Biostatistics without the mathematics. Part 2 - Inferential statistics

Abstract

The central maxim of inferential statistics is generalization from the sample to the population. Descriptive statistics describes a sample data set (which is an organized collection of data on a common theme), depicting its central tendency and dispersion, while inferential statistics focuses on drawing inferences regarding the population by analyzing the sample data. To do this it resorts largely to the hypothesis testing approach whose goal is to reject the null hypothesis. The result is usually returned as a p value that denotes the maximum probability of getting the observed result assuming the null hypothesis to be true. A large number of hypothesis tests are available and the one to be applied depends upon the research question, the nature of the variables of interest and the number of groups that are to be compared. The standard Student’s t-test is used for comparing the means of two independent or paired data sets that are normally distributed. One-way analysis of variance (ANOVA) and its counterpart in repeated measures extends the comparison of means to more than two populations. There are non-parametric counterparts of each of these tests that compare medians of data sets that are not normally distributed. Categorical variables can be compared between independent groups by chi-square test or Fisher’s exact test, while McNemar’s chi-square test and Cochran’s Q test can be employed for comparing paired proportions. Strength of association between two numerical variables can be quantified by a correlation coefficient, such as Pearson’s product moment coefficient of correlation r or Spearman’s rank-correlation coefficient r, and Kendall’s tau. The relative risk and odds ratio are used to quantify association between two binary categorical variables. The intraclass correlation coefficient can be calculated as a measure of the agreement between related sets of numerical data. The Bland-Altman plot is a graphical method for doing the same. Cohen’s kappa statistic measures agreement between categorical variables. With the increasing availability and user-friendly nature of statistical software, the drudgery associated with statistical computation is now gone, leaving the researcher free to concentrate on the correct application of techniques rather than worry about the calculation. Key words: hypothesis testing, p value, type I error, type II error, parametric tests, non-parametric tests