Statistical Analysis Methods
Statistical analysis methods are systematic procedures for collecting, summarizing, interpreting, and drawing conclusions from data. This guide explains the core concepts, decision points, and practical steps involved in selecting and applying statistical methods, with an emphasis on life sciences and biomedical research. It is written for researchers, data analysts, and students who need a clear, source bounded framework to design analyses and avoid common pitfalls. The NLM Bookshelf provides an authoritative introduction to foundational statistical principles NCBI Bookshelf. For those analyzing biological data, the EMBL EBI training materials offer practical guidance on method selection and implementation EMBL-EBI Training.
At a Glance
The following table summarizes common statistical analysis methods, their typical use cases, and key assumptions. This overview is a starting point, deeper exploration of each method is encouraged using the sources cited throughout this guide.
| Method | Typical Use Case | Key Assumptions |
|---|---|---|
| t test (independent) | Compare means between two groups | Normality, equal variance |
| Paired t test | Compare means within matched pairs | Normality of differences |
| ANOVA (one way) | Compare means among three or more groups | Normality, equal variance, independence |
| Linear regression | Model relationship between continuous predictor and outcome | Linearity, normality of residuals, homoscedasticity |
| Logistic regression | Model binary outcome (e.g., disease vs. no disease) | Linearity of log odds, independence |
| Nonparametric tests (e.g., Mann Whitney U, Kruskal Wallis) | Compare groups when normality is violated | Independent samples, ordinal or continuous data |
| Survival analysis (Kaplan Meier, Cox regression) | Analyze time to event data, accounting for censoring | Proportional hazards (Cox) |
| Multiple testing correction (e.g., Bonferroni, FDR) | Adjust p values when many hypotheses are tested | Independence or positive dependence |
Decision Criteria for Selecting a Statistical Method
Choosing the correct statistical method depends on three main factors: the research question, the type of data, and the underlying assumptions.
First, define the research question. Is the goal to compare groups, test an association, predict an outcome, or analyze time to an event? For example, a study comparing glucose lowering efficacy of two insulin formulations would use a t test or ANOVA for continuous outcomes, as seen in the comparative effectiveness study of Glargine 300 versus Degludec 100 PubMed. A study identifying predictors of frailty might use logistic regression or survival analysis depending on whether the outcome is binary or time to event PubMed.
Second, classify your data. Continuous variables (e.g., gene expression levels, blood pressure) often allow parametric methods if assumptions hold. Categorical variables (e.g., treatment group, genotype) require chi square tests, logistic regression, or nonparametric alternatives. Ordinal data (e.g., disease severity scores) may be best analyzed with nonparametric tests or ordinal regression.
Third, check assumptions. Parametric tests assume normally distributed residuals, equal variances, and independence. When these are violated, consider transformations or nonparametric methods. The Galaxy Training Network provides workflows that include diagnostic plotting to verify assumptions for RNA seq and other omics data Galaxy Training Network.
A practical decision tree is available through the Bioconductor project documentation, which guides users from raw sequencing data to appropriate statistical modeling Bioconductor.
Practical Workflow for Implementing a Statistical Analysis
The following workflow integrates steps from hypothesis formulation through interpretation. Each step should be documented to ensure reproducibility.
Formulate a clear hypothesis. Specify the null hypothesis (e.g., no difference in mean expression between groups) and the alternative hypothesis. Pre register your analysis plan when possible.
Design the study and collect data. Determine sample size using power analysis. Consider randomization, blinding, and blocking factors to reduce bias. The NCBI Sequence Read Archive exemplifies how raw data should be deposited for public verification NCBI Sequence Read Archive.
Explore and clean the data. Compute summary statistics, visualize distributions with histograms and boxplots, and identify outliers or missing values. Dedicate time to data cleaning because errors here propagate through all subsequent steps.
Select the statistical method. Use the decision criteria above. For a typical genomic comparison, you might choose a negative binomial model (e.g., DESeq2) or a linear model with empirical Bayes moderation (e.g., limma). Both are implemented in Bioconductor packages Bioconductor.
Check assumptions. Generate Q Q plots, residual vs. fitted plots, and test for normality (Shapiro Wilk) and homogeneity of variance (Levene's test). If assumptions are not met, apply a transformation (log, square root) or switch to a nonparametric method.
Run the analysis. Use software such as R, Python, or specialized tools. For bioinformatics, the Galaxy platform offers reproducible workflow environments with built in statistical modules Galaxy Training Network. Ensure that all parameters are recorded.
Correct for multiple comparisons. If testing many variables (e.g., thousands of genes), apply corrections like Benjamini Hochberg false discovery rate (FDR) or Bonferroni. This step is critical to control Type I error inflation.
Interpret results. Report effect sizes, confidence intervals, and p values. Avoid dichotomizing results solely by p < 0.05. Consider the practical significance of findings.
Validate and reproduce. Cross validate predictive models, or use an independent dataset to confirm results. The EMBL EBI training materials emphasize the importance of external validation in biomarker studies.
Common Mistakes in Statistical Analysis
Even experienced analysts can fall into traps. Here are frequent errors and how to avoid them.
P hacking or data dredging. Running many tests without correction or selectively reporting significant results inflates false positives. Pre specify your primary analysis and use multiple testing adjustments.
Ignoring assumptions. Applying a parametric test to highly skewed or heteroscedastic data can lead to invalid conclusions. Always check residual plots and consider transformations or robust methods.
Misinterpreting p values. A p value is not the probability that the null hypothesis is true. It does not measure the size of an effect or the practical importance of a result. Pair p values with effect sizes and confidence intervals.
Overlooking confounding variables. In observational studies, failing to adjust for confounders produces biased estimates. Use multivariable regression or stratification to address confounding, as demonstrated in the analysis of frailty predictors PubMed.
Ignoring correlation or clustering. Observations from the same subject, family, or batch are not independent. Use mixed effects models or cluster robust standard errors to account for dependencies.
Using the wrong error term in ANOVA. When repeated measures or nested designs exist, using the overall error instead of the appropriate interaction term inflates Type I error.
Limits and Uncertainty in Statistical Interpretation
No statistical method yields absolute certainty. Acknowledging the boundaries of interpretation is vital for honest science.
Statistical significance does not equal scientific importance. A tiny effect can achieve a very low p value with a large sample size. Conversely, a large effect may fail to reach significance in a small study. Always examine the magnitude of the effect and its confidence interval.
Causality cannot be inferred from association alone, regardless of p values. Randomized controlled trials are the gold standard for causal claims. Observational studies can only identify associations, and unmeasured confounding is always a possibility. The comparative insulin study used a retrospective design, so authors carefully noted residual confounding as a limitation PubMed.
Generalizability depends on the study population. Results from a sample may not extend to other groups. Describe the sample characteristics and discuss external validity.
Reproducibility is threatened by analytical flexibility. Different researchers analyzing the same data with different methods often reach different conclusions. Preregistration, code sharing, and sensitivity analyses help mitigate this problem.
Missing data can introduce bias. Modern methods like multiple imputation are preferable to complete case analysis if the missing at random assumption holds.
Frequently Asked Questions
Q1: How do I choose between a parametric and nonparametric test?
Parametric tests are more powerful when their assumptions (normality, equal variance) are met. If the data are clearly non normal or the sample size is very small, nonparametric tests provide a safer alternative. Use a normality test (e.g., Shapiro Wilk) and a variance test (e.g., Levene) to guide your choice. The Galaxy Training Network includes tutorials for assessing these assumptions in high throughput data.
Q2: What is the difference between multiple testing correction methods?
Bonferroni correction controls the family wise error rate (the chance of at least one false positive) and is very conservative. False discovery rate (FDR) correction controls the expected proportion of false positives among rejected hypotheses and is more powerful for genomic studies where many true signals exist. Choose Bonferroni when false positives are extremely costly, choose FDR otherwise.
Q3: When should I use logistic regression instead of a chi square test?
Logistic regression handles binary outcomes while allowing adjustment for multiple covariates. A chi square test simply tests independence between two categorical variables and does not adjust for confounders. Use logistic regression when you need to control for age, sex, or other variables.
Q4: How do I handle outliers in my data?
First, determine if the outlier is due to a measurement error or a true biological extreme. If an error, correct or remove it with documentation. If a genuine value, consider using robust statistical methods (e.g., trimmed means, robust regression) or transforming the data. Do not remove outliers arbitrarily as this can bias results.
References and Further Reading
- NCBI Bookshelf. Statistical analysis methods introduction. https://www.ncbi.nlm.nih.gov/books/
- EMBL EBI Training. Statistical analysis in bioinformatics. https://www.ebi.ac.uk/training/
- Galaxy Training Network. Workflows for omics data analysis including statistics. https://training.galaxyproject.org/
- Bioconductor. Software and documentation for statistical analysis of genomic data. https://bioconductor.org/
- NCBI Sequence Read Archive. Public repository for raw sequencing data. https://www.ncbi.nlm.nih.gov/sra
- Comparative effectiveness of Glargine 300 U/mL vs. Degludec 100 U/mL. Nutr Metab Cardiovasc Dis. 2022. https://pubmed.ncbi.nlm.nih.gov/35961826/
- Biological and Neuroimaging Markers as Predictors of Frailty. J Gerontol A Biol Sci Med Sci. 2021. https://pubmed.ncbi.nlm.nih.gov/33246338/