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    "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">This editorial follows on from a previously published editorial which explained the role of inferential statistics in the scientific method&#46;<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a> The aim of this second editorial is to highlight the most common errors in the interpretation of the p-value and statistical significance&#44; in line with recent articles and comments in impact journals such as <span class="elsevierStyleItalic">Nature</span> that echo initiatives such as that of more than 800 prestigious scientists who call for an end to the use of significance thresholds and the dichotomous notion of statistical significance&#46;<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2&#8211;5</span></a></p><p id="par0010" class="elsevierStylePara elsevierViewall">To understand the above&#44; we must remember that the aim of so-called inferential statistics is to evaluate the role of chance in our results&#46; This can be quantified or estimated by obtaining the standard error&#44; calculating the probability that the results can be explained by chance under the null hypothesis or H0&#44; giving us a p-value in statistical significance tests&#46; This approach&#44; known as null hypothesis significance testing &#40;NHST&#41;&#44; was invented in the 1920s and 1930s by Ronald Aylmer Fisher &#40;recognized as the father of inferential statistics&#41;&#44; in order to determine which fertilizer increased maize production to the greatest extent&#46; NHST involves a dichotomous approach&#44; as follows&#58; if the p-value is less than a statistical significance threshold &#40;0&#46;05 based on the consensus of an alpha risk of 5&#37;&#41;&#44; the null hypothesis is rejected and the alternative hypothesis is therefore accepted&#46;</p><p id="par0015" class="elsevierStylePara elsevierViewall">This has resulted in a reductionist interpretation&#44; in which if p&#60;0&#46;05&#44; a result is considered significant &#40;e&#46;g&#46; a 120&#8239;ml difference in FEV1 between groups in favor of a new inhaled therapy molecule versus another standard treatment&#41; and &#8220;there are differences between the two treatments&#8221;&#44; whereas if the same treatment with the same 120&#8239;ml difference has a p of&#44; for instance&#44; 0&#46;06&#44; it is considered non-significant&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">The main objective of this editorial is to make clear that non-statistically significant differences are not synonymous with equivalence&#46; The fact that a result is not statistically significant does not necessarily imply that the interventions are equivalent&#46; However&#44; the authors of a published study were alarmed to find that in more than 50&#37; of articles&#44; when p is non-significant&#44; it is erroneously concluded that &#8220;there are no differences between the 2 treatments&#8221; or&#44; worse still&#44; both drugs or interventions are considered to be &#8220;equal or equivalent&#8221;&#46;<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2&#44;6&#8211;9</span></a></p><p id="par0025" class="elsevierStylePara elsevierViewall">This editorial does not aim to provide a comprehensive explanation of statistics&#44; but we should remember that when we accept the null hypothesis &#40;Ho&#41;&#44; a beta error emerges&#44; which is the probability of not having found differences when they actually exist&#44; that is&#44; the probability of not rejecting the null hypothesis when it is false&#46; The complementary aspect is statistical power &#40;1 &#8212; beta error&#41;&#44; which is the probability of finding statistically significant differences if they really do exist&#46;</p><p id="par0030" class="elsevierStylePara elsevierViewall">There is an example in English where a researcher is compared to Michael Jordan &#40;the basketball player&#41;<a class="elsevierStyleCrossRef" href="#bib0050"><span class="elsevierStyleSup">10</span></a> and another&#44; adapted to Spanish&#44; where the ability of a researcher and Leo Messi &#40;the soccer player&#41; to shoot penalties is compared&#46;<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">11</span></a></p><p id="par0035" class="elsevierStylePara elsevierViewall">In the latter example&#44; both shoot 8 penalties from the same positions with a defensive wall of 5 players&#46; Messi scores 8 goals&#44; all in the back of the net&#44; and the researcher scores 4 and misses another 4&#46; Later&#44; at home that night&#44; the researcher enters the data in the computer to check whether statistically there is much difference between their scores and those of Messi&#44; and calculates the p-value using Fisher&#8217;s exact test &#40;2-tailed&#41;&#46; The p-value is 0&#46;077&#46; In other words&#44; the difference is not statistically significant&#46;</p><p id="par0040" class="elsevierStylePara elsevierViewall">If the researcher goes to bed&#44; happy in the knowledge that there are no differences between their penalty shootout results and Messi&#8217;s&#44; he is being easily fooled&#44; because in reality it is clear that there are differences between the two&#46; Therefore&#44; if we accept the null hypothesis we will be falling into the beta-type error&#44; which in this case is high because the power of the study to detect differences is low due to the low sample size &#40;number of penalties shot&#41;&#46;</p><p id="par0045" class="elsevierStylePara elsevierViewall">Let&#8217;s not forget that the standard error can be used in both the p-value approach to significance and also in the construction of 95&#37; confidence intervals &#40;95&#37; CI&#41;&#46; The latter also support the rejection of the null hypothesis&#44; but the width of the intervals&#44; whether narrow or wide&#44; reports the so-called &#8220;effect size&#8221;&#44; and as such the precision of the study&#46;</p><p id="par0050" class="elsevierStylePara elsevierViewall">Logically&#44; in the case of the example of Messi&#44; the 95&#37; CI of the difference in percentage of goals will be very wide&#44; that is&#44; very imprecise&#46; If we increase the number of penalty shots to&#44; for example&#44; 80&#44; we would see how the standard error decreases because the sample size increases and the same difference in the percentage of goals &#40;100&#37; for Messi and 50&#37; for the researcher&#41; becomes statistically significant &#40;p&#8239;&#60;&#8239;0&#46;001&#41;&#44; with a much more precise 95&#37; CI&#46;</p><p id="par0055" class="elsevierStylePara elsevierViewall">Finally&#44; the International Conference on Harmonization &#40;ICH&#41; defines an equivalence trial as a clinical trial in which the main objective is to show that the response to the 2 treatments differs by an amount that is not clinically important&#46;<a class="elsevierStyleCrossRef" href="#bib0060"><span class="elsevierStyleSup">12</span></a> Thus&#44; in order to truly compare a hypothesis of equivalence between Messi and the researcher&#44; you would need to&#58; &#40;a&#41; have set non-inferiority and non-superiority limits &#40;which would establish the percentage differences in goals scored that would be considered as equivalent&#41;&#59; b&#41; have determined the 95&#37; CI of the percentage difference instead of the p-value of significance&#44; and &#40;c&#41; have verified that the 95&#37; CI was within these limits&#46;</p></span>"
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Editorial
P of significance: Is it better to avoid it if it is poorly understood?
p de significación: ¿mejor no usarla si se interpreta mal?
Miguel Santibáñeza,
Corresponding author
santibanezm@unican.es

Corresponding author.
, Juan Luis García-Riverob, Esther Barreiroc,d,e
a Grupo de Investigación de Salud Global, Universidad de Cantabria, Instituto de Investigación Marqués de Valdecilla (IDIVAL), Santander, Cantabria, Spain
b Servicio de Neumología, Hospital de Laredo, Cantabria, Spain
c Servicio de Neumología-Debilidad muscular y caquexia en las enfermedades respiratorias crónicas y el cáncer de pulmón, IMIM-Hospital del Mar, Barcelona, Spain
d Departament de Ciències Experimentals i de la Salut (CEXS), Universitat Pompeu Fabra (UPF), Parc de Recerca Biomèdica de Barcelona (PRBB), Barcelona, Spain
e Centro de Investigación en Red de Enfermedades Respiratorias (CIBERES), Instituto de Salud Carlos III (ISCIII), Barcelona, Spain
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    "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">This editorial follows on from a previously published editorial which explained the role of inferential statistics in the scientific method&#46;<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a> The aim of this second editorial is to highlight the most common errors in the interpretation of the p-value and statistical significance&#44; in line with recent articles and comments in impact journals such as <span class="elsevierStyleItalic">Nature</span> that echo initiatives such as that of more than 800 prestigious scientists who call for an end to the use of significance thresholds and the dichotomous notion of statistical significance&#46;<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2&#8211;5</span></a></p><p id="par0010" class="elsevierStylePara elsevierViewall">To understand the above&#44; we must remember that the aim of so-called inferential statistics is to evaluate the role of chance in our results&#46; This can be quantified or estimated by obtaining the standard error&#44; calculating the probability that the results can be explained by chance under the null hypothesis or H0&#44; giving us a p-value in statistical significance tests&#46; This approach&#44; known as null hypothesis significance testing &#40;NHST&#41;&#44; was invented in the 1920s and 1930s by Ronald Aylmer Fisher &#40;recognized as the father of inferential statistics&#41;&#44; in order to determine which fertilizer increased maize production to the greatest extent&#46; NHST involves a dichotomous approach&#44; as follows&#58; if the p-value is less than a statistical significance threshold &#40;0&#46;05 based on the consensus of an alpha risk of 5&#37;&#41;&#44; the null hypothesis is rejected and the alternative hypothesis is therefore accepted&#46;</p><p id="par0015" class="elsevierStylePara elsevierViewall">This has resulted in a reductionist interpretation&#44; in which if p&#60;0&#46;05&#44; a result is considered significant &#40;e&#46;g&#46; a 120&#8239;ml difference in FEV1 between groups in favor of a new inhaled therapy molecule versus another standard treatment&#41; and &#8220;there are differences between the two treatments&#8221;&#44; whereas if the same treatment with the same 120&#8239;ml difference has a p of&#44; for instance&#44; 0&#46;06&#44; it is considered non-significant&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">The main objective of this editorial is to make clear that non-statistically significant differences are not synonymous with equivalence&#46; The fact that a result is not statistically significant does not necessarily imply that the interventions are equivalent&#46; However&#44; the authors of a published study were alarmed to find that in more than 50&#37; of articles&#44; when p is non-significant&#44; it is erroneously concluded that &#8220;there are no differences between the 2 treatments&#8221; or&#44; worse still&#44; both drugs or interventions are considered to be &#8220;equal or equivalent&#8221;&#46;<a class="elsevierStyleCrossRefs" href="#bib0010"><span class="elsevierStyleSup">2&#44;6&#8211;9</span></a></p><p id="par0025" class="elsevierStylePara elsevierViewall">This editorial does not aim to provide a comprehensive explanation of statistics&#44; but we should remember that when we accept the null hypothesis &#40;Ho&#41;&#44; a beta error emerges&#44; which is the probability of not having found differences when they actually exist&#44; that is&#44; the probability of not rejecting the null hypothesis when it is false&#46; The complementary aspect is statistical power &#40;1 &#8212; beta error&#41;&#44; which is the probability of finding statistically significant differences if they really do exist&#46;</p><p id="par0030" class="elsevierStylePara elsevierViewall">There is an example in English where a researcher is compared to Michael Jordan &#40;the basketball player&#41;<a class="elsevierStyleCrossRef" href="#bib0050"><span class="elsevierStyleSup">10</span></a> and another&#44; adapted to Spanish&#44; where the ability of a researcher and Leo Messi &#40;the soccer player&#41; to shoot penalties is compared&#46;<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">11</span></a></p><p id="par0035" class="elsevierStylePara elsevierViewall">In the latter example&#44; both shoot 8 penalties from the same positions with a defensive wall of 5 players&#46; Messi scores 8 goals&#44; all in the back of the net&#44; and the researcher scores 4 and misses another 4&#46; Later&#44; at home that night&#44; the researcher enters the data in the computer to check whether statistically there is much difference between their scores and those of Messi&#44; and calculates the p-value using Fisher&#8217;s exact test &#40;2-tailed&#41;&#46; The p-value is 0&#46;077&#46; In other words&#44; the difference is not statistically significant&#46;</p><p id="par0040" class="elsevierStylePara elsevierViewall">If the researcher goes to bed&#44; happy in the knowledge that there are no differences between their penalty shootout results and Messi&#8217;s&#44; he is being easily fooled&#44; because in reality it is clear that there are differences between the two&#46; Therefore&#44; if we accept the null hypothesis we will be falling into the beta-type error&#44; which in this case is high because the power of the study to detect differences is low due to the low sample size &#40;number of penalties shot&#41;&#46;</p><p id="par0045" class="elsevierStylePara elsevierViewall">Let&#8217;s not forget that the standard error can be used in both the p-value approach to significance and also in the construction of 95&#37; confidence intervals &#40;95&#37; CI&#41;&#46; The latter also support the rejection of the null hypothesis&#44; but the width of the intervals&#44; whether narrow or wide&#44; reports the so-called &#8220;effect size&#8221;&#44; and as such the precision of the study&#46;</p><p id="par0050" class="elsevierStylePara elsevierViewall">Logically&#44; in the case of the example of Messi&#44; the 95&#37; CI of the difference in percentage of goals will be very wide&#44; that is&#44; very imprecise&#46; If we increase the number of penalty shots to&#44; for example&#44; 80&#44; we would see how the standard error decreases because the sample size increases and the same difference in the percentage of goals &#40;100&#37; for Messi and 50&#37; for the researcher&#41; becomes statistically significant &#40;p&#8239;&#60;&#8239;0&#46;001&#41;&#44; with a much more precise 95&#37; CI&#46;</p><p id="par0055" class="elsevierStylePara elsevierViewall">Finally&#44; the International Conference on Harmonization &#40;ICH&#41; defines an equivalence trial as a clinical trial in which the main objective is to show that the response to the 2 treatments differs by an amount that is not clinically important&#46;<a class="elsevierStyleCrossRef" href="#bib0060"><span class="elsevierStyleSup">12</span></a> Thus&#44; in order to truly compare a hypothesis of equivalence between Messi and the researcher&#44; you would need to&#58; &#40;a&#41; have set non-inferiority and non-superiority limits &#40;which would establish the percentage differences in goals scored that would be considered as equivalent&#41;&#59; b&#41; have determined the 95&#37; CI of the percentage difference instead of the p-value of significance&#44; and &#40;c&#41; have verified that the 95&#37; CI was within these limits&#46;</p></span>"
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Article information
ISSN: 15792129
Original language: English
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