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Related Concept Videos

Boxplot01:12

Boxplot

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Box plots (also called box-and-whisker plots or box-whisker plots) give an excellent graphical image of the concentration of the data. They also show how far the extreme values are from most data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them. To construct a box plot, use a horizontal or vertical number line and a rectangular box. The...
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Modified Boxplots00:57

Modified Boxplots

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A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...
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5-Number Summary01:04

5-Number Summary

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In a dataset, the 5-number summary includes the minimum data value, the data value of the first quartile, the median data value or data value of the second quartile, the data value of the third quartile, and the maximum data value. These 5 data values can be visualized as a box and whisker plot.
In a box plot, the minimum and maximum data values represent the lower and upper whiskers in the graph, and the median is designated as the center of the box in the chart. The first quartile and third...
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Quartile01:15

Quartile

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Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...
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Microsoft Excel: Median, Quartile range, and Box Plots01:29

Microsoft Excel: Median, Quartile range, and Box Plots

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In Microsoft Excel, calculating the median, interquartile range, and creating box plots can help understand the distribution of your data.
Median and Quartile Range: The median is calculated using the formula `=MEDIAN(range)', which provides the middle value of your data set. Quartiles divide your data into four equal parts. To find the first and third quartiles, use ‘=QUARTILE(range, 1)' and ‘=QUARTILE(range, 3)', respectively. The interquartile range (IQR), which...
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Residual Plots01:07

Residual Plots

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A residual plot is a statistical representation of data used to analyze correlation and regression results. It helps verify the requirements for drawing specific conclusions about correlation and regression. To obtain the residual plot, first, the residual for each data value is calculated, which is simply the vertical distance between the observed and the predicted value obtained from the regression equation.
When the residual values are plotted against the variable x, it is called a residual...
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Rapid Analysis and Exploration of Fluorescence Microscopy Images
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Visualizing Multiple Quantile Plots.

Marko A A Boon1, John H J Einmahl2, Ian W McKeague3

  • 1Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|January 28, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces triple-quantile (QQQ) plots for visualizing and comparing three independent data distributions. It provides a novel method for constructing confidence tubes, enhancing statistical analysis for multiple populations.

Keywords:
Confidence regionEmpirical likelihoodThree-sample comparison

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Area of Science:

  • Statistics
  • Data Visualization
  • Multivariate Analysis

Background:

  • Quantile-quantile (QQ) plots are standard for comparing two distributions.
  • Extending QQ plots to more than two populations is challenging.
  • Visualizing and quantifying differences across multiple datasets requires advanced methods.

Purpose of the Study:

  • To develop a method for visualizing triple-quantile (QQQ) plots.
  • To extend QQ plots to three dimensions for comparing three independent populations.
  • To provide simultaneous distribution-free confidence tubes for these plots.

Main Methods:

  • Definition of the triple-quantile (QQQ) plot as a 3D curve Q(p) = (Q1(p), Q2(p), Q3(p)).
  • Utilizing the empirical likelihood method to derive confidence tubes.
  • Application to economic and epidemiological case studies.

Main Results:

  • Successful visualization of triple-quantile plots.
  • Development of associated confidence tubes for statistical inference.
  • Demonstration of applicability in real-world economic and epidemiological data.

Conclusions:

  • Triple-quantile plots offer a powerful graphical tool for comparing three population distributions.
  • The proposed confidence tubes provide a robust method for assessing significance.
  • This method enhances the comparison of multivariate data distributions.