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Related Concept Videos

Percentile01:18

Percentile

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A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. It represents the percentages of data values that are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15th percentile.
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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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Review and Preview01:10

Review and Preview

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In statistics, several tools are used to interpret the data. Measures of central tendency represent the characteristics of the data, such as mean, median, and mode. Additionally, measures of variance like standard deviation and range are used to find the spread of data from the mean. Relative standing measures the distance between data locations. Commonly used measures of relative standings are percentile, z score, and quartiles.
Percentiles are a type of fractile that partition data into...
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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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Relative Frequency Histogram01:14

Relative Frequency Histogram

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The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...
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Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
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Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
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Quantile-based classifiers.

C Hennig1, C Viroli2

  • 1Department of Statistical Science, University College London, 1-19 Torrington Place, London WC1E 6BT, U.K. , c.hennig@ucl.ac.uk.

Biometrika
|June 10, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces quantile classifiers for high-dimensional data with small sample sizes. These classifiers effectively minimize misclassification errors, achieving high accuracy even with numerous variables.

Keywords:
High-dimensional dataMedian-based classifierMisclassification rateSkewness

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • High-dimensional data classification with limited samples presents significant challenges.
  • Existing methods may struggle with the curse of dimensionality and small datasets.

Purpose of the Study:

  • To introduce and evaluate a novel quantile classifier for high-dimensional, small-sample data.
  • To demonstrate the classifier's ability to consistently identify optimal parameters and achieve high classification accuracy.

Main Methods:

  • Utilizing distance-based classification with componentwise distances to within-class quantiles.
  • Employing a single, dimension-independent parameter (quantile percentage).
  • Optimizing the quantile percentage by minimizing training sample misclassification error.

Main Results:

  • The chosen quantile percentage is consistent with asymptotically optimal quantiles.
  • Under specific assumptions, classification accuracy converges to unity as the number of variables increases.
  • The optimal quantile classifier demonstrates low misclassification rates in simulations and real-world data.

Conclusions:

  • Quantile classifiers offer a robust solution for classifying high-dimensional data with small sample sizes.
  • The method is effective across various data distributions, including skewed predictor variables.
  • The classifier provides a promising approach for practical applications requiring accurate data classification.