Box-and-whisker plots

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. 

Periodic checks of possible errors (e.g., box-and-whiskers plotting)... 

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. 

The use of the tally column makes it easy to ensure that no data are missed. Ranking the data is not necessary but it makes it a lot easier to plot and to generate a box and whisker plot. 

Taking the data from Table 14, the simplest box and whisker plot using whiskers extending to the extreme values is shown in Figure 24. The median lies between rank 42 and 43 as the number of data points is even. In this instance the values are the same, 31.9%. The inter-quartile distances are at rank points 21 (31.4%) and 64 (32.2%) as they lie half way between the median and the lower and upper extreme values respectively. Note that here the possibility of there being outliers which should be excluded is ignored. 

Many modern computer packages have routines that will generate stem and leaf and box and whisker plots as well as many more complicated ones for looking at multivariate data. 

FIGURE 6 Summary of measurements of in situ rates of bacterial DOC consumption, calculated as the sum of bacterial production and respiration, and in vitro rates of DOC consumption, calculated from declines in DOC during batch incubations. Box-and-whisker plots show median, and upper/lower quartiles (box), and the range of values (bars). Extreme outliers are denoted by open circles. The in situ consumption rates are from the global dataset of simultaneous measurements of bacterial production and respiration collected by del Giorgio and Cole (1998), with the addition of unpublished data (see text). Because the in situ rates have been measured under a range of temperature, for this comparison the bioassay rates have not been corrected for temperature. 

Alternative approaches using box and whisker plots, pie charts and different types of visualizations of density functions are discussed in Ibrekk Morgan (1987) and Morgan Henrion (1990). Each has advantages for specific tasks, but the performance of a display depends upon the information that a subject is trying to extract (central tendency or variation). 

Figure 18.5 Surface water NO2 + NO3 concentrations measured at stations located in the oligo-haline (A), mesohaline (B), and polyhaline (C) regions of Chesapeake Bay. The box and whisker plots contain all values for each month in the 20 year data set (1985-2004). Dark squares and circles represent NO2 + NO3 concentrations during all wet and dry years, respectively, in this 20 year data set. Data were from the Chesapeake Bay Water Quality Monitoring Program (2004).

Figure 24-1 i Age-reiated changes in cystatin C and creatinine superimposed upon the reference interval (horizontal dashed iines). Box and Whisker plot the box represents 25 to 75th percentile with a horizontal line at the median the whiskers extend to the highest and lowest values. (From Newman DJ, Cystatin C. Ann Clin Biochem 2002 39 89-104.)... 

Detection of aberrant (outlier) or suspected values The Grubbs test is the statistical test used to identify if there are some aberrant (outlier) or suspected values, the risk taken is also 5% (Feinberg, 2001). Aberrant or suspected values can also be checked graphically through Box and Whiskers plots. 

Figure 4.5.3 Box and whisker plots of the log concentrations (pg L Q of various trace elements measured under repeatability conditions on the Meuse River at Eijsden...

Zinc and scandium. The nonnormality of the distributions of Zn and Sc can be seen in the plots of residuals versus factors (Figure 4.5.5). Under these circumstances it is necessary to either apply a normalizing transformation, or to use nonparametric statistical procedures. Since the data distributions for Zn and Sc both demonstrate deviation from normality the statistical analyses of these two elements have been dealt with in the same paragraph. The box and whisker plots for these elements are presented in Figure 4.5.6 to provide further insight into their distributions. 

Figure 4.5.6 Box and whisker plots for concentrations (pg L 1) of zinc and scandium...

The heights of the bars or columns usually represent the mean values for the various groups, and the T-shaped extension denotes the standard deviation (SD), or more commonly, the standard error of the mean (discussed in more detail in Section 7.3.2.3). Especially if the standard error of the mean is presented, this type of graph tells us very litde about the data - the only descriptive statistic is the mean. In contrast, consider the box and whisker plot (Figure 7.2) which was first presented in Tukey s book Exploratory Data Analysis. The ends of the whiskers are the maximum and minimum values. The horizontal line within the central box is the median, fhe value above and below which 50% of the individual values lie. The upper limit of the box is the upper or third quartile, the value above which 25% and below which 75% of fhe individual values lie. Finally, the lower limit of the box is the lower or first quartile, the values above which 75% and below which 25% of individual values lie. For descriptive purposes this graphical presentation is very informative in giving information about the distribution of the data. 

Note that the box and whisker plot presents the median, the maximum and minimum values (and hence the range) and the first and third quartiles (and hence the interquartile range). 

Concentration Type tirst dose trough = 1 steady-state trough = 2 FIGURE 8.4 Box and whisker plot of trough concentrations. 

Figure 2.6 Scatter plots and box and whisker plots of 5-fluorouracil (5-FU) clearance as a function of patient demographics. Data presented in Table 2.3. Solid line is the least squares fit to the data. Note that some plots are shown on a log-scale.

Figure 7.9 Box and whiskers plot comparing the parameter estimates under a sparse sampling design using various estimation algorithms.

Figure 7.22 and Fig. 7.23 present scatter plots and box and whisker plots of the true clearance for each individual against their EBE for clearance using... 

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