Statistical Analysis
Statistical analysis is the application of mathematical frameworks to quantify uncertainty, test hypotheses, and draw inferences from data. This guide is for life scientists who need a practical, source bounded approach to selecting and executing analyses correctly, from experimental design through reporting. The NCBI Bookshelf provides thorough reference material on foundational statistical concepts used in biomedical research. Use this guide to navigate core decisions, avoid common traps, and interpret results with appropriate caution. For hands on training in biological data analysis, the EMBL EBI Training resources offer structured modules that supplement the principles covered here.
At a Glance
| Core Concept | Key Decision | Practical Note |
|---|---|---|
| Hypothesis testing | Choose parametric or nonparametric test | Parametric tests assume normality, nonparametric tests are safer with small or skewed samples |
| Effect size estimation | Report confidence intervals alongside p values | A p value alone does not convey magnitude or practical importance |
| Multiple testing correction | Apply Bonferroni, FDR, or similar methods | Ignoring corrections inflates false positive rates in high throughput data |
| Model selection | Linear vs generalized linear vs mixed effects | Match model type to outcome distribution and correlation structure |
| Power analysis | Compute required sample size a priori | Underpowered studies waste resources and miss real effects |
Decision Criteria for Statistical Tests
Selecting the correct test depends on the data type, the number of groups, whether observations are paired, and the distributional assumptions that can be satisfied. The Galaxy Training Network offers automated workflows that help implement these decisions for common bioinformatics scenarios.
Data type determines the family of tests. Continuous outcomes often allow t tests or ANOVA under normality, or Mann Whitney U or Kruskal Wallis otherwise. Categorical outcomes use chi square or Fisher exact tests. Ordinal data benefit from nonparametric methods.
Number of groups guides whether to use a two sample test (t test, Mann Whitney) or a multi group test (ANOVA, Kruskal Wallis). Post hoc comparisons require adjustment for multiple testing to control family wise error.
Paired or independent matters. Pre post designs, matched subjects, or repeated measures demand paired tests (paired t test, Wilcoxon signed rank) or mixed models that account for within subject correlation.
Assumption checks are nonnegotiable. Test normality with Shapiro Wilk or Q Q plots. Check homoscedasticity with Levene test or variance plots. If assumptions fail, switch to a robust alternative or apply a transformation. The Bioconductor project provides packages for diagnostic plotting and assumption testing in genomic data.
A Practical Workflow for Statistical Analysis
Follow this sequence to reduce errors and produce interpretable results.
1. Define the Research Question and Hypothesis
State the primary outcome and the null hypothesis clearly. For example, in comparing two insulins, the question might be whether glargine 300 U/mL shows noninferior glycemic control compared with degludec 100 U/mL, as in the study by Nutr Metab Cardiovasc Dis. This study used a noninferiority design with predefined margins.
2. Plan the Analysis Before Data Collection
Specify the primary test, the significance threshold (usually 0.05), and whether tests will be one or two sided. Perform a power analysis to determine sample size. Use pilot data or published effect sizes. Repositories like the NCBI Sequence Read Archive can supply relevant summary statistics for power calculations in sequencing studies.
3. Perform Exploratory Data Analysis (EDA)
Summarize data with descriptive statistics and visualizations. Check for missing values, outliers, and errors. Plot distributions to judge symmetry and variance homogeneity. EDA guides later test selection and may reveal unexpected patterns.
4. Verify Assumptions
Apply normality and variance tests as described in the Decision Criteria section. If data deviate substantially, consider a nonparametric alternative or a data transformation (e.g., log for count data). For linear models, examine residual plots.
5. Execute the Primary Analysis
Run the chosen test. For example, an independent t test for two groups, or one way ANOVA for more than two groups. Always include effect size measures (Cohen d, eta squared) and confidence intervals. In high throughput settings, use specialized software such as Bioconductor packages that handle thousands of simultaneous tests with appropriate corrections.
6. Validate with Sensitivity Analyses
Repeat the analysis using a different assumption (e.g., nonparametric version) or after removing influential outliers. Consistent results increase confidence. For multivariable models, check for collinearity and interaction terms.
7. Report Transparently
State the test used, the test statistic, degrees of freedom, p value, and effect size. Provide confidence intervals. Describe any data transformations or outlier handling. A secondary analysis of the MAPT study J Gerontol A Biol Sci Med Sci illustrates how biological and neuroimaging markers were analyzed using Cox regression with frailty as the outcome, reporting hazard ratios, confidence intervals, and p values for each predictor.
Common Mistakes in Statistical Analysis
P Hacking: Running multiple tests and only reporting significant results. Preregister your analysis plan. Use a single primary outcome. Report all tested comparisons.
Ignoring Assumptions: Using a t test on severely skewed data without checking normality. Refer to the NCBI Bookshelf for guidance on assumption validation.
Overlooking Multiple Comparisons: Applying many tests without adjustment. Use Bonferroni for a small number of planned comparisons or false discovery rate (FDR) for large scale omics data.
Misinterpreting Non Significance: A p value above 0.05 does not prove the null hypothesis. It only indicates insufficient evidence. Consider equivalence tests or bayesian approaches to confirm absence of effect.
Confusing Correlation with Causation: Observational data cannot establish cause without careful design. Use causal inference methods if causal claims are intended.
Data Dredging: Searching for patterns without a hypothesis leads to spurious findings. Use separate discovery and validation datasets, or apply cross validation.
Limits of Statistical Interpretation
Statistical results always carry uncertainty. A p value is not the probability that the null hypothesis is true, it is the probability of observing data as extreme if the null were true. Confidence intervals indicate the precision of the estimate but do not guarantee that the true effect lies within the interval 95% of the time for a single study (the long run frequency interpretation applies over repeated sampling).
Reproducibility is limited by analytical flexibility. Using different preprocessing steps or test choices can yield different conclusions. The EMBL EBI Training emphasizes the importance of reproducible pipelines and containerized environments to mitigate this.
Generalizability depends on the study population. Results from a highly selected cohort may not apply to broader groups. Always discuss external validity.
Causal inference requires strong assumptions: no unmeasured confounders, correct model specification, and appropriate temporal ordering. Statistical association alone does not imply causation.
Effect sizes should be interpreted in context. A small effect with a very large sample may be statistically significant but not practically important. Conversely, a large effect in a small study may be unreliable due to wide confidence intervals.
Frequently Asked Questions
What is the difference between a t test and ANOVA? A t test compares means between two groups. ANOVA compares means among two or more groups and uses an F test to assess overall group differences. Pairwise post hoc tests follow a significant ANOVA to identify which groups differ. The Galaxy Training Network provides tutorials for choosing between these tests.
When should I use a nonparametric test instead of a parametric test? Use nonparametric tests when data are ordinal, strongly skewed, or violate normality even after transformation, or when sample sizes are very small. They do not assume a specific distribution but have lower power when parametric assumptions are met.
How do I correct for multiple comparisons? The simplest method is Bonferroni correction: divide the significance threshold by the number of tests. However, it can be too conservative. For many tests, such as in gene expression studies, use false discovery rate (FDR) control via the Benjamini Hochberg procedure. The Bioconductor package multtest implements these corrections.
What is power analysis and why is it important? Power analysis calculates the sample size needed to detect an effect of a given size with a specified probability (typically 80%). It prevents underpowered studies that cannot detect meaningful differences and avoids wasting resources on too large samples. Power depends on effect size, alpha, sample size, and study design.
References and Further Reading
- NCBI Bookshelf: Statistical Analysis Overview , Comprehensive biomedical reference on statistical methods.
- EMBL EBI Training: Statistical Analysis for Bioinformatics , Practical courses on data analysis and statistics.
- Galaxy Training Network: Statistics and Machine Learning , Workflows for statistical tests in genomics.
- Bioconductor: Statistical Software for Genomics , Open source packages for high throughput data analysis.
- NCBI Sequence Read Archive , Repository of sequencing data for power calculations and benchmarking.
- Comparative effectiveness of Glargine 300 U/mL vs. Degludec 100 U/mL , Example of a noninferiority trial design and analysis.
- Biological and Neuroimaging Markers as Predictors of 5 Year Incident Frailty , Secondary analysis showing Cox regression and confidence interval reporting.