Visualizing samples with box plots

Fiber optic interferometers have a wide range of applications including biological and chemical measurements. Nevertheless, in case of a reflective interferometer setup, standard silver mirrors cannot be used in every measurement, due to their chemical activity. In this work, we investigate the surface quality of a thin optical layer of silicon nitride (SiN) which can serve as an alternative material for silver mirrors. We present measurements carried out with a Fabry-Perot fiber optic interferometer working in a reflective mode. Measurement results allow us to determine the surface quality of the investigated layer. Full Text: PDF ReferencesK. Karpienko, M.S. Wróbel, M. Jedrzejewska-Szczerska, "Determination of refractive index dispersion using fiber-optic low-coherence Fabry-Perot interferometer: implementation and validation", Opt Express, 53, 077103 (2014). CrossRef Jedrzejewska-Szczerska M., Gnyba M., Kosmowski B. B. "Low-coherence fibre-optic interferometric sensors", Acta Phys. Pol. A 120, 621 (2011). CrossRef M. Jedrzejewska-Szczerska "Response of a new low-coherence Fabry-Perot sensor to hematocrit levels in human blood",Sensors 14(4), 6965 (2014). CrossRef M. Kosowska, D. Majchrowicz, K.J. Sankaran, M. Ficek, K. Haenen, M. Szczerska, "Doped Nanocrystalline Diamond Films as Reflective Layers for Fiber-Optic Sensors of Refractive Index of Liquids", Materials 12, 2124 (2019). CrossRef Shou-YiChang, Yi-Chung Huang, "Analyses of interface adhesion between porous SiO2 low-k film and SiC/SiN layers by nanoindentation and nanoscratch tests", Microelectron. Eng. 84(2), 319 (2007). CrossRef X. Wang, C. Wang, X. Shen, F. Sun, "Potential Material for Fabricating Optical Mirrors: Polished Diamond Coated Silicon Carbide". Appl. Opt. 56, 4113 (2017). CrossRef G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, "Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer", Appl. Opt. 42, 3882 (2003). CrossRef H. Mäckel, R. Lüdemann, "Detailed study of the composition of hydrogenated SiNx layers for high-quality silicon surface passivation", J. Appl, Phys. 92, 2602 (2002). CrossRef N. Atman, M. Krzywinski, "Visualizing samples with box plots", Nat. Methods, 11(2), 119 (2014). CrossRef M. Vignesh, R. Balaji, "Data analysis using Box and Whisker Plot for Lung Cancer", International Conference on Innovations in Power and Advanced Computing Technologies,(2017). CrossRef

<p>Interrogation of CD79B at the protein level in the discovery set and <i>KLHL6</i>-mutated tumors. <i>P</i> values for comparisons between two groups in box plots are calculated with the Mann–Whitney <i>U</i> test. Individual channels shown for the white dashed areas are shown right to the microscopy images. <b>A,</b> IF microscopy image of a GC in a reactive lymph node showing the highest CD79B intensity in the mantle zone, whereas KLHL6 positivity is restricted to the GC. Scale bar, 100 µm. <b>B</b> and <b>C,</b> Box and dot plots with <i>y</i>-axis showing (<b>B</b>) quantified CD79B intensity and (<b>C</b>) <i>CD79B</i> gene expression (from RNA sequencing) according to KLHL6<sup>GC+</sup> IHC (<i>x</i>-axis). <b>D,</b> Box and dot plots of quantified CD79B intensity according KLHL6<sup>GC+</sup> IHC phenotype within different molecular subtypes determined by gene expression profiling. <b>E,</b> Representative IF microscopy images of KLHL6<sup>GC-</sup> tumors showing plasma membrane–like CD79B staining. Sections stained for CD79B, KLHL6, and DNA (DAPI) and images obtained with optical sectioning and 40× objective. Scale bar, 20 µm. <b>F,</b> Oncoprint of patients (columns) with <i>KLHL6</i> and/or <i>CD79B</i> mutations (<i>n</i> = 23). <b>G,</b> Box and dot plot of CD79B intensity according to <i>KLHL6</i> BTB domain encoding mutation status. Amino acid changes of all <i>KLHL6</i> mutations for available cases are annotated, and the presence of <i>CD79B</i> mutations is indicated with a color. <b>H,</b> Box and dot plot showing CD79B intensity according to <i>CD79B</i> mutations with Y197 hot spot considered separately. Color of the dots indicates KLHL6<sup>GC</sup> IHC status and amino acid changes of <i>CD79B</i> mutations are annotated. <b>I,</b> Representative IF microscopy images of tumors with different <i>KLHL6</i> mutations co-stained for CD79B, KLHL6, and DNA (DAPI). Images within dashed area indicate additional <i>KLHL6</i>-mutated DLBCL tumors not included in the discovery cohort. Scale bar, 20 µm applies to all images.</p>

<p>Interrogation of CD79B at the protein level in the discovery set and <i>KLHL6</i>-mutated tumors. <i>P</i> values for comparisons between two groups in box plots are calculated with the Mann–Whitney <i>U</i> test. Individual channels shown for the white dashed areas are shown right to the microscopy images. <b>A,</b> IF microscopy image of a GC in a reactive lymph node showing the highest CD79B intensity in the mantle zone, whereas KLHL6 positivity is restricted to the GC. Scale bar, 100 µm. <b>B</b> and <b>C,</b> Box and dot plots with <i>y</i>-axis showing (<b>B</b>) quantified CD79B intensity and (<b>C</b>) <i>CD79B</i> gene expression (from RNA sequencing) according to KLHL6<sup>GC+</sup> IHC (<i>x</i>-axis). <b>D,</b> Box and dot plots of quantified CD79B intensity according KLHL6<sup>GC+</sup> IHC phenotype within different molecular subtypes determined by gene expression profiling. <b>E,</b> Representative IF microscopy images of KLHL6<sup>GC-</sup> tumors showing plasma membrane–like CD79B staining. Sections stained for CD79B, KLHL6, and DNA (DAPI) and images obtained with optical sectioning and 40× objective. Scale bar, 20 µm. <b>F,</b> Oncoprint of patients (columns) with <i>KLHL6</i> and/or <i>CD79B</i> mutations (<i>n</i> = 23). <b>G,</b> Box and dot plot of CD79B intensity according to <i>KLHL6</i> BTB domain encoding mutation status. Amino acid changes of all <i>KLHL6</i> mutations for available cases are annotated, and the presence of <i>CD79B</i> mutations is indicated with a color. <b>H,</b> Box and dot plot showing CD79B intensity according to <i>CD79B</i> mutations with Y197 hot spot considered separately. Color of the dots indicates KLHL6<sup>GC</sup> IHC status and amino acid changes of <i>CD79B</i> mutations are annotated. <b>I,</b> Representative IF microscopy images of tumors with different <i>KLHL6</i> mutations co-stained for CD79B, KLHL6, and DNA (DAPI). Images within dashed area indicate additional <i>KLHL6</i>-mutated DLBCL tumors not included in the discovery cohort. Scale bar, 20 µm applies to all images.</p>

Abstract: We studied how graph design principles can predict specific reasoning mechanisms that occur when misinterpreting box plots, and, more specifically, the misinterpretation of the area as a representation of frequency or proportion of observations, instead of density. In previous studies this misinterpretation has been shown to be heuristic in nature and is elicited by the fact that box plots do not use space in a natural way. Graph design principles provide a theoretical framework for assuming that the orientation of a box plot could influence its interpretation. By analyzing reaction times and accuracy rates for different item types, we explored whether there indeed is an influence of the orientation of a box plot on the way it is interpreted. Results indicate that the misinterpretation manifests itself in both orientations to the same extent, suggesting that the orientation of a box plot does not influence the reasoning mechanisms it provokes.Key wo rds: du al-process theory, gra ph design, misinterpretation, heuristic, box plotsINTERPRETACIA RAMCEKOVÝCH GRAFOV: VPLYV PRIESTOROVEJ ORIENTACIES. L e m, C. V a n d e b e e k, P. O n g h e n a , L. V e r s c h a f f e l, W. V a n D o o r e nSuhrn: Sk umali sme ako principy navrhu grafov predikuju specificke mechanizmy usudzovania, k u k torým dochadza pri sk reslenej interpretacii ramcekových grafov, presnejsie, pri ich sk reslenej interpretacii a ko reprezentacie frekvencie alebo miery pozorovani, a nie hustoty. Predchadzajuce studie uk aza li, ze skreslena interpretacia ma heuristický charakter a vyvolava ju sk utocnost, ze ramcekove grafy nevyuziva ju priestor prirodzeným sposobom. Principy navrhovania grafov posk ytuju teoretický ramec pre predpoklad, ze priestorova orientacia ramcekoveho gra fu moze ovplyvnit jeho interpreta ciu . Pomocou analýzy reakcných casov a miery presnosti pre rozne typy poloziek sme zistova li, ci priestorova orientacia ramcekoveho grafu sku tocne vplýva na sposob, ak ým je interpretova ný. Výsledky naznacuju, ze skreslena interpretacia sa vyskytova la v rovnak ej miere v oboch priestorových orientaciach, na zaklade coho mozno predpokladat, ze priestorova orienta cia ra mcekoveho gra fu neovplyvnuje mechanizmy usudzovania, ktore vyvolava.Lem, Onghena, Ver scha ffel, and Van Dooren (2013b) recently showed that box plots are misinterpreted frequently and that the incorrect interpretation of the area of the box plot can be assigned to incorrect heuris- tic reasoning. A limitation of this study is, however, that it only used horizontally po- sitioned box plots, while it is also common practice to make use of vertically positioned box plots, particularly when multiple groups are being compared (e.g., McGill, Tukey, Larsen, 1978; Williamson, Parker, Kendrick, 1989). Based on graph design principles (Tversky, 1997), some arguments can be given that make it likely that less interpreta- tion difficulties will occur when the box plot is represented vertically. In the present study, we compared the way horizontally and verti- cally positioned box plots are interpreted, using a dual processing perspective.The Heuristic Misinterpretation of Box PlotsThe misinterpretation, which is the focus in this study, was documented first by Bakker, Biehler, and Konold (2005). They found that the area of the box plot is often perceived by students as displaying the fre- quency or proportion of observations in that interval, instead of the density. Bakker et al. ascribed this misinterpretation to the fact that students link the use of box plots to the use of graphical r epresen tations previously learned in school (e.g., histograms and bar graphs, see also Lem, Onghena, Verschaffel, Van Dooren, 2012). In box plots the area of the box indicates how dense the observa- tions are in that interval: The smaller an area, the higher the density of observations in that interval. This makes box plots very different from other graphical representations, such as bar graphs and histograms, in which a larger area of the bar reflects a higher fre- quency of observations. …

Guidelines for Reporting of Figures and Tables for Clinical Research in Urology.

Graphical considerations for presenting data

As box plots have come to be included in the 2022 revised mathematics curriculum, a need for research has emerged to support corresponding textbook development. This study aimed to analyze eight foreign textbooks dealing with box plots and related concepts to explore how to organize a textbook unit. The perspective for analysis was determined considering the conventions of textbook development in Korea and the standards presented in the curriculum, including definitions and teaching sequence of relevant concepts, core tasks and use of technology. Concept definitions were generative, intensional, or extensional, while the predominant teaching sequence was median-quartile-interquartile range(IQR)-box plot. The core tasks mainly included drawing box plots and comparing data sets. Use of technology was mostly in the form of auxiliary tools. Drawing on the results, we suggest that quartiles can be defined generatively or intensionally, and box plots extensionally; a teaching sequence can begin with remarks on median, proceeding to quratile, IQR, and box plot; core tasks may include drawing box plots and comparing data sets, with optional tasks on interpreting box plots and observing distributions; technology can be used to facilitate calculation of descriptive statistics and to highlight the characteristics of box plots.

CCR3 as a single selection marker compared to CD123/HLADR to isolate basophils in flow cytometry: Some comments

Box plots are frequently misinterpreted and educational attempts to correct these misinterpretations have not been successful. In this study, we used two instruc- tional techniques that seemed powerful to change the misinterpretation of the area of the box in box plots, both separately and in combination, leading to three experimental conditions, next to a control condition. First, we used multiple external representations: Histograms were used as an overlay on box plots in order to give students a better insight in the way box plots represent data distributions. Second, we used refutational text to explicitly name and invalidate the area misinterpretation of box plots. Third, we combined multiple external representations and refutational text. A box plot test showed that students in the refutation and combination condition scored statistically significant better than students in the control condition with respect to the misinterpre- tation of interest. The condition with multiple external representations scored in between. The implications of these results for theory and educational practice are discussed.

To the Editor In biomedical research, it is often necessary to compare multiple data sets with different distributions. The bar plot, or histogram, is typically used to compare data sets on the basis of simple statistical measures, usually the mean with s.d. or s.e.m. However, summary statistics alone may fail to convey underlying differences in the structure of the primary data (Fig. 1a), which may in turn lead to erroneous conclusions. The box plot, also known as the box-and-whisker plot, represents both the summary statistics and the distribution of the primary data. The box plot thus enables visualization of the minimum, lower quartile, median, upper quartile and maximum of any data set (Fig. 1b). The first documented description of a box plot–like graph by Spear1 defined a range bar to show the median and interquartile range (IQR, or middle 50%) of a data set, with whiskers extended to minimum and maximum values. The most common implementation of the box plot, as defined by Tukey2, has a box that represents the IQR, with whiskers that extend 1.5 times the IQR from the box edges; it also allows for identification of outliers in the data set. Whiskers can also be defined to span the 95% central range of the data3. Other variations, including bean plots4 and violin plots, reveal additional details of the data distribution. These latter variants are less statistically informative but allow better visualization of the data distribution, such as bimodality (Fig. 1b), that may be hidden in a standard box plot. Figure 1 Data visualization with box plots Despite the obvious advantages of the box plot for simultaneous representation of data set and statistical parameters, this method is not in common use, in part because few available software tools allow the facile generation of box plots. For example, the standard spreadsheet tool Excel is unable to generate box plots. Here we describe an open-source application, called BoxPlotR, and an associated web portal that allow rapid generation of customized box plots. A user-defined data matrix is uploaded as a file or pasted directly into the application to generate a basic box plot with options for additional features. Sample size may be represented by the width of each box in proportion to the square root of the number of observations5. Whiskers may be defined according to the criteria of Spear1, Tukey2 or Altman3. The underlying data distribution may be visualized as a violin or bean plot or, alternatively, the actual data may be displayed as overlapping or nonoverlapping points. The 95% confidence interval that two medians are different may be illustrated as notches defined as ±(1.58 × IQR/√n) (ref. 5). There is also an op on to plot the sample means and their confidence intervals. More complex statistical comparisons may be required to ascertain significance according to the specific experimental design6. The output plots may be labeled; customized by color, dimensions and orientation; and exported as publication-quality .eps, .pdf or .svg files. To help ensure that generated plots are accurately described in publications, the application generates a description of the plot for incorporation into a figure legend. The interactive web application is written in R (ref. 7) with the R packages shiny, beanplot4, vioplot, beeswarm and RColorBrewer, and it is hosted on a shiny server to allow for interactive data analysis. User data are held only temporarily and discarded as soon as the session terminates. BoxPlotR is available at http://boxplot.tyerslab.com/ and may be downloaded to run locally or as a virtual machine for VMware and VirtualBox.

Ventilatory signals from 12 bluegill (Lepomis macrochirus) sunfish were collected with the aid of an on-line minicomputer as part of a biological monitoring system. Our results from three experiments demonstrate a potential for applying these graphic techniques to on-line biomonitoring systems.Key words: biological monitoring, ventilatory behavior, biomonitoring, bluegill sunfish, breathing, water quality, box plots, line plots

The main objective of this work is to show the different proposals of multivariate graphs in the monitoring of investment projects such as box and whisker plots, stem and box plots, scatter plots, dendrogram, Chernoff faces, Andrews curves, graphs of star and radar charts. This study is justified because there is not much dissemination of this type of graphics, and neither all statistical software allows to implement them RStudio is an exception. It is an exploratory study with a non-experimental, cross-sectional, and descriptive design. The population was made up of 23 departments of Peru together with the Constitutional Province of Callao. Since the information for the department of Tumbes turned out to be incomplete, it had decided to eliminate it. Therefore, the final sample consisted of 23 observations and 07 variables with information on monitoring the execution of investment projects in Peru in the year 2021. Multivariate analysis graphical techniques had used using the RStudio integrated development environment for their prosecution. The results show various trends, clusters, and descriptive analysis of the 23 observations of the sample regarding the monitoring of execution in investment projects through the different multivariate graphs. We can conclude that through these graphs it was possible to identify similarities between the study units as well as groupings and atypical values (outliers). In addition, it is possible to describe how was the execution of investment projects in each of the departments and the province of Callao that are part of the sample.

In this paper, we propose a method for monitoring the evolution of data described by histograms of values. Our proposal consists to define new order statistics on the quantile functions associated with the empirical distributions, represented by the histogram-data. We introduce the Median, the First and the Third Quartile quantile functions, as well as a generalized representation of the box and whiskers plot. For example, the proposed representations and indices are useful for identifying and classifying outliers, arriving along the time in a data stream environment.

Functional box plots satisfy two needs; visualization of functional data, and the calculation of important box plot statistics. Data visualization illuminates key characteristics of functional sets missed by statistical tests and summary statistics. The calculation of box plot statistics for functional sets permits a novel comparison more suited to functional data. The functional box plot uses a depth method to visualize and rank smooth functional curves in terms of a mean, box, whiskers, and outliers. The functional box plot improves upon other classic functional data analysis tools such as functional principal components and discriminant analysis for outlier detection. This research adds wavelet analysis as a generating mechanism along with depth for functional box plots to visualize functional data and calculate relevant statistics. The wavelet analysis of variance box plot tool gives competitive error rates in Gaussian test cases with magnitude outliers, and outperforms the functional box plot, for Gaussian test cases with shape outliers. Further, we show wavelet analysis is well suited at approximating irregular and noisy functional data and show the enhanced capability of WANOVA box plots to classify shape outliers which follow a different pattern than other functional data for both simulated and real data instances.

In this chapter, we explore the challenges of learning about box plots and question the rationale for introducing box plots to middle school students (up to 14 years old). Box plots are very valuable tools for data analysis and for those who know how to interpret them. Research has shown, however, that some of their features make them particularly difficult for young students to use in authentic contexts. These difficulties include: a) box plots generally do not allow perceiving individual cases; b) box plots operate differently than other displays students encounter; c) the median is not as intuitive to students as we once suspected; d) quartiles divide the data into groups in ways that few students (or even teachers) really understand. We recommend that educators consider these features as they determine whether, how, and when to introduce box plots to students.