Statistical inference and hypothesis testing are crucial tools in epidemiology and biostatistics. These methods help researchers draw conclusions about populations from sample data, enabling evidence-based decisions in public health.
Hypothesis testing involves formulating null and alternative hypotheses, then using statistical tests to evaluate them. Understanding p-values, significance levels, and confidence intervals is key to interpreting results and assessing their practical importance in public health contexts.
Statistical Inference in Public Health
Fundamentals of Statistical Inference
- Statistical inference draws conclusions about populations based on sample data, enabling evidence-based decisions in public health
- Central limit theorem states sampling distribution of the mean approaches normal distribution as sample size increases (regardless of population distribution)
- Sampling methods affect representativeness and generalizability of statistical inferences
- Simple random sampling (every individual has equal chance of selection)
- Stratified sampling (population divided into subgroups before sampling)
- Cluster sampling (groups of individuals selected rather than individuals)
- Type I and Type II errors pose risks in statistical inference
- Type I error rejects a true null hypothesis (false positive)
- Type II error fails to reject a false null hypothesis (false negative)
- Statistical power measures probability of correctly rejecting a false null hypothesis
- Influenced by sample size, effect size, and significance level
- Higher power increases likelihood of detecting true effects
Advanced Concepts in Statistical Inference
- Bayesian inference incorporates prior knowledge and updates probabilities with new data
- Contrasts with frequentist approaches that rely solely on observed data
- Useful in situations with limited data or strong prior beliefs
- Sampling distribution represents all possible sample statistics from repeated sampling
- Forms basis for inferential statistics and hypothesis testing
- Shape affected by sample size and population parameters
- Confidence intervals provide range of plausible values for population parameters
- 95% confidence interval most commonly reported in public health research
- Wider intervals indicate less precise estimates
- Effect sizes quantify magnitude of differences or relationships between variables
- Cohen's d for continuous outcomes (small: 0.2, medium: 0.5, large: 0.8)
- Odds ratios for categorical outcomes (1 indicates no effect)
Hypothesis Testing with Statistical Methods
Formulating and Testing Hypotheses
- Null and alternative hypotheses form foundation of hypothesis testing
- Null hypothesis typically represents no effect or difference
- Alternative hypothesis represents researcher's expectation or claim
- Parametric tests assume normally distributed data and are used for continuous outcomes
- t-tests compare means between two groups (independent or paired)
- ANOVA compares means across multiple groups
- Non-parametric tests used when data violate assumptions of parametric tests or for ordinal outcomes
- Mann-Whitney U test (alternative to independent t-test)
- Kruskal-Wallis test (alternative to one-way ANOVA)
- Chi-square tests employed for categorical data to assess associations between variables
- Used in epidemiological studies to compare observed and expected frequencies
- Assumptions include independence of observations and adequate sample size
Advanced Statistical Methods
- Regression analyses model relationships between variables and predict outcomes
- Linear regression for continuous dependent variables
- Logistic regression for binary dependent variables
- Multiple regression incorporates multiple independent variables
- Multiple comparison procedures adjust for increased Type I error risk in multiple hypothesis tests
- Bonferroni correction divides significance level by number of tests
- False Discovery Rate controls proportion of false positives among rejected hypotheses
- Meta-analysis combines results from multiple studies to increase statistical power
- Provides overall effect size estimate across populations
- Assesses heterogeneity between studies
- Bootstrapping resamples data to estimate sampling distribution and calculate confidence intervals
- Useful when theoretical distributions are unknown or assumptions are violated
- Provides robust estimates of standard errors and confidence intervals
Interpreting Statistical Significance
Understanding P-values and Significance Levels
- P-values represent probability of obtaining results as extreme as observed, assuming null hypothesis is true
- Smaller p-values indicate stronger evidence against null hypothesis
- Do not directly measure magnitude of effect or practical importance
- Significance level (ฮฑ) sets threshold for rejecting null hypothesis
- Commonly set at 0.05 in public health research
- Represents acceptable Type I error rate
- Confidence intervals provide range of plausible values for population parameters
- 95% confidence interval interpreted as range that would contain true parameter in 95% of repeated samples
- Narrower intervals indicate more precise estimates
- Statistical versus practical significance distinguishes between chance results and meaningful implications
- Statistically significant results may not always be practically important
- Consider effect sizes and context when interpreting results
Advanced Interpretation Techniques
- Effect sizes quantify magnitude of differences or relationships between variables
- Cohen's d for continuous outcomes (small: 0.2, medium: 0.5, large: 0.8)
- Relative risk and odds ratios for categorical outcomes
- Power analysis determines sample size needed to detect meaningful effects
- Considers desired power, effect size, and significance level
- Helps researchers plan studies with adequate statistical power
- Sensitivity and specificity assess performance of diagnostic tests
- Sensitivity measures true positive rate
- Specificity measures true negative rate
- Receiver Operating Characteristic (ROC) curves evaluate trade-off between sensitivity and specificity
- Area under curve (AUC) indicates overall test performance
- Perfect test has AUC of 1, random guessing has AUC of 0.5
Evaluating Statistical Inference in Research
Critical Appraisal of Statistical Methods
- Publication bias skews available evidence in public health literature
- Statistically significant results more likely to be published
- Can lead to overestimation of effect sizes in meta-analyses
- P-hacking and data dredging compromise research integrity
- Manipulating data or analyses to achieve statistically significant results
- Can lead to false positive findings and irreproducible results
- Reproducibility crisis highlights importance of transparent reporting
- Detailed description of statistical methods and results crucial
- Pre-registration of study protocols helps prevent selective reporting
- Sensitivity analyses assess robustness of statistical inferences
- Vary assumptions or data to test stability of results
- Crucial for policy recommendations and decision-making
Ethical Considerations and Advanced Techniques
- Ethical considerations in statistical inference include potential harm from errors
- Type I errors may lead to unnecessary interventions or resource allocation
- Type II errors may result in missed opportunities for effective public health measures
- Bayesian decision theory incorporates prior knowledge and uncertainty into decision-making
- Combines prior beliefs with new data to update probabilities
- Useful in situations with limited data or strong prior information
- Propensity score matching reduces bias in observational studies
- Balances covariates between treatment and control groups
- Improves causal inference in non-randomized studies
- Multilevel modeling accounts for hierarchical structure in data
- Analyzes nested data (individuals within communities within countries)
- Allows for estimation of effects at different levels of analysis