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Making Sense of Effect Size in Meta-Analysis

Based For Medical Research

Dr. Nancy Agnes, Head, Technical Operations, Pubrica, sales@pubrica.com

Keywords: Meta-analysis, fixed-effect model,

impacts meta-analysis, statistical analysis, cohen's d

effect size, random effects model

I. INTRODUCTION

Effect size is a statistical idea that helps measure the

strength and connection between two variables on a

numeric scale.

It simply refers to the size and the difference found

between the two groups. It's simple to compute,

understand, and apply to any educational or social

science outcome that can be quantified. It's especially

useful for calculating the efficiency of a certain

intervention concerning other interventions.

It is useful for calculating the efficiency of a certain

intervention in relation to other interventions. It

enables us to look further from the simple 'Does it

function or not?' question to "How well does it work

in a variety of contexts?" and significantly more

complex, by focusing on the most crucial feature of

an intervention. Rather than its statistical

significance, it promotes a different scientific

approach to the accumulation of knowledge. For

these reasons, the effect size is considered an

effective tool in reporting and interpreting

effectiveness.

For example, if we have data on the weight of men

and women and notice that, on average, men have

more weight than women, women's weight is known

as the effect size.

Statistical effect size helps us decide whether the

difference is genuine or a difference in factors.

II. SIGNIFICANCE OF EFFECT SIZE

Formulae for evaluating the effect sizes do not often

found in many statistics textbooks (other than those

devoted to meta-analysis), are not included in various

statistics computer packages and are occasionally

taught in standard research approaches courses. For

these above-stated reasons, even the researcher who

found interest in using measures of effect size is

afraid to use them in conventional practice and find it

quite hard to know exactly how to do it.

III. EFFECT SIZE IN META-ANALYSIS

In Meta-analysis, the effect size is concerned about

various studies and afterwards joins all the studies

into a single analysis.

In statistical analysis, the effect size is typically

estimated in three ways:

(1) The standardized mean difference,

(2) Odd ratio,

(3) Correlation coefficient.

IV. FORMULATION FOR EFFECT SIZE

Karl Pearson created Pearson r correlation, and it is

broadly utilized in statistics.[3] This parameter of

effect size is signified by r—the estimation of the

effect size of the Pearson r connection shifts is found

in-between -1 to +1.

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Where

r = correlation coefficient

N = number of pairs of scores

∑XY = sum of the products of paired scores

∑x = sum of x scores

∑y = sum of y scores

∑x2= sum of squared x scores

∑y2= sum of squared y scores

V. STANDARDIZED MEANS DIFFERENCE

When a research study depends on the population

mean and standard deviation, at that point, the

accompanying technique is utilized to know the effect

size:

VI. COHEN'S D EFFECT SIZE

Cohen's d is known as the distinction of two

population means, and the standard deviation

separates it from the data.

Mathematically Cohen's effect size is signified by:

Where s can be calculated by using the following

formula:

Hedges' g method of effect size: This is the modified

form of Cohen's d method. We can write Hedges' g

method of effect size as follows:

VII. FIXED EFFECTS MODEL

The fixed-effect model gives a weighted average of a

progression of study estimates. The opposite of the

appraisals' difference is usually utilized as study

weight. More extensive studies will offer more than

smaller studies to the weighted average. Thus, when

concentrates inside a meta-analysis are overwhelmed

by an extensive study, the discoveries from smaller

studies are practically ignored.

This assumption is ordinarily unrealistic as an

examination is frequently inclined to several

heterogeneity sources; for example, treatment impacts

may contrast as indicated by region, measurements

levels, and study conditions.

VIII. RANDOM EFFECTS MODEL

A typical model used to synthesize heterogeneous

study is the irregular impacts model of meta-analysis.

This is the weighted average of the effect sizes of a

gathering of studies. The weight that is applied in this

interaction of weighted averaging with an arbitrary

impacts meta-investigation is accomplished in two

stages:

Step 1: Inverse variance weighting.

Step 2: Un-weighting of inverse variance weighting

by REVC (Random Effects Variance Component).

IX. FUTURE ENHANCEMENTS

The more significant variability in effect size e (also

called heterogeneity) is the more prominent in un-

weighting.

This can conclude that the arbitrary impacts meta-

analysis result turns out to be just the un-weighted

average effect size across the studies. At the other

limit, when all effect sizes are comparable (or

inconstancy doesn't surpass testing error), no REVC

is applied, and the irregular impacts meta-

examination defaults to just a fixed impact meta-

investigation (just opposite variance weighting).

REFERENCES

[1] Ens, D. (2013). Calculating and reporting effect

sizes to facilitate cumulative science: a practical

primer for t-tests and ANOVAs. Front.

Psychol. 4:863. doi: 10.3389/fpsyg.2013.00863

[2] Assen, M. A. L. M., van Aert, R. C. M., and

Wicherts, J. M. (2015). Meta-analysis using effect

size distributions of only statistically significant

studies. Psychol. Methods 20, 293–309. doi:

10.1037/met0000025

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