Modeling and Fitting Two-Way Tables Containing Outliers
A model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error-free. Neither missing values nor replication is present. The model consists of the sum of a customary additive part that can be fit using least squares and a part t...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2023/6352058 |
| _version_ | 1797903071371591680 |
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| author | David L. Farnsworth |
| author_facet | David L. Farnsworth |
| author_sort | David L. Farnsworth |
| collection | DOAJ |
| description | A model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error-free. Neither missing values nor replication is present. The model consists of the sum of a customary additive part that can be fit using least squares and a part that is composed of outliers. Recommendations are made for methods for identifying cells containing outliers and fitting the model. A graph of the observations is used to determine the outliers’ locations. For all cells containing an outlier, replacement values are determined simultaneously using a classical missing-data tool. The result is called the adjusted table. The inserted values are such that, when a mean-based fitting of the adjusted table is performed, the residuals in those cells are zero. The outlying portion of the observation in each of those cells is the difference of the observation and the replacement value. In this way, outliers are removed from further analyses of the adjusted table. This is particularly helpful because outliers can greatly contaminate and alter computations and conclusions. Subsequently, the causes of the outliers might be determined, and statistical estimation and testing can be implemented on the adjusted table. |
| first_indexed | 2024-04-10T09:27:11Z |
| format | Article |
| id | doaj.art-f9f6d66b7b9044b88858a80c699e8b46 |
| institution | Directory Open Access Journal |
| issn | 1687-0425 |
| language | English |
| last_indexed | 2024-04-10T09:27:11Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj.art-f9f6d66b7b9044b88858a80c699e8b462023-02-20T01:57:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences1687-04252023-01-01202310.1155/2023/6352058Modeling and Fitting Two-Way Tables Containing OutliersDavid L. Farnsworth0School of Mathematical SciencesA model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error-free. Neither missing values nor replication is present. The model consists of the sum of a customary additive part that can be fit using least squares and a part that is composed of outliers. Recommendations are made for methods for identifying cells containing outliers and fitting the model. A graph of the observations is used to determine the outliers’ locations. For all cells containing an outlier, replacement values are determined simultaneously using a classical missing-data tool. The result is called the adjusted table. The inserted values are such that, when a mean-based fitting of the adjusted table is performed, the residuals in those cells are zero. The outlying portion of the observation in each of those cells is the difference of the observation and the replacement value. In this way, outliers are removed from further analyses of the adjusted table. This is particularly helpful because outliers can greatly contaminate and alter computations and conclusions. Subsequently, the causes of the outliers might be determined, and statistical estimation and testing can be implemented on the adjusted table.http://dx.doi.org/10.1155/2023/6352058 |
| spellingShingle | David L. Farnsworth Modeling and Fitting Two-Way Tables Containing Outliers International Journal of Mathematics and Mathematical Sciences |
| title | Modeling and Fitting Two-Way Tables Containing Outliers |
| title_full | Modeling and Fitting Two-Way Tables Containing Outliers |
| title_fullStr | Modeling and Fitting Two-Way Tables Containing Outliers |
| title_full_unstemmed | Modeling and Fitting Two-Way Tables Containing Outliers |
| title_short | Modeling and Fitting Two-Way Tables Containing Outliers |
| title_sort | modeling and fitting two way tables containing outliers |
| url | http://dx.doi.org/10.1155/2023/6352058 |
| work_keys_str_mv | AT davidlfarnsworth modelingandfittingtwowaytablescontainingoutliers |