Homogeneity (statistics)

In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. In meta-analysis, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity). Homogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset.


statisticalstatistical analysisstatistician
., Difference in differences estimation and instrumental variables, among many others) that produce consistent estimators. The basic steps of a statistical experiment are: Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity.


Furthermore, the concept of disease heterogeneity appears to conflict with the long-standing premise in epidemiology that individuals with the same disease name have similar etiologies and disease processes. To resolve these issues and advance population health science in the era of molecular precision medicine, "molecular pathology" and "epidemiology" was integrated to create a new interdisciplinary field of "molecular pathological epidemiology" (MPE), defined as "epidemiology of molecular pathology and heterogeneity of disease".

Funnel plot

A funnel plot is a graph designed to check for the existence of publication bias; funnel plots are commonly used in systematic reviews and meta-analyses. In the absence of publication bias, it assumes that studies with high precision will be plotted near the average, and studies with low precision will be spread evenly on both sides of the average, creating a roughly funnel-shaped distribution. Deviation from this shape can indicate publication bias. Funnel plots, introduced by Light and Pillemer in 1984 and discussed in detail by Matthias Egger and colleagues, are useful adjuncts to meta-analyses. A funnel plot is a scatterplot of treatment effect against a measure of study precision.

List of statistics articles

List of statistical topicsList of statistics topicsIndex of statistics articles
Study heterogeneity. Subcontrary mean – redirects to Harmonic mean. Subgroup analysis. Subindependence. Substitution model. SUDAAN – software. Sufficiency (statistics) – see Sufficient statistic. Sufficient dimension reduction. Sufficient statistic. Sum of normally distributed random variables. Sum of squares (disambiguation) – general disambiguation. Sum of squares (statistics) – see Partition of sums of squares. Summary statistic. Support curve. Support vector machine. Surrogate model. Survey data collection. Survey sampling. Survey methodology. Survival analysis. Survival rate. Survival function. Survivorship bias. Symmetric design. Symmetric mean absolute percentage error.


If one performs a meta-analysis of repeated surveys of a fixed population (say with a given sample size, so margin of error is the same), one expects the results to fall on normal distribution with standard deviation equal to the margin of error. However, in the presence of study heterogeneity where studies have different sampling bias, the distribution is instead a compound distribution and will be overdistributed relative to the predicted distribution.

Systematic review

systematic reviewsreviewsystematic literature review
Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) Statement, "an evidence-based minimum set of items for reporting in systematic reviews and meta-analyses". PRISMA Extension for Scoping Reviews (PRISMA-ScR): Checklist and explanation. Animated Storyboard: What Are Systematic Reviews? - Cochrane Consumers and Communication Group. Sysrev - a free platform with open access systematic reviews.

Causal inference

causalcausal relationshipslack of one
Second, the instrumental variables technique may be employed to remove any reverse causation by introducing a role for other variables (instruments) that are known to be unaffected by the dependent variable. Third, the principle that effects cannot precede causes can be invoked, by including on the right side of the regression only variables that precede in time the dependent variable. Fourth, other regressors are included to ensure that confounding variables are not causing a regressor to spuriously appear to be significant.

Individual participant data

Common aims for a IPD meta-analysis are Over the past few decades, meta-analyses conducted with IPD (also known as IPD meta-analyses) have become increasingly popular. * Individual participant data meta-analysis information at the Cochrane website to evaluate the safety or efficacy of medical interventions. to identify modifiers of treatment effect. to evaluate the accuracy of diagnostic tests. to evaluate the association of prognostic markers. to develop multivariable prediction models (rules). to evaluate the predictive performance of prognostic models.

Endogeneity (econometrics)

endogenousendogeneityreverse causality
Heterogeneity. Dependent and independent variables. by Mark Thoma. Seth Godin's simple views on endogeneity.

Seed-based d mapping

SDM meta-analysesseed based
SDM is software written by the SDM project to aid the meta-analysis of voxel-based neuroimaging data. It is distributed as freeware including a graphical interface and a menu/command-line console. It can also be integrated as an SPM extension. * SDM software and documentation from the SDM Project. The main statistical analysis is the mean analysis, which consists in calculating the mean of the voxel values in the different studies. This mean is weighted by the inverse of the variance and accounts for inter-study heterogeneity (QH maps). Subgroup analyses are mean analyses applied to groups of studies to allow the study of heterogeneity.

Control function (econometrics)

control function
Instrumental variables, for example, attempt to model the endogenous variable X as an often invertible model with respect to a relevant and exogenous instrument Z. Panel data use special data properties to difference out unobserved heterogeneity that is assumed to be fixed over time. Control functions were introduced by Heckman and Robb, although the principle can be traced back to earlier papers. A particular reason why they are popular is because they work for non-invertible models (such as discrete choice models) and allow for heterogeneous effects, where effects at the individual level can differ from effects at the aggregate.

Galbraith plot

It can be used to examine heterogeneity in a meta-analysis, as an alternative or supplement to a forest plot. A Galbraith plot is produced by first calculating the standardized estimates or z-statistics by dividing each estimate by its standard error (SE). The Galbraith plot is then a scatter plot of each z-statistic (vertical axis) against 1/SE (horizontal axis). Larger studies (with smaller SE and larger 1/SE) will be observed to aggregate away from the origin. Plot. Funnel plot. Galbraith plots are available within the metafor package in R, along with various other diagnostic and summary plots. MIX 2.0 Software to perform meta-analysis and create Galbraith plots in Excel.

Random effects model

random effectsrandom effectvariance component
How to Conduct a Meta-Analysis: Fixed and Random Effect Models.


homoscedastichomogeneity of variancehomoskedastic
Homogeneity (statistics). Heterogeneity.


medicalmedical scienceclinical medicine
Evidence-based medicine is a contemporary movement to establish the most effective algorithms of practice (ways of doing things) through the use of systematic reviews and meta-analysis. The movement is facilitated by modern global information science, which allows as much of the available evidence as possible to be collected and analyzed according to standard protocols that are then disseminated to healthcare providers. The Cochrane Collaboration leads this movement. A 2001 review of 160 Cochrane systematic reviews revealed that, according to two readers, 21.3% of the reviews concluded insufficient evidence, 20% concluded evidence of no effect, and 22.5% concluded positive effect.

Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
One strong critic of significance testing suggested a list of reporting alternatives: effect sizes for importance, prediction intervals for confidence, replications and extensions for replicability, meta-analyses for generality. None of these suggested alternatives produces a conclusion/decision. Lehmann said that hypothesis testing theory can be presented in terms of conclusions/decisions, probabilities, or confidence intervals. "The distinction between the ... approaches is largely one of reporting and interpretation."


acupuncturistacupuncture pointacupuncture points
A 2016 systematic review and meta-analysis found that acupuncture was "associated with a significant reduction in sleep disturbances in women experiencing menopause-related sleep disturbances."

Data integration

Customer data integrationintegrationintegrate
Large-scale questions in science, such as global warming, invasive species spread, and resource depletion, are increasingly requiring the collection of disparate data sets for meta-analysis. This type of data integration is especially challenging for ecological and environmental data because metadata standards are not agreed upon and there are many different data types produced in these fields. National Science Foundation initiatives such as Datanet are intended to make data integration easier for scientists by providing cyberinfrastructure and setting standards.

Bipolar disorder

bipolarmanic depressionmanic depressive
Polymorphisms in BDNF, DRD4, DAO, and TPH1 have been frequently associated with bipolar disorder and were initially successful in a meta-analysis, but failed after correction for multiple testing. On the other hand, two polymorphisms in TPH2 were identified as being associated with bipolar disorder. Due to the inconsistent findings in a genome-wide association study, multiple studies have undertaken the approach of analyzing single-nucleotide polymorphisms (SNPs) in biological pathways.

Punctuated equilibrium

punctuated equilibriastasisequilibrium
More modern studies, including a meta-analysis examining 58 published studies on speciation patterns in the fossil record showed that 71% of species exhibited stasis, and 63% were associated with punctuated patterns of evolutionary change. According to Michael Benton, "it seems clear then that stasis is common, and that had not been predicted from modern genetic studies." A paramount example of evolutionary stasis is the fern Osmunda claytoniana. Based on paleontological evidence it has remained unchanged, even at the level of fossilized nuclei and chromosomes, for at least 180 million years.

Plot (graphics)

plotdata plotplots
Funnel plot : This is a useful graph designed to check the existence of publication bias in meta-analyses. Funnel plots, introduced by Light and Pillemer in 1994 and discussed in detail by Egger and colleagues, are useful adjuncts to meta-analyses. A funnel plot is a scatterplot of treatment effect against a measure of study size. It is used primarily as a visual aid to detecting bias or systematic heterogeneity. Dot plot (statistics) : A dot chart or dot plot is a statistical chart consisting of group of data points plotted on a simple scale. Dot plots are used for continuous, quantitative, univariate data. Data points may be labelled if there are few of them.

Management of prostate cancer

It was often suggested to change the voiding position of symptomatic males, however study results showed heterogeneity. A meta-analysis of people with prostate enlargement and healthy males showed a significant reduction of residual volume, while a trend towards an improved urinary flow rate and decreased voiding time was found. The effect of changing ones position is thought to arise from relaxation of the pelvic musculature, which are contracted in the standing position thereby influencing urodynamics.

Influence of mass media

Media influencemedia theorymedia effects
After conducting a meta-analysis on micro-level media effects theories, Valkenburg, Peter & Walther (2016) identified five main features: There are two propositions of this selectivity paradigm: (a) among the constellation of messages potentially attracting their attention, people only go to a limited portion of messages; (b) people are only influenced by those messages they select (Klapper 1960, Rubin 2009 ). Researchers had noticed the selectivity of media use decades ago, and considered it as a key factor limiting media effects.