Investigating the ecological fallacy through sampling distributions constructed from finite populations

Torres David J. () and Rouson Damain ()
Additional contact information
Torres David J.: Department of Mathematics and Physical Science, Northern New Mexico College, Española, NM 87532, USA
Rouson Damain: Computer Languages and Systems Software Group, Lawrence Berkeley National Laboratory, Berkeley, California, USA

Monte Carlo Methods and Applications, 2024, vol. 30, issue 4, 331-363

Abstract: Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the sampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same.

Keywords: Ecological fallacy; sampling distributions; Pearson R; Monte Carlo simulation; linear regression; multiple regression (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2024-2013 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:30:y:2024:i:4:p:331-363:n:1001

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2024-2013

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().