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Revista argentina de cirugía
versión impresa ISSN 2250-639Xversión On-line ISSN 2250-639X
Rev. argent. cir. vol.115 no.3 Cap. Fed. ago. 2023
http://dx.doi.org/10.25132/raac.v115.n3.edmli
The following is an answer from Microsoft Bing GPT chat to the question: what is effect size?
“Effect size is a measure of the strength of a phenomenon in statistics. It is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population1. Effect size refers to a way of quantifying the magnitude of difference between two groups2. There are three ways to measure effect size, depending on the type of analysis one is performing: 1. Standardized mean difference 2. Correlation coefficient 3. Odds ratio2.”
Citations 3 and 4 are suggested but not referenced in the answer.
Artificial intelligence is fashionable in the medical literature and will become a topic of discussion in scientific settings. However, my idea is to leave artificial intelligence for another occasion and take this opportunity to introduce the concept and importance of the effect size in clinical research studies in contrast to reporting the p-value, which is a measure of the probability that the results are due to chance and only if the study is properly designed in terms of applicability. From the chat response, I highlight the concept of the magnitude of the difference between two groups because a low p-value may coincide with an effect size without clinical relevance.
There are different measures for effect size to compare 2 means, The most common effect sizes are Cohen’s d, Hedges’ g and Glass’ delta3. I leave relative risk, odds ratios, correlation coefficients, etc., for another occasion because they are beyond the scope of this editorial and I prefer to introduce concepts slowly.
d formula is mean 1 - mean 2/pooled standard deviation (SDpooled)4. A d of 0.2 is considered a small effect size, a d of 0.5 is considered a medium effect size, and a d of 0.8 or larger is considered a large effect size2. If the result is negative, although it is mathematically correct, it is not used to facilitate its interpretation. It is also known as standardized mean difference because the units of the result is the number of standard deviations in which the means differ. Standardized mean difference is a common measure in meta-analyses.
With only relevant data mean
(data1) # mean group 1
[1] 41.21997
mean(data2) # mean group 2
[1] 61.2
sd_pooled(data1, data2) # pooled standard deviation
[1] 27.63153
t.test(data2, data1) # Student’s t-test of the 2 samples without statistical significance
t = 1.6169, df = 17.724, p-value = 0.1236 # Welch Two Sample t-test
Calculation of Cohen’s d according to the formula
mean(data2) - mean(data1))/ sd_pooled
(data1,data2)
[1] 0.7230879
Calculation of Cohen’s on R, library (effectsize)
cohens_d(data2, data1)
Cohen’s d | 95% CI
---------------------------------
0.72 | [0.37, 1.92
- Estimated using pooled SD. interpret_cohens_d(0.72)
[1] “medium”
(Rules: cohen1988)
Here, the effect size is moderate and the p-value is not significant. The result may be the other way around. Low effect size and significant p-value
There are other estimations for proportions, as Cohen’s h, with the same interpretation, Cramer’s V, etc. Another example in R, library (pwr)5,9 with one line of script
library (pwr)
ES.h (0.5,0.4) ### proportions 0.5 and 0.4 in each sample (50 and 40%) - Cohen’s h
[1] 0.2013579 # the effect size is low
Thus, finding a statistically significant p-value is not to celebrate as if we had found an “Aleph” in the basement10, but rather to interpret it with caution and perform a deeper analysis of our data with other statistical tools. An isolated p-value is overrated, and the effect size should be estimated in clinical research studies.
Referencias bibliográficas /References
1. Tamaño del efecto - Wikipedia, la enciclopedia libre [ Links ]
2. https://statologos.com/tamano-del-efecto/ o Tamaño del efecto: qué es y por qué es importante (https_statologos.com) para evitar anuncios [ Links ]
3. ¿Por qué reportar el tamaño del efecto? - Comunicar. Escuela de Autores (https://www.grupocomunicar.com/wp/escuela-deautores/por-que-reportar-el-tamano-del-efecto/) [ Links ]
4. ¿Qué es el tamaño del efecto? | Estadísticas (physiotutors.com) https://www.physiotutors.com/es/wiki/effect-size/ [ Links ]
5. R Core Team (2023). _R: A Language and Environment for Statistical Computing_. R Foundation for Statistical Computing, Vienna, Austria. <https://www.R-project.org/>. [ Links ]
6. Ben-Shachar M, Lüdecke D, Makowski D (2020). effectsize: Estimation of Effect Size Indices and Standardized Parameters. Journal of Open Source Software. 2020;5(56): 2815. doi: 10.21105/joss.02815 [ Links ]
7. Statology. https://www.statology.org/pooled-standard-deviation-in-r/ [ Links ]
8. Statology. https://www.statology.org/cohens-d-in-r/ [ Links ]
9. Champely S (2020). _pwr: Basic Functions for Power Analysis_. R package version 1.3-0, <https://CRAN.R-project.org/package=pwr>. [ Links ]
10. Borges JL. El Aleph. Buenos Aires: Losada; 1949. [ Links ]