The Relationship Among the Standard Deviation of a Dataset and the Standard Deviation and Average Two Part of This Set

TL;DR

This paper explores the mathematical relationship between the overall standard deviation of a dataset and the mean and standard deviation of its two parts, especially in the context of meta-analysis with missing data.

Contribution

It introduces a new analysis of how the standard deviation of a dataset relates to the mean and standard deviation of its segments, aiding meta-analytical methods.

Findings

Derived formulas linking overall and partial standard deviations and means

Provides insights for meta-analysis involving incomplete data

Enhances understanding of dispersion measures in combined datasets

Abstract

Meta-analysis involves combining summary information for related but independent studies. It uses different relationship to combine position measure as well as dispersion measures. The objective of this study is to discuss a relationship among the standard deviation of a data set and the standard deviation and mean of two part of this set. The problem was proposed in a systematic review with meta-analysis that combined two studies with missing data.