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Outliers and Influential Points

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...

What Are Outliers?

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Outliers are observed data points that are far from the least squares line. They have unusual values and need to be examined carefully. Though an outlier may result from erroneous data, at other times, it may hold valuable information about the population under study and should be included in the data. Hence, it is crucial to examine what causes a data point to be an outlier.
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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 number is...

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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...

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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:

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Related Experiment Video

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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

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Published on: June 26, 2013

Detecting outlying samples in a parallel factor analysis model.

Sanne Engelen¹, Mia Hubert

¹Department of Mathematics, LStat, Katholieke Universiteit Leuven, Celestijnenlaan 200B, BE-3001 Heverlee, Belgium.

Analytica Chimica Acta

|October 4, 2011

Summary

This summary is machine-generated.

This study introduces a robust Parallel Factor Analysis (PARAFAC) method to handle multi-way data, effectively identifying and excluding outliers for more reliable analysis. The approach ensures accurate modeling even with contaminated datasets.

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Area of Science:

Multivariate data analysis
Chemometrics
Signal processing

Background:

The Parallel Factor Analysis (PARAFAC) model is widely used for analyzing multi-way data, offering a compact representation of complex structures.
Traditional PARAFAC estimation relies on alternating least squares (ALS), which is highly sensitive to outlying observations.
The presence of outliers can significantly compromise the accuracy and reliability of PARAFAC models.

Purpose of the Study:

To develop a robust method for PARAFAC that is resilient to outlying observations.
To enhance the applicability of PARAFAC in real-world scenarios where data contamination is common.
To provide a reliable tool for multi-way data analysis in the presence of outliers.

Main Methods:

A novel robust PARAFAC algorithm is proposed.
The method identifies an outlier-free subset of the data for robust model estimation.
An outlier map is generated to detect and visualize outlying observations.

Main Results:

The robust PARAFAC method demonstrates significant resilience against outlying observations.
Simulations and practical examples confirm the effectiveness and robustness of the proposed approach.
Accurate PARAFAC models can be obtained even when the data contains outliers.

Conclusions:

The presented robust PARAFAC method offers a reliable alternative to classical techniques when dealing with potentially contaminated multi-way data.
This approach enhances the utility of PARAFAC in various scientific fields by addressing the critical issue of outliers.
The outlier map provides valuable insights into data quality and potential sources of error.