Statistical Methods
Statistical methods are the mathematical tools and frameworks used to collect, analyze, interpret, and draw conclusions from data. They allow researchers to distinguish signal from noise, estimate effects, test hypotheses, and make predictions. This guide is for life scientists, bioinformaticians, and clinical researchers who need a practical, source bounded approach to selecting and applying statistical methods in their work. It covers core concepts, decision points, a step by step workflow, quality checks, common pitfalls, and the inherent limits of interpretation. For authoritative technical references, start with the NCBI Bookshelf which provides freely accessible biomedical texts and the EMBL-EBI Training resources that offer structured courses on biological data analysis.
Statistical thinking is essential at every stage of a research project. Without it, results may be misleading or irreproducible. This guide assumes you have basic familiarity with data types and experimental design. It does not replace a formal statistics course but provides a framework you can apply immediately. The Galaxy Training Network offers hands on workflows that illustrate many of the principles discussed here.
At a Glance
| Element | Key Points |
|---|---|
| Core Concepts | Descriptive vs. inferential statistics, population vs. sample, parameter vs. statistic, null and alternative hypotheses, p value and confidence intervals. |
| Decision Criteria | Data type (continuous, categorical, count), number of groups, paired vs. independent samples, normality assumptions, research question (difference, association, prediction). |
| Workflow Steps | 1. Define question and hypotheses. 2. Design study. 3. Collect and clean data. 4. Explore data. 5. Choose method. 6. Perform analysis. 7. Check assumptions. 8. Interpret results. |
| Quality Checks | Power analysis, multiple testing correction, assumption diagnostics (homogeneity of variance, normality), sensitivity analysis. |
| Common Mistakes | P hacking, ignoring non independence, over interpretation of p values, using parametric tests on non normal small samples without verification. |
| Limits of Interpretation | Causation requires experiment, p value is not effect size, statistical significance is not clinical relevance, external validity depends on sampling. |
Foundational Concepts
Before selecting a method, you must understand the two broad branches of statistics. Descriptive statistics summarize data (mean, median, standard deviation, frequency). Inferential statistics draw conclusions about a population from a sample (t tests, ANOVA, regression). Your research goal determines which branch is primary. A practical reference is the Bioconductor documentation, which provides many statistical packages designed for genomic data analysis and often includes vignettes that explain the underlying methods.
The choice of method hinges on the nature of your data. Continuous data (e.g., gene expression levels) can be analyzed with parametric tests if assumptions hold. Categorical data (e.g., presence/absence of a mutation) require chi square or logistic regression. Count data (e.g., number of sequencing reads) often need Poisson or negative binomial models. Public repositories like the NCBI Sequence Read Archive host many datasets that illustrate these data types. For example, a recent study on metabolic risk factors used a t test and ANOVA to compare continuous variables across gender groups 7.
Choosing a Statistical Method
Decision making is systematic. Use the following criteria in order:
1. What is your research question? If you are comparing groups, use tests like the t test (two groups) or ANOVA (more than two). If you are assessing association, use correlation (continuous) or chi square (categorical). If you are predicting an outcome, use regression. 2. What type is your outcome variable? Continuous outcomes often allow parametric tests, binary outcomes call for logistic regression. 3. How many groups or variables? For one sample, you compare to a known value. For two independent samples, use an independent t test, for paired data (before/after), use a paired t test. 4. Are the data normal? For small samples (n < 30 per group), check normality with a Shapiro Wilk test or Q Q plot. If violated, use nonparametric alternatives (Mann Whitney U, Wilcoxon signed rank, Kruskal Wallis). For large samples, the Central Limit Theorem often allows parametric methods even with non normal data.
A practical example comes from a study on storytelling based learning in medical education. The authors used a controlled pretest posttest design and applied a paired t test within groups and an independent t test between groups 6. Their choice was appropriate because the outcome (exam scores) was continuous and the data met normality assumptions. In contrast, a study on pulpitis related content on social media used chi square tests for categorical comparisons 9.
A Practical Workflow for Statistical Analysis
Follow these steps to implement a rigorous analysis.
Step 1. Define the scientific question and translate it into a statistical hypothesis. State the null hypothesis (no effect or no difference) and the alternative hypothesis. For example, "The mean expression of gene X is different between treatment and control."
Step 2. Design the study and determine sample size. Use a power analysis to ensure your study can detect a meaningful effect. The EMBL-EBI Training includes modules on experimental design for omics studies.
Step 3. Collect data and perform quality control. Check for missing values, outliers, and data entry errors. Tools from Galaxy Training Network can help automate these checks.
Step 4. Explore the data. Generate summary statistics and visualizations (histograms, boxplots, scatter plots). This step reveals patterns and potential violations of assumptions.
Step 5. Select the statistical method based on the decision criteria above. Document your choice.
Step 6. Run the analysis using appropriate software (R, Python, SPSS, or Galaxy). For specialized genomic analyses, rely on Bioconductor packages that implement state of the art methods with built in diagnostics.
Step 7. Check model assumptions. After fitting the model, examine residuals for normality, homoscedasticity, and independence. If assumptions are violated, consider transformations (log, square root) or switch to a robust / nonparametric method.
Step 8. Interpret results in context. Report effect sizes and confidence intervals alongside p values. Do not dichotomize results solely as significant or not.
Quality Checks and Validation
Every analysis should include pre registered checks to avoid false discoveries. Multiple testing correction is mandatory when you perform many comparisons (e.g., in differential expression analysis). Use Bonferroni, Benjamini Hochberg, or other false discovery rate controls. The Galaxy Training Network includes a tutorial on multiple testing correction for RNA seq data.
Sensitivity analysis tests how robust your conclusions are to variations in the method or data exclusion. For example, repeat the analysis after removing outliers or using a different transformation. Power analysis should be conducted before data collection, but post hoc power is often criticized. Instead, report the effect size and confidence interval to show the precision of your estimate.
Internal validation can be done by splitting data into training and test sets for predictive models. For clinical studies, external validation on an independent cohort is ideal. The systematic review on risk factors for tubo ovarian abscess provides a meta analytic example of how multiple studies are combined with careful quality assessment 10.
Common Mistakes
P hacking or data dredging. Performing many tests and only reporting significant results. Pre specify your analysis plan.
Ignoring non independence. When data are clustered (e.g., multiple measurements from the same patient), use mixed effects models. Using a standard t test inflates the Type I error rate.
Misinterpreting the p value. A p value is not the probability that the null hypothesis is true. It is the probability of seeing the observed data (or more extreme) assuming the null is true.
Using a parametric test on small, non normal data without checking. For sample sizes below 30, always test normality. In a study on sella turcica bridging, the authors used appropriate parametric tests after confirming normality 8.
Equating statistical significance with practical importance. A tiny effect can be significant with a large sample. Always examine the effect size.
Limits and Uncertainty
Statistical methods have inherent limitations. Causation cannot be inferred from observational studies regardless of the p value. Randomized controlled trials are needed. The storytelling study 6 used a quasi experimental design, so confounding may remain. Generalizability depends on your sampling frame. A study on dental anxiety using salivary opiorphin 11 may not apply to all populations. Model assumptions are usually approximations. Real data are messy, and violations may be tolerable if sample sizes are large and effects are strong. Always report limitations transparently.
Statistical methods are tools, not truth machines. They require domain knowledge, careful planning, and honest reporting. Use resources like the NCBI Bookshelf for deeper theory and Bioconductor for implementation.
Frequently Asked Questions
1. When should I use a nonparametric test instead of a parametric test? Use a nonparametric test when your data are ordinal, when the sample size is very small (e.g., n < 10 per group) and normality cannot be assumed, or when the data contain extreme outliers that cannot be transformed. Common examples are the Mann Whitney U test (independent groups) and the Wilcoxon signed rank test (paired data).
2. What is the difference between a confidence interval and a credible interval? A confidence interval is a frequentist concept: 95% of intervals from repeated sampling will contain the true parameter. A credible interval is Bayesian: there is a 95% probability that the parameter lies in that interval given the data. In practice, they often yield similar numbers, but the interpretation differs.
3. How do I choose between ANOVA and a t test when comparing multiple groups? ANOVA is appropriate when you compare three or more groups. Using multiple t tests inflates the family wise error rate. After a significant ANOVA, follow up with post hoc tests (e.g., Tukey HSD) to find which groups differ.
4. What should I do if my residuals are not normal after transformation? Consider robust regression methods that are less sensitive to normality violations. Alternatively, use generalized linear models (GLMs) with an appropriate distribution (e.g., Gamma for skewed positive data). Bootstrapping can also provide valid inference without normality.
References and Further Reading
- NCBI Bookshelf: Statistical Analysis and Data Management , Free textbooks covering fundamentals and advanced methods.
- EMBL-EBI Training: Statistics and Data Analysis , Online courses with practical exercises for life scientists.
- Galaxy Training Network: Statistics for Omics Data , Interactive workflows for RNA seq, ChIP seq, and more.
- Bioconductor: Statistics Resources , R packages and vignettes for genomic analysis.
- NCBI Sequence Read Archive , Public sequencing data for practicing analysis.
- Study on storytelling based learning and statistical methods used , Example of paired and independent t tests in education research.
- Metabolic risk factors study using ANOVA and t tests , Illustrates group comparisons with continuous data.
- Sella turcica bridging study with parametric tests , Demonstrates assumption checking.
- Pulpitis social media study using chi square tests , Categorical data analysis example.
- Risk factors for tubo ovarian abscess meta analysis , Systematic review and meta analytic methods.
- Salivary opiorphin as biomarker for dental anxiety , Example of biomarker validation with statistical inference.