F Other Observers Conducted the Research Again in the Same Setting They Would Reach Similar Results
J Grad Med Educ. 2012 Sep; iv(3): 279–282.
Using Consequence Size—or Why the P Value Is Not Plenty
Statistical significance is the least interesting matter about the results. You should depict the results in terms of measures of magnitude –non only, does a treatment affect people, simply how much does it bear on them.
-Gene V. Glass one
The primary product of a research inquiry is one or more measures of effect size, not P values.
-Jacob Cohen 2
These statements about the importance of issue sizes were fabricated by two of the most influential statistician-researchers of the past half-century. Yet many submissions to Journal of Graduate Medical Education omit mention of the effect size in quantitative studies while prominently displaying the P value. In this paper, we target readers with little or no statistical background in order to encourage you to better your comprehension of the relevance of event size for planning, analyzing, reporting, and agreement educational activity research studies.
What Is Effect Size?
In medical educational activity research studies that compare different educational interventions, effect size is the magnitude of the departure betwixt groups. The absolute event size is the divergence between the average, or hateful, outcomes in 2 dissimilar intervention groups. For instance, if an educational intervention resulted in the comeback of subjects' examination scores by an average total of 15 of l questions as compared to that of another intervention, the accented result size is 15 questions or 3 grade levels (thirty%) meliorate on the examination. Absolute effect size does not take into account the variability in scores, in that not every subject achieved the boilerplate outcome.
In some other instance, residents' self-assessed confidence in performing a procedure improved an average of 0.4 point on a Likert-type calibration ranging from 1 to 5, after simulation training. While the absolute consequence size in the kickoff instance appears clear, the effect size in the 2nd example is less apparent. Is a 0.4 alter a lot or trivial? Bookkeeping for variability in the measured improvement may aid in interpreting the magnitude of the modify in the second case.
Thus, result size can refer to the raw departure between grouping ways, or absolute result size, every bit well as standardized measures of effect, which are calculated to transform the event to an easily understood scale. Absolute upshot size is useful when the variables under study accept intrinsic significant (eg, number of hours of sleep). Calculated indices of consequence size are useful when the measurements have no intrinsic meaning, such as numbers on a Likert calibration; when studies have used dissimilar scales so no directly comparing is possible; or when result size is examined in the context of variability in the population under study.
Calculated effect sizes can also quantitatively compare results from dissimilar studies and thus are commonly used in meta-analyses.
Why Report Result Sizes?
The effect size is the main finding of a quantitative written report. While a P value can inform the reader whether an event exists, the P value will non reveal the size of the effect. In reporting and interpreting studies, both the noun significance (event size) and statistical significance (P value) are essential results to be reported.
For this reason, outcome sizes should exist reported in a newspaper's Abstract and Results sections. In fact, an estimate of the effect size is frequently needed before starting the research endeavor, in order to summate the number of subjects likely to be required to avert a Type Two, or β, error, which is the probability of last in that location is no issue when one actually exists. In other words, y'all must determine what number of subjects in the study will be sufficient to ensure (to a particular degree of certainty) that the study has adequate ability to support the null hypothesis. That is, if no difference is found between the groups, then this is a truthful finding.
Why Isn't the P Value Plenty?
Statistical significance is the probability that the observed difference between ii groups is due to take a chance. If the P value is larger than the alpha level called (eg, .05), whatsoever observed departure is assumed to exist explained past sampling variability. With a sufficiently large sample, a statistical test will well-nigh ever demonstrate a significant difference, unless there is no result whatsoever, that is, when the effect size is exactly zip; yet very small differences, even if pregnant, are often meaningless. Thus, reporting simply the significant P value for an analysis is non adequate for readers to fully understand the results.
For example, if a sample size is 10 000, a significant P value is likely to be found even when the difference in outcomes betwixt groups is negligible and may not justify an expensive or time-consuming intervention over another. The level of significance by itself does not predict result size. Unlike significance tests, result size is independent of sample size. Statistical significance, on the other paw, depends upon both sample size and outcome size. For this reason, P values are considered to be confounded considering of their dependence on sample size. Sometimes a statistically significant outcome means only that a huge sample size was used.3
A usually cited example of this problem is the Physicians Health Study of aspirin to prevent myocardial infarction (MI).4 In more than 22 000 subjects over an average of 5 years, aspirin was associated with a reduction in MI (although not in overall cardiovascular mortality) that was highly statistically significant: P < .00001. The study was terminated early due to the conclusive evidence, and aspirin was recommended for general prevention. However, the effect size was very modest: a risk divergence of 0.77% with r two = .001—an extremely small effect size. As a consequence of that report, many people were advised to accept aspirin who would not experience benefit yet were besides at risk for adverse effects. Farther studies found even smaller effects, and the recommendation to utilise aspirin has since been modified.
How to Calculate Effect Size
Depending upon the type of comparisons nether study, effect size is estimated with different indices. The indices fall into ii main report categories, those looking at effect sizes between groups and those looking at measures of association between variables ( table 1 ). For ii independent groups, effect size can be measured by the standardized difference betwixt ii means, or hateful (group one) – mean (group 2) / standard deviation.
TABLE i
Common Outcome Size Indicesa
The denominator standardizes the difference by transforming the absolute deviation into standard deviation units. Cohen's term d is an example of this blazon of consequence size index. Cohen classified effect sizes as pocket-size (d = 0.2), medium (d = 0.5), and big (d ≥ 0.8).5 Co-ordinate to Cohen, "a medium effect of .five is visible to the naked eye of a conscientious observer. A modest upshot of .two is noticeably smaller than medium only not so small equally to be trivial. A large effect of .8 is the same altitude to a higher place the medium as pocket-sized is below it."half-dozen These designations big, medium, and modest exercise not take into account other variables such equally the accurateness of the assessment instrument and the diversity of the study population. However these ballpark categories provide a general guide that should likewise be informed by context.
Betwixt group means, the result size can besides be understood as the average percentile distribution of group ane vs. that of group 2 or the amount of overlap between the distributions of interventions 1 and 2 for the two groups nether comparison. For an upshot size of 0, the hateful of group 2 is at the 50th percentile of group one, and the distributions overlap completely (100%)—that is , there is no difference. For an effect size of 0.8, the mean of group 2 is at the 79thursday percentile of group 1; thus, someone from group ii with an boilerplate score (ie, mean) would have a higher score than 79% of the people from group one. The distributions overlap by but 53% or a non-overlap of 47% in this situation ( table ii ).five , half dozen
TABLE 2
Differences between Groups, Outcome Size measured past Drinking glass's Δa
What Is Statistical Power and Why Do I Need Information technology?
Statistical power is the probability that your study will find a statistically significant deviation betwixt interventions when an actual difference does be. If statistical power is high, the likelihood of deciding there is an effect, when one does exist, is high. Power is 1-β, where β is the probability of wrongly concluding there is no effect when one really exists. This type of error is termed Type II error. Like statistical significance, statistical power depends upon effect size and sample size. If the effect size of the intervention is big, it is possible to detect such an event in smaller sample numbers, whereas a smaller result size would crave larger sample sizes. Huge sample sizes may observe differences that are quite small and perchance lilliputian.
Methods to increase the power of your report include using more strong interventions that have bigger effects, increasing the size of the sample/subjects, reducing measurement error (use highly valid consequence measures), and raising the α level merely only if making a Type I error is highly unlikely.
How To Calculate Sample Size?
Earlier starting your study, summate the power of your study with an estimated result size; if power is too depression, you lot may need more subjects in the study. How can y'all estimate an effect size before carrying out the study and finding the differences in outcomes? For the purpose of calculating a reasonable sample size, effect size can be estimated by pilot study results, similar work published by others, or the minimum departure that would be considered important by educators/experts. There are many online sample size/power calculators available, with explanations of their use (BOX).7 , eight
Power must be calculated prior to starting the study; post-hoc calculations, sometimes reported when prior calculations are omitted, accept limited value due to the incorrect assumption that the sample issue size represents the population upshot size.
Of involvement, a β error of 0.2 was chosen by Cohen, who postulated that an α error was more serious than a β mistake. Therefore, he estimated the β mistake at four times the α: 4 × 0.05 = 0.20. Although arbitrary, as this has been copied by researchers for decades, use of other levels will need to be explained.
Summary
Effect size helps readers understand the magnitude of differences found, whereas statistical significance examines whether the findings are probable to be due to hazard. Both are essential for readers to understand the full impact of your work. Study both in the Abstract and Results sections.
Footnotes
Gail 1000 Sullivan, MD, MPH, is Editor-in-Master, Journal of Graduate Medical Education; Richard Feinn, PhD, is Assistant Professor, Department Psychiatry, University of Connecticut Health Center.
References
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4. Bartolucci AA, Tendera M, Howard Thousand. Meta-analysis of multiple primary prevention trials of cardiovascular events using aspirin. Am J Cardiol. 2011;107(12):1796–801. [PubMed] [Google Scholar]
6. Coe R. It'due south the result size, stupid: what "consequence size" is and why it is important. Newspaper presented at the 2002 Annual Conference of the British Educational Research Association, University of Exeter, Exeter, Devon, England, September 12–14, 2002. http://www.leeds.ac.uk/educol/documents/00002182.htm. Accessed March 23, 2012. [Google Scholar]
Articles from Periodical of Graduate Medical Education are provided here courtesy of Accreditation Council for Graduate Medical Education
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/
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