Version 1
: Received: 9 August 2024 / Approved: 9 August 2024 / Online: 12 August 2024 (04:18:45 CEST)
How to cite:
Cheema, S.; Beh, E. J.; Hudson, I. L. How Informative is the Marginal Information of a 2x2 Table for Assessing Association? The Aggregate Informative Index. Preprints2024, 2024080724. https://doi.org/10.20944/preprints202408.0724.v1
Cheema, S.; Beh, E. J.; Hudson, I. L. How Informative is the Marginal Information of a 2x2 Table for Assessing Association? The Aggregate Informative Index. Preprints 2024, 2024080724. https://doi.org/10.20944/preprints202408.0724.v1
Cheema, S.; Beh, E. J.; Hudson, I. L. How Informative is the Marginal Information of a 2x2 Table for Assessing Association? The Aggregate Informative Index. Preprints2024, 2024080724. https://doi.org/10.20944/preprints202408.0724.v1
APA Style
Cheema, S., Beh, E. J., & Hudson, I. L. (2024). How Informative is the Marginal Information of a 2x2 Table for Assessing Association? The Aggregate Informative Index. Preprints. https://doi.org/10.20944/preprints202408.0724.v1
Chicago/Turabian Style
Cheema, S., Eric J Beh and Irene L. Hudson. 2024 "How Informative is the Marginal Information of a 2x2 Table for Assessing Association? The Aggregate Informative Index" Preprints. https://doi.org/10.20944/preprints202408.0724.v1
Abstract
The analysis of aggregate data has received increasing attention in the statistical discipline over the past 20 years. Much of this attention has been focused on estimating the cells frequencies of a 2×2 contingency table given only the marginal totals; the analyses proposed have been received with missed reviews. More recently, the focus has shifted toward analysing the overall association structure rather than on the estimation of the cell frequencies. This article provides some insight int how informative the aggregate data of a single 2×2 contingency table is for assessing the association. The information contained in the margins of the table is quantified using the squared deviation of the expected cell frequencies over the possible range of values, where the row and column totals are known and fixed. The new measure we discuss to quantify this association is referred to as the aggregate informative index (AII) and is shown to be the standardized area under the squared deviation curve.
Keywords
aggregate data; aggregate association index; ecological inference; Pearson’s chi-squared statistic
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
