the middle of a dataset. mode the mode is the value of a set of data that appears most often. comparison among mean, median and mode values = type example result mean( 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 11 ) / 9 4 median 2, 3, 3, 3, 3, 3, 4, 4, 11 3 mode 2, 3, 3, 3, 3, 3, 4, 4, 11 3 box plot box plot is a method for graphically depicting groups of numerical data. the maximum and minimum values are represented by the lines, and the interquartile range (iqr) represent 25–75% of the data. outliers may be plotted as circles. correlation coefficients although correlations between two different kinds of data could be inferred by graphs, such as scatter plot, it is necessary validate this though numerical information. for this reason, correlation coefficients are required. they provide a numerical value that reflects the strength of an association. pearson correlation coefficient scatter diagram that demonstrates the pearson correlation for different values of ρ.pearson correlation coefficient is a measure of association between two variables, x and y. this coefficient, usually represented by ρ (rho) for the population and r for the sample, assumes values between −1 and 1, where ρ = 1 represents a perfect positive correlation, ρ = −1 represents a perfect negative correlation, and ρ = 0 is no linear correlation. inferential statistics it is used to make inferences about an unknown population, by estimation and/or hypothesis testing. in other words, it is desirable to obtain parameters to describe the population of interest, but since the data is limited, it is necessary to make use of a representative sample in order to estimate them. with that, it is possible to test previously defined hypotheses and apply the conclusions to the entire population. the standard error of the mean is a measure of variability that is crucial to do inferences. hypothesis testing hypothesis testing is essential to make inferences about populations aiming to answer research questions, as settled in "research planning" section. authors defined four steps to be set: the hypothesis to be tested: as stated earlier, we have to work with the definition of a null hypothesis (h0), that is going to be tested, and an alternative hypothesis. but they must be defined before the experiment implementation. significance level and decision rule: a decision rule depends on the level of significance, or in other words, the acceptable error rate (α). it is easier to think that we define a critical value that determines the statistical significance when a test statistic is compared with it. so, α also has to be predefined before the experiment. experiment and statistical analysis: this is when the experiment is really implemented following the appropriate experimental design, data is collected and the more suitable statistical tests are evaluated. inference: is made when the null hypothesis is rejected or not rejected, based on the evidence that the comparison of p-values and α brings. it is pointed that the failure to reject h0 just means that there is not enough evidence to support its rejection, but not that this hypothesis is true. confidence intervals a confidence interval is a range of values that can contain the true real parameter value in given a certain level of confidence. the first step is to estimate the best-unbiased estimate of the population parameter. the upper value of the interval is obtained by the sum of this estimate with the multiplication between the standard error of the mean and the confidence level. the calculation of lower value is similar, but instead of a sum, a subtraction must be applied. statistical considerations power and statistical error when testing a hypothesis, there are two types of statistic errors possible: type i error and type ii error. the type i error or false positive is the incorrect rejection of a true null hypothesis and the type ii error or false negative is the failure to reject a false null hypothesis. the significance level denoted by α is the type i error rate and should be chosen before performing the test. the type ii error rate is denoted by β and statistical power of the test is 1 − β. p-value the p-value is the probability of obtaining results as extreme as or more extreme than those observed, assuming the null hypothesis (h0) is true. it is also called the calculated probability. it is common to confuse the p-value with the significance level (α), but, the α is a predefined threshold for calling significant results. if p is less than α, the null hypothesis (h0) is rejected. multiple testing in multiple tests of the same hypothesis, the probability of the occurrence of falses positives (familywise error rate) increase and some strategy are used to control this occurrence. this is commonly achieved by using a more stringent threshold to reject null hypotheses. the bonferroni correction defines an acceptable global significance level, denoted by α* and each test is individually compared with a value of α = α*/m. this ensures that the familywise error rate in all m tests, is less than or equal to α*. when m is large, the bonferroni correction may be overly conservative. an alternative to the bonferroni correction is to control the false discovery rate (fdr). the fdr controls the expected proportion of the rejected null hypotheses (the so-called discoveries) that are false (incorrect rejections). this procedure ensures that, for independent tests, the false discovery rate is at most q*. thus, the fdr is less conservative than the bonferroni correction and have more power, at the cost of more false positives. mis-specification and robustness checks the main hypothesis being tested (e.g., no association between treatments and outcomes) is often accompanied by other technical assumptions (e.g., about the form of the probability distribution of the outcomes) that are also part of the null hypothesis. when the technical assumptions are violated in practice, then the null may be frequently rejected even if the main hypothesis is true. such rejections are said to be due to model mis-specification. verifying whether the outcome of a statistical test does not change when the technical assumptions are slightly altered (so-called robustness checks) is the main way of combating mis-specification. model selection criteria model criteria selection will select or model that more approximate true model. the akaike's information criterion (aic) and the bayesian information criterion (bic) are examples of asymptotically efficient criteria. developments and big data recent developments have made a large impact on biostatistics. two important changes have been the ability to collect data on a high-throughput scale, and the ability to perform much more complex analysis using computational techniques. this comes from the development in areas as sequencing technologies, bioinformatics and machine learning (machine learning in bioinformatics). use in high-throughput data new biomedical technologies like microarrays, next-generation sequencers (for genomics) and mass spectrometry (for proteomics) generate enormous amounts of data, allowing many tests to be performed simultaneously. careful analysis with biostatistical methods is required to separate the signal from the noise. for example, a microarray could be used to measure many thousands of genes simultaneously, determining which of them have different expression in diseased cells compared to normal cells. however, only a fraction of genes will be differentially expressed. multicollinearity often occurs in high-throughput biostatistical settings. due to high intercorrelation between the predictors (such as gene expression levels), the information of one predictor might be contained in another one. it could be that only 5% of the predictors are responsible for 90% of the variability of the response. in such a case, one could apply the biostatistical technique of dimension reduction (for example via principal component analysis). classical statistical techniques like linear or logistic regression and linear discriminant analysis do not work well for high dimensional data (i.e. when the number of observations n is smaller than the number of features or predictors p: n < p). as a matter of fact, one can get quite high r2-values despite very low predictive power of the statistical model. these classical statistical techniques (esp. least squares linear regression) were developed for low dimensional data (i.e. where the number of observations n is much larger than the number of predictors p: n >> p). in cases of high dimensionality, one should always consider an independent validation test set and the corresponding residual sum of squares (rss) and r2 of the validation test set, not those of the training set. often, it is useful to pool information from multiple predictors together. for example, gene set enrichment analysis (gsea) considers the perturbation of whole (functionally related) gene sets rather than of single genes. these gene sets might be known biochemical pathways or otherwise functionally related genes. the advantage of this approach is that it is more robust: it is more likely that a single gene is found to be falsely perturbed than it is that a whole pathway is falsely perturbed. furthermore, one can integrate the accumulated knowledge about biochemical pathways (like the jak-stat signaling pathway) using this approach. bioinformatics advances in databases, data mining, and biological interpretation the development of biological databases enables storage and management of biological data with the possibility of ensuring access for users around the world. they are useful for researchers depositing data, retrieve information and files (raw or processed) originated from other experiments or indexing scientific articles, as pubmed. another possibility is search for the desired term (a gene, a protein, a disease, an organism, and so on) and check all results related to this search. there are databases dedicated to snps (dbsnp), the knowledge on genes characterization and their pathways (kegg) and the description of gene function classifying it by cellular component, molecular function and biological process (gene ontology). in addition to databases that contain specific molecular information, there are others that are ample in the sense that they store information about an organism or group of organisms. as an example of a database directed towards just one organism, but that contains much data about it, is the arabidopsis thaliana genetic and molecular database – tair. phytozome, in turn, stores the assemblies and annotation files of dozen of plant genomes, also containing visualization and analysis tools. moreover, there is an interconnection between some databases in the information exchange/sharing and a major initiative was the international nucleotide sequence database collaboration (insdc) which relates data from ddbj, embl-ebi, and ncbi. nowadays, increase in size and complexity of molecular datasets leads to use of powerful statistical methods provided by computer science algorithms which are developed by machine learning area. therefore, data mining and machine learning allow detection of patterns in data with a complex structure, as biological ones, by using methods of supervised and unsupervised learning, regression, detection of clusters and association rule mining, among others. to indicate some of them, self-organizing maps and k-means are examples of cluster algorithms; neural networks implementation and support vector machines models are examples of common machine learning algorithms. collaborative work among molecular biologists, bioinformaticians, statisticians and computer scientists is important to perform an experiment correctly, going from planning, passing through data generation and analysis, and ending with biological interpretation of the results. use of computationally intensive methods on the other hand, the advent of modern computer technology and relatively cheap computing resources have enabled computer-intensive biostatistical methods like bootstrapping and re-sampling methods. in recent times, random forests have gained popularity as a method for performing statistical classification. random forest techniques generate a panel of decision trees. decision trees have the advantage that you can draw them and interpret them (even with a basic understanding of mathematics and statistics). random forests have thus been used for clinical decision support systems. applications public health public health, including epidemiology, health services research, nutrition, environmental health and health care policy & management. in these medicine contents, it's important to consider the design and analysis of the clinical trials. as one example, there is the assessment of severity state of a patient with a prognosis of an outcome of a disease. with new technologies and genetics knowledge, biostatistics are now also used for systems medicine, which consists in a more personalized medicine. for this, is made an integration of data from different sources, including conventional patient data, clinico-pathological parameters, molecular and