Choosing the right statistical test: A guide for data analysis

Introduction Statistical tests are vital in data analysis, allowing researchers and analysts to derive significant insights and make informed decisions. However, selecting the appropriate statistical test can be overwhelming due to data type, research objectives, and assumptions. Choosing an incorrect test can produce inaccurate outcomes and compromise the credibility of one's research. This article offers a comprehensive manual on determining the suitable statistical test for different scenarios, assisting researchers in navigating the complexities of data analysis. The steps involved in selecting the correct statistical test are as follows: Step 1: Understanding the research question: Having a clear-cut idea about what we want to achieve from data analysis is essential. The following questions need to be answered: a. Are you comparing two groups? b. Are you testing for the relationship between variables? c. Are you identifying significance. Answering these questions will help you focus on the specific tests relevant to your analysis. Step 2: Identify the type of data: The statistical test is determined based on the level of measurement of the variables. a. Is it nominal (categorical)? b. Is it ordinal (ranked)? c. Is it interval (numerical with equal interval)? d. Is it ratio (numerical with true zero)? Statistical tests vary according to the type of data. For example, parametric tests such as t tests and Analysis of Variance (ANOVA) require continuous data, while non-parametric tests like chi-square and Mann–Whitney can be used with categorical or ordinal data. Understanding the level of measurement helps in selecting the proper statistical methods for your analysis. In continuous data (parametric), regression examines the relationship between a dependent variable and one or more independent variables. Linear regression predicts a numerical outcome, whereas logistic regression predicts a categorical outcome. Spearman's rank correlation measures the strength and direction when one variable consistently increases or decreases as another variable but not at a constant rate. In contrast, Pearson's correlation is used when variables have a linear relationship. Step 3: Assess how the data are distributed: a. Check for normal distribution of data. If the data are normally distributed, then parametric tests are used. b. Consider non-parametric tests if data are not normally distributed. Parametric and non-parametric distributions: Before exploring specific examinations, it is essential to understand the difference between parametric and non-parametric tests. Parametric tests assume that data adhere to a specific distribution, typically a normal distribution. In contrast, non-parametric tests are not dependent on any distribution and make minimal assumptions about the data. Employ parametric tests when the assumptions are satisfied and opt for non-parametric tests when the data violate these assumptions. Kolmogorov–Smirnov (KS) test: A robust statistical instrument, the KS test, compares distributions. The methodology includes both one-sample and two-sample tests. The former assesses whether a given sample belongs to a reference distribution, while the latter compares two samples to ascertain whether they are drawn from the same population. The fact is that the KS test is non-parametric, masking it suitable for various types of data without assuming any specific distribution structures. It ensures accurate P values even with small sample sizes. The KS test generates a statistic based on the largest difference between two cumulative distribution functions. This primary purpose of the test is to determine whether distributions differ, without providing insights into the reasons behind these differences. It is sensitive to outliers, which may affect the results. Despite this limitation, the test serves for various purposes, such as evaluating treatment efficacy in studies, checking model predictions, identifying outliers in data streams, and conducting goodness-of-fit tests. Shapiro–Wilk test: This test is particularly useful for small to moderate sample sizes (5–5000) in determining whether the sample is normally distributed. Step 4: Consider the number of groups, types of samples, and size of groups: Statistical tests vary as per groups and samples. a. Comparison between two or more groups? b. Data from independent or paired samples? Suppose two independent groups have normal distribution, use the t test. For non-parametric data, use the Mann–Whitney U test. In paired samples, use the paired t test for parametric data and the Wilcoxon signed rank test for non-parametric data. When comparing more than two independent groups with a normal distribution, use ANOVA (the statistical test). For non-normal distributions, use the Kruskal–Wallis test. In paired samples with normally distributed data, use repeated measures ANOVA. For non-parametric data, use the Friedman test Table 1.Table 1:: Summary of standard statistical testsStep 5: Choose the appropriate statistical test: A well-defined research question helps determine the appropriate statistical tests, considering data type, distribution, and the number of groups or samples involved. Additional factors that need to be considered while selecting statistical tests are as follows: a. Sample size: Ensure that your sample size is adequate for achieving statistical power, which is the ability to detect actual effects. b. Post-hoc tests: If the analysis shows significant differences, post hoc tests must be conducted to determine which groups exhibit statistically significant variations. c. Effect size: It is essential to calculate effect sizes to evaluate the magnitude of observed differences rather than solely relying on P values. Other commonly used statistical tests are percentage, mean, median, mode, quartiles, and receiver operating (ROC) characteristic curves. Percentage: Express a part of a whole as a fraction of 100. It is simple to use but limited to a particular context. Mean: Represents the average of data and is easy to calculate. However, it is sensitive to outliers and inappropriate for skewed data. Median: Represents the middle value of orderly arranged data and divides the data into two equal portions. It is easy to understand and compute, making it suitable for skewed data. However, since it is not based on all observations, it may not be a true representative. Mode: Represents the most frequently observations. It is simple but does not represent all the data, and multiple responses are possible. Quartiles: Divide data into four equal parts, identify outliers, and help identify data trends, but interpretation can be challenging. ROC curve: Used to evaluate the efficacy of diagnostic tests or develop models using machine learning. The statistical test used is the ROC curve. Conclusion Choosing the right statistical test is crucial for meaningful data analysis. Researchers can make informed decisions regarding the appropriate statistical test to perform by considering the nature of the data, the research question, the assumptions, and the study objectives. It is essential to assess the distribution of data, decide between parametric and non-parametric tests, and consider the issues related to sample size. The correct implementation of statistical tests enables researchers to discover valuable insights, validate hypotheses, and contribute significantly to advancing knowledge in their respective fields. Financial support and sponsorship Nil. Conflicts of interest There are no conflicts of interest.