.4 is a box plot for the carbonate data of figure 5.2. Specific plots, such as Youden two-sample plots for method performance studies, are discussed below. 

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