A Note on Estimating Unreported Sample Statistics for Meta-Analysis
Asian Journal of Probability and Statistics · pp. 12–20 · Published 19 May 2021
10.9734/ajpas/2021/v13i130298Abstract
A major challenge confronting meta-analysts seeking to synthesize existing empirical research on a given topic is the frequent failure of primary studies to fully report their sample statistics. Because such research cannot be included in a meta-analysis unless the unreported statistics can somehow be recovered, a number of methods have been devised to estimate the sample mean and standard deviation from other quantities. This note compares several recently proposed sets of estimators that rely on extrema and/or quartiles to estimate unreported statistics for any given sample. The simplest method relies on an underlying model of normality, while the more complex methods are explicitly designed to accommodate non-normality. Our empirical comparison uses a previously developed data set containing 58 samples, ranging in size from 48 to 2,528 observations, from a standard depression screening instrument, the nine-item Patient Health Questionnaire (PHQ-9). When only the median and extrema are known, we find that the estimation method based on normality yields the most accurate estimates of both the mean and standard deviation, despite the existence of asymmetry throughout the data set; and when other information is given, the normality-based estimators have accuracy comparable to that of the other estimators reviewed here. Additionally, if the sample size is unknown, the method based on normality is the only feasible approach. The simplicity of the normality-based approach provides an added convenience for practitioners.
References (17)
- 1 Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range [DOI]
- 2 Estimating the mean and variance from the median, range, and the size of a sample [DOI]
- 3 Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range [DOI]
- 4 Empirical Evidence for Selective Reporting of Outcomes in Randomized Trials [DOI]
- 5 Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis [DOI]
- 6 Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review [DOI]
- 7 A systematic review identifies a lack of standardization in methods for handling missing variance data [DOI]
- 8 Effect sizes can be calculated for studies reporting ranges for outcome variables in systematic reviews [DOI]
- 9 Estimating Mean and Standard Deviation from the Sample Size, Three Quartiles, Minimum, and Maximum [DOI]
- 10 Stability of the Distribution of Patient Health Questionnaire-9 Scores Against Age in the General Population: Data From the National Health and Nutrition Examination Survey [DOI]
- 11 Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation (ABC) [DOI]
- 12 Reported methods for handling missing change standard deviations in meta-analyses of exercise therapy interventions in patients with heart failure: A systematic review [DOI]
- 13 Estimating the mean and variance from the five-number summary of a log-normal distribution [DOI]
- 14 A Systematic Review of Methods for Handling Missing Variance Data in Meta-Analyses of Interventions in Type 2 Diabetes Mellitus [DOI]
- 15 Meta-analysis without study-specific variance information: Heterogeneity case [DOI]
- 16 The Adequacy of Reporting Randomized, Controlled Trials in the Evaluation of Antidepressants [DOI]
- 17 Unreported Summary Statistics in Trial Publications and Risk of Bias in Stroke Rehabilitation Systematic Reviews: An International Survey of Review Authors and Examination of Practical Solutions [DOI]
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