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Know your data: Evaluation of normality for continuous variables and tools to deal with non-normal distributions
Conoce tus datos: evaluación de la normalidad de variables continuas y estrategias para tratar con distribuciones no normales
Adrian Rodriguez
Università Cattolica del Sacro Cuore, Rome, Italy
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The phenotype of the different cell populations was determined by flow cytometry. 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To synthesize the data, researchers can use a measure of central tendency, such as the mean or median, accompanied by measures of dispersion, such as the standard deviation, the interquartile range or the range. However, although many researchers are tempted to use the mean arbitrarily, it is not always the best way to summaries a series of data. If the variable in question does not have a normal (or Gaussian) distribution, the median is usually a better estimate as a measure of central tendency.</p><p id="par0010" class="elsevierStylePara elsevierViewall">Something similar happens when we have to decide which statistical analysis or test to use to compare a continuous quantitative variable in 2 or more groups. Many researchers tend to use the Student's t-test or the one-way ANOVA to compare the means between different groups. However, these statistical tests have several assumptions that must be met and, probably, the most important is that the variable is distributed normally. Alternatives to these are the Mann Whitney U test or the Kruskal–Wallis test, which do not assume any particular distribution of the data. This means that they can always be used, regardless of whether the variable of interest is distributed normally or not.</p><p id="par0015" class="elsevierStylePara elsevierViewall">This article reviews the different ways of establishing whether a variable follows a normal distribution or not, and the alternatives that we can use in the case of dealing with non-normal distributions.</p><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0005">Normality analysis</span><p id="par0020" class="elsevierStylePara elsevierViewall">When studying the normality of the data, it is convenient to follow a multiple approach in which we evaluate the data using the different tools available. There are specific statistical tests to check if the data follow a normal distribution. The best-known tests are the Shapiro–Wilk test and the Kolmogorov–Smirnov test. However, these tests are very sensitive to the sample size, and it is not convenient to rely solely on them to make a decision. However, there are a series of simple graphs that we can represent and that can help us decide if the data follows a normal distribution. These graphs are the histograms, the <span class="elsevierStyleItalic">box plot</span>, and the Q-Q plots.</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0010">Graphs</span><p id="par0025" class="elsevierStylePara elsevierViewall">To illustrate how to interpret these graphs, we will take a series of hypothetical data summarized in <a class="elsevierStyleCrossRef" href="#tbl0005">Table 1</a>. This table shows the weight and daily consumption of cigarettes of a hypothetical series of 20 subjects. If we look at the table, we can see that, in the row of cigarette consumption, there are a large number of people (specifically 7 of 20) who are not smokers. This is usually common in surveys on alcohol and tobacco consumption, where there is a high percentage of the population that are not smokers or consume alcohol.</p><elsevierMultimedia ident="tbl0005"></elsevierMultimedia><p id="par0030" class="elsevierStylePara elsevierViewall">The first graphs represented in <a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a> are the histograms for both variables (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>A and B for cigarette consumption and weight, respectively). A histogram represents the frequency with which a certain value of the variable appears versus the values of that variable. Thus, for the first case, the X axis shows the number of cigarettes per day and the Y axis shows the frequency with which that value of cigarettes per day appears in our sample. In the second case, the X axis shows the weight of the participants and the Y axis shows the frequency with which these weights appear. These histograms are very useful to clarify if the data of our variable of interest follows a normal distribution. In the first case (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>A) a histogram appears with what is called “scewed right”. This occurs when there is a high percentage of the data that have small values of the variable. We could easily deduce that the data is not distributed according to a normal distribution. However, in the case of weight (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>B), the histogram is shaped like “bell-curve”, so it seems that the data does follow a normal distribution.</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0035" class="elsevierStylePara elsevierViewall">Then, in <a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>C and D, the <span class="elsevierStyleItalic">box-plot</span> (box and whisker plot) is represented. This is a particularly useful graph, not only to evaluate the distribution of the data but also as a summary of them. This diagram consists of the following parts: a horizontal line with the rectangle (or box), which represents the median of the 50th percentile. It should be remembered that the median is the value of the data that leaves the bottom 50% of the values below it and the top 50% above it. The 25th percentile is the below the box. That is, the value that leaves 25% of the smallest data below and the remaining 75% above. Therefore, the top of the box is the 75th percentile. Finally, 2 segments (or “whiskers”) join. In one case, the 75th percentile with the highest value and, in the other case, the 25th percentile with the lowest value. These graphs are very useful because, with a quick look, we can know the maximum and minimum values of the sample, the value of the median and what are the 25th and 75th percentiles. In addition, in the case at hand, they can also help to clarify whether the data follows an approximate normal distribution. When the <span class="elsevierStyleItalic">box-plot</span> has quite a lot of symmetry, it indicates that the data is distributed normally. In the case of cigarette smoking (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>C), the <span class="elsevierStyleItalic">box-plot</span> is clearly not symmetrical, since the lowest point and the 25th percentile coincide. However, for the weight variable (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>D) the <span class="elsevierStyleItalic">box-plot</span> is quite symmetrical, which is further proof that the data can be considered normally distributed.</p><p id="par0040" class="elsevierStylePara elsevierViewall">The last type of graph that we can analyse when evaluating the normality of the data is the quantile-quantile graphs, better known as Q-Q plots. These graphs can be generated with most statistical packages (SPSS, R or Stata, etc.). If the points on the graph are located on the theoretical line, the distribution can be considered as normal. Obviously, it cannot be expected that all the points are exactly on the line, but it is easy to see whether the deviation from normality is great or not. For example, in the case of the consumption of cigarettes (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>E) it can be deduced that the points are very far from being uniformly on the line, while in the case of weight (<a class="elsevierStyleCrossRef" href="#fig0005">Fig. 1</a>F) the points are quite close to the line.</p><p id="par0045" class="elsevierStylePara elsevierViewall">Thus, these 3 graphs allow us to easily conclude that, in our hypothetical data set, cigarette consumption does not meet the requirements to be considered a normally distributed variable, but weight does.</p></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0015">Specific statistical tests</span><p id="par0050" class="elsevierStylePara elsevierViewall">Although in the vast majority of cases, these 3 graphs can be considered as conclusive, many authors prefer to use specific statistical tests to analyse the normality of the data. These tests are called Shapiro–Wilk and Kolmogorov–Smirnov tests. In both cases, the null hypothesis is that the results follow a normal distribution. Thus, assuming the classic 95% confidence level, if p < 0.05, the null hypothesis is rejected, and it is concluded that the distribution is not normal. However, these tests should be complementary to the graphs described above, especially since they are very sensitive to the sample size. If the sample size is small, we can obtain a p > 0.05 and we would conclude that the distribution is normal, when the reality is that the distribution is far from normal. On the other hand, very large sample sizes favour the statistical test being significant (p < 0.05) even for small deviations from normal, and we could erroneously conclude that the distribution is not normal, when in fact it could be considered as such. Therefore, these tests must be used with great discretion, and the aim should be to use them as complementary tests to the normality graphs, which offer more and better information. By applying the Shapiro–Wilk test to our set of hypothetical data we see that, for weight, p = 0.84 and for the consumption of cigarettes p = 0.004. Thus, again, in this first case we would retain the null hypothesis normality data, while in the case of the cigarette consumption variable we would discard the null hypothesis and conclude that the data is not distributed normally.</p></span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0020">Description of the data</span><p id="par0055" class="elsevierStylePara elsevierViewall">Once we have seen how to evaluate the normality of the data, we must consider how to report that data in an article or communication, and what types of statistical tests to apply in each case. When the data follow a normal distribution, the most common occurrence is to report the mean as a measure of central tendency of said data, and the standard deviation (or standard error in some cases) as a measure of dispersion. On the other hand, the confidence intervals of the mean can be reported, generally at 95%. For example, in the case of our hypothetical weight variable, the mean (standard deviation) is 70 (4) kg, and the 95% confidence interval for the average is (68–72).</p><p id="par0060" class="elsevierStylePara elsevierViewall">On the other hand, in the case of cigarette consumption, the mean would not be a good measure of central tendency, since the distribution is far from normal. Thus, the alternative is to use measures of central tendency that do not assume any distribution of the data. Without a doubt, the most used is the median. As a measure of dispersion, the interquartile path is generally used (which is the difference between the 25th and 75th percentiles), although the percentiles or the range (minimum and maximum values) can also be reported. In our hypothetical data set, the median cigarette consumption is 5. The 25th and 75th percentiles are, respectively, 0 and 11 cigarettes, so the interquartile range is 11. The range is 0–30.</p></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Data analysis</span><p id="par0065" class="elsevierStylePara elsevierViewall">When analysing data, it is important to keep in mind that there is nothing inherently wrong in the fact that the data does not follow a normal distribution. There are simply variables that are not distributed according to this model. Luckily, we have tools so that the data ends up well expressed and summarised in both cases. In addition, it should be borne in mind that, whenever possible, the mean is usually used. But this does not mean that using the median in the case of normal distributions is incorrect; the median can always be used, since it does not presuppose a specific distribution of the data. However, there is a clear consensus among statisticians that, whenever possible, it is better to use the mean as a measure of central tendency and the so-called parametric tests for hypothesis contrasts.</p><p id="par0070" class="elsevierStylePara elsevierViewall">Once again, the statistical tests will depend on the distribution of the data.<a class="elsevierStyleCrossRef" href="#bib0005"><span class="elsevierStyleSup">1</span></a> This article aims to be an introduction to the study of the normality of the data, so not all statistical tests will be explained in detail. However, it is important to have an overview, to know when a certain statistical test can be applied and to take into account the assumptions to be analysed. To illustrate, I will focus on the tests to compare a quantitative variable between 2 or more groups.</p><p id="par0075" class="elsevierStylePara elsevierViewall">The so-called “parametric” alternatives estimate a parameter of a given distribution, so it is assumed that the dependent variable of interest follows that distribution (in our case, the normal distribution). Thus, before proceeding to apply this type of statistical test, we must check the normality of the data. This check is only critical when we have small sample sizes, as explained below. For example, when we want to compare the means between 2 or more independent groups, we would use the Student’s t-test or the one-way analysis of variance (one-way ANOVA), respectively. However, when we have small sample sizes and the data does not follow a normal distribution, non-parametric methods can be used. Specifically, in this case, we would be talking about the Mann–Whitney U test (sometimes known as “Wilcoxon Rank-Sum test”) or the Kruskal–Wallis test, which would be the non-parametric alternatives to the Student's t test and the one-way ANOVA, respectively. The primary difference is that the non-parametric tests do not assume any type of data distribution to estimate a specific parameter and, therefore, they can be used for any data set.</p><p id="par0080" class="elsevierStylePara elsevierViewall">Although it is true that non-parametric tests are relatively known and used in medical literature, some authors advise against their use, while others use them for any type of analysis. In the opinion of the author, non-parametric tests are useful in some cases, but parametric tests are normally preferable, provided that due assumptions are met, since they provide confidence intervals in addition to a p-value, and they can be generalised to be used in more complex statistical analyses.</p></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0030">Alternatives to non-parametric tests</span><p id="par0085" class="elsevierStylePara elsevierViewall">One of the alternatives that we can use when the distribution of the data is not normal, and when we do not want to resort to non-parametric tests, is to perform a data transformation.<a class="elsevierStyleCrossRef" href="#bib0010"><span class="elsevierStyleSup">2</span></a> In many cases, if we perform a mathematical operation on the data (for example, a decimal logarithm or a square root), the transformed data does follow a normal distribution and, therefore, we could use parametric tests. Although some authors have defended its use, the truth is that its use is not widespread in medical literature. The reason is that the statistics must be carried out on the transformed data. Therefore, the reported confidence intervals will also be based on the transformed data and their interpretation may result in errors or be somewhat complex.</p><p id="par0090" class="elsevierStylePara elsevierViewall">Throughout this article I have repeated several times that the assumption of normality in parametric tests is only essential when the sample size is small. Although there is no established cut-off point, there is a fairly broad consensus that, when sample sizes are greater than 80–100, the premise of normal distribution loses importance, in a way, when choosing between a parametric test or a non-parametric one.<a class="elsevierStyleCrossRef" href="#bib0015"><span class="elsevierStyleSup">3</span></a> This is because of the so-called central limit theorem.<a class="elsevierStyleCrossRef" href="#bib0020"><span class="elsevierStyleSup">4</span></a> Without going into detail, this theorem establishes that, although the distribution of the data is not normal, the distribution of the means is normal. This theorem allows parametric tests to be applied when the sample size is high, even when the variable of interest is not distributed normally.</p></span><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0035">Conclusion</span><p id="par0095" class="elsevierStylePara elsevierViewall">When reporting a measure of central tendency for a certain quantitative variable or when choosing a certain statistical test, in many cases it is important to examine the normality of the data. For this, we have different tools, such as graphs and statistical tests, which can be very useful for this purpose. The contrasting statistical hypothesis testing for normal distribution should be interpreted with caution, and always as a complementary test to the graphic description of the data.</p></span><span id="sec0040" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0040">Financing</span><p id="par0100" class="elsevierStylePara elsevierViewall">The author confirms that there has been no financial support for the preparation of this article.</p></span><span id="sec0045" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0045">Conflict of interests</span><p id="par0105" class="elsevierStylePara elsevierViewall">The author confirms that there is no conflict of interests.</p></span><span id="sec0050" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0050">Thanks</span><p id="par0110" class="elsevierStylePara elsevierViewall">The author thanks the Alfonso Martín Escudero Foundation for the financing of the postdoctoral fellowship he currently enjoys.</p></span></span>" "textoCompletoSecciones" => array:1 [ "secciones" => array:11 [ 0 => array:2 [ "identificador" => "sec0005" "titulo" => "Normality analysis" ] 1 => array:2 [ "identificador" => "sec0010" "titulo" => "Graphs" ] 2 => array:2 [ "identificador" => "sec0015" "titulo" => "Specific statistical tests" ] 3 => array:2 [ "identificador" => "sec0020" "titulo" => "Description of the data" ] 4 => array:2 [ "identificador" => "sec0025" "titulo" => "Data analysis" ] 5 => array:2 [ "identificador" => "sec0030" "titulo" => "Alternatives to non-parametric tests" ] 6 => array:2 [ "identificador" => "sec0035" "titulo" => "Conclusion" ] 7 => array:2 [ "identificador" => "sec0040" "titulo" => "Financing" ] 8 => array:2 [ "identificador" => "sec0045" "titulo" => "Conflict of interests" ] 9 => array:2 [ "identificador" => "sec0050" "titulo" => "Thanks" ] 10 => array:1 [ "titulo" => "References" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "fechaRecibido" => "2019-04-29" "fechaAceptado" => "2019-05-09" "NotaPie" => array:1 [ 0 => array:2 [ "etiqueta" => "☆" "nota" => "<p class="elsevierStyleNotepara" id="npar0005">Please cite this article as: Rodriguez A. Conoce tus datos: evaluación de la normalidad de variables continuas y estrategias para tratar con distribuciones no normales. Med Clin (Barc). 2020;154:142–145.</p>" ] ] "multimedia" => array:2 [ 0 => array:8 [ "identificador" => "fig0005" "etiqueta" => "Fig. 1" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr1.jpeg" "Alto" => 3552 "Ancho" => 2507 "Tamanyo" => 284067 ] ] "detalles" => array:1 [ 0 => array:3 [ "identificador" => "at0005" "detalle" => "Fig. " "rol" => "short" ] ] "descripcion" => array:1 [ "en" => "<p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">Graphs to demonstrate the normality of the data: histograms (A and B), box plots (C and D) and Q-Q plots (E and F) for the variables ‘number of cigarettes’ and ‘weight’.</p>" ] ] 1 => array:8 [ "identificador" => "tbl0005" "etiqueta" => "Table 1" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "detalles" => array:1 [ 0 => array:3 [ "identificador" => "at0010" "detalle" => "Table " "rol" => "short" ] ] "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">Subject \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">1 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">2 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">3 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">4 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">5 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">6 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">7 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">8 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">9 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">10 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">11 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">12 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">13 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">14 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">15 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">16 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">17 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">18 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">19 \t\t\t\t\t\t\n \t\t\t\t\t\t</th><th class="td" title="\n \t\t\t\t\ttable-head\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t" scope="col">20 \t\t\t\t\t\t\n \t\t\t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Cigarettes \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">15 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">5 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">30 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">8 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">5 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">20 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">18 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">25 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">Weight (kg) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">61 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">72 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">65 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">73 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">69 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">69 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">70 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">70 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">78 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">71 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">77 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">70 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">75 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">75 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">69 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">66 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">67 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">68 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">62 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="\n \t\t\t\t\ttable-entry\n \t\t\t\t " align="left" valign="\n \t\t\t\t\ttop\n \t\t\t\t">68 \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab2245935.png" ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">Daily cigarette consumption and weight (kg) in a hypothetical series of 20 subjects.</p>" ] ] ] "bibliografia" => array:2 [ "titulo" => "References" "seccion" => array:1 [ 0 => array:2 [ "identificador" => "bibs0005" "bibliografiaReferencia" => array:4 [ 0 => array:3 [ "identificador" => "bib0005" "etiqueta" => "1" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Parametric vs non-parametric methods for data analysis" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "D.G. Altman" 1 => "J.M. Bland" ] ] ] ] ] "host" => array:1 [ 0 => array:2 [ "doi" => "10.1136/bmj.a3167" "Revista" => array:5 [ "tituloSerie" => "BMJ" "fecha" => "2009" "volumen" => "338" "paginaInicial" => "a3167" "link" => array:1 [ 0 => array:2 [ "url" => "https://www.ncbi.nlm.nih.gov/pubmed/19342403" "web" => "Medline" ] ] ] ] ] ] ] ] 1 => array:3 [ "identificador" => "bib0010" "etiqueta" => "2" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Log transformation: application and interpretation in biomedical research" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:4 [ 0 => "C. Feng" 1 => "H. Wang" 2 => "N. Lu" 3 => "X.M. Tu" ] ] ] ] ] "host" => array:1 [ 0 => array:2 [ "doi" => "10.1002/sim.5486" "Revista" => array:6 [ "tituloSerie" => "Stat Med" "fecha" => "2013" "volumen" => "32" "paginaInicial" => "230" "paginaFinal" => "239" "link" => array:1 [ 0 => array:2 [ "url" => "https://www.ncbi.nlm.nih.gov/pubmed/22806695" "web" => "Medline" ] ] ] ] ] ] ] ] 2 => array:3 [ "identificador" => "bib0015" "etiqueta" => "3" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Dealing with non-normal data" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "K.L. Sainani" ] ] ] ] ] "host" => array:1 [ 0 => array:2 [ "doi" => "10.1016/j.pmrj.2012.10.013" "Revista" => array:6 [ "tituloSerie" => "PM R" "fecha" => "2012" "volumen" => "4" "paginaInicial" => "1001" "paginaFinal" => "1005" "link" => array:1 [ 0 => array:2 [ "url" => "https://www.ncbi.nlm.nih.gov/pubmed/23245662" "web" => "Medline" ] ] ] ] ] ] ] ] 3 => array:3 [ "identificador" => "bib0020" "etiqueta" => "4" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Central limit theorem: the cornerstone of modern statistics" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "S.G. Kwak" 1 => "J.H. Kim" ] ] ] ] ] "host" => array:1 [ 0 => array:2 [ "doi" => "10.4097/kjae.2017.70.2.144" "Revista" => array:6 [ "tituloSerie" => "Korean J Anesthesiol" "fecha" => "2017" "volumen" => "70" "paginaInicial" => "144" "paginaFinal" => "156" "link" => array:1 [ 0 => array:2 [ "url" => "https://www.ncbi.nlm.nih.gov/pubmed/28367284" "web" => "Medline" ] ] ] ] ] ] ] ] ] ] ] ] ] "idiomaDefecto" => "en" "url" => "/23870206/0000015400000004/v1_202002201732/S2387020619305650/v1_202002201732/en/main.assets" "Apartado" => array:4 [ "identificador" => "44145" "tipo" => "SECCION" "en" => array:2 [ "titulo" => "Special article" "idiomaDefecto" => true ] "idiomaDefecto" => "en" ] "PDF" => "https://static.elsevier.es/multimedia/23870206/0000015400000004/v1_202002201732/S2387020619305650/v1_202002201732/en/main.pdf?idApp=UINPBA00004N&text.app=https://www.elsevier.es/" "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S2387020619305650?idApp=UINPBA00004N" ]
