What Is Statistics in Medical Research?
Medical research produces data that are inherently variable. Two patients with the same diagnosis and the same treatment rarely have identical outcomes. Measured blood pressure fluctuates within the same person across minutes. Observed differences between a treatment group and a control group might reflect a genuine drug effect, or they might simply reflect the ordinary noise of sampling. Statistics provides the formal machinery to distinguish signal from noise.
That machinery covers several tasks: summarising what was measured (descriptive statistics), drawing inferences about populations from samples (inferential statistics), quantifying associations between exposures and outcomes, evaluating the accuracy of tests and predictions, and communicating uncertainty through measures such as confidence intervals.
Statistical evidence must always be weighed alongside study design quality, measurement accuracy, biological plausibility, effect magnitude, and clinical context. A statistically significant result does not by itself prove that a treatment works, that a causal pathway exists, or that the effect is large enough to matter to patients.
Statistics in Medical Research at a Glance
| Research question | Statistical role | Typical tools |
|---|---|---|
| What happened in this sample? | Descriptive statistics | Mean, median, SD, proportions |
| Is there evidence of a difference? | Hypothesis testing | t-test, chi-square, ANOVA |
| How large is the difference? | Effect size | Mean difference, Cohen's d, RR, OR |
| How precise is our estimate? | Uncertainty quantification | Confidence intervals, SE |
| Are two variables associated? | Correlation | Pearson r, Spearman ρ |
| What predicts an outcome? | Regression | Linear, logistic, Cox regression |
| How well does a test detect disease? | Diagnostic accuracy | Sensitivity, specificity, PPV, NPV |
| What is the risk of an event? | Risk analysis | Risk ratio, odds ratio, risk difference |
| How long until an event occurs? | Time-to-event analysis | Kaplan-Meier, Cox model, HR |
| How do multiple treatment arms compare? | Multi-group comparison | ANOVA, Kruskal-Wallis |
Why Statistics Is Important in Medical Research
Medical decisions affect lives, so the standard of evidence they rest on must be high. Statistics provides the formal basis for that standard. Here is what it makes possible.
Describing patient populations
Before any comparison or test, researchers need to characterise their study participants. Age distributions, baseline blood pressure readings, body mass index values, cholesterol levels, and disease prevalence all need to be summarised in ways that other clinicians can understand and reproduce. Descriptive statistics provides the vocabulary: mean and median for the centre, standard deviation and IQR for spread, and proportions and rates for categorical outcomes.
Comparing treatment and control groups
The central question in a randomised controlled trial is whether observed differences between treatment and control arms exceed what sampling variability alone could produce. Without statistical testing, there is no principled answer to that question. Depending on the outcome variable and study design, researchers might apply a two-sample t-test, a chi-square test, or a survival model.
Quantifying uncertainty
Every sample estimate — whether a mean blood pressure reduction or an odds ratio for disease risk — carries uncertainty because it comes from a sample, not the full population. The confidence interval translates that uncertainty into a range of plausible values, giving readers a more complete picture than a point estimate alone.
Testing research hypotheses
Researchers begin with a null hypothesis — usually that there is no effect or no difference — and ask whether the data are inconsistent with it. Hypothesis testing formalises that question through a test statistic and a p-value, producing a decision that can be pre-specified and reported transparently.
Evaluating diagnostic tests
Sensitivity and specificity measure how reliably a test identifies patients who do and do not have a condition. Positive and negative predictive values tell clinicians what a positive or negative result means for an individual patient given the prevalence in their setting. Statistics supplies all four metrics and the tools to compare tests against each other.
Supporting evidence-based medicine
Systematic reviews and meta-analyses pool results across studies to produce more precise estimates of treatment effects than any single trial can provide. Forest plots, heterogeneity statistics, and publication-bias assessments all depend on statistical methods. Evidence-based medicine is, in a real sense, applied biostatistics at scale.
Types of Data in Medical Research
The appropriate statistical method depends on the nature of the data being analysed. Applying a method designed for continuous measurements to a binary outcome, or vice versa, produces results that are either wrong or uninterpretable.
| Data type | Description | Medical example | Typical summary |
|---|---|---|---|
| Nominal categorical | Categories with no natural order | Blood type (A, B, AB, O) | Frequency, proportion |
| Binary / dichotomous | Exactly two categories | Disease present / absent | Proportion, risk, odds |
| Ordinal | Ordered categories, unequal gaps | Pain score (none / mild / moderate / severe) | Median, percentiles |
| Continuous | Any value within a range | Systolic blood pressure (mmHg) | Mean, SD, IQR |
| Discrete count | Non-negative integers | Number of hospital admissions | Mean, rate, Poisson model |
| Time-to-event | Duration until an event occurs | Days from treatment start to relapse | Median survival, hazard ratio |
Beyond variable type, researchers distinguish the outcome variable (the measurement being explained) from independent variables or predictors. Variables that are associated with both the exposure and the outcome — without lying on the causal pathway — are confounders, and they require special handling in the analysis.
Descriptive Statistics in Medical Research
Descriptive statistics summarise the data that were actually collected. They do not support inference to a wider population; that is the role of inferential methods. Every well-written medical paper begins by describing the characteristics of its study participants, often in a "Table 1."
Centre and spread
For continuous variables measured on an approximately symmetric distribution, the mean and standard deviation are the standard summaries. When data are skewed — as is common for laboratory values, length of hospital stay, and cost — the median and IQR are more informative because they are not pulled by extreme values.
Systolic Blood Pressure in 10 Hypothetical Patients (mmHg)
Data: 120, 124, 126, 128, 130, 132, 135, 138, 142, 165
n = 10. Sort in ascending order: 120, 124, 126, 128, 130, 132, 135, 138, 142, 165.
Mean = (120+124+126+128+130+132+135+138+142+165) / 10 = 1340 / 10 = 134.0 mmHg. The high value of 165 pulls the mean upward relative to most of the data.
Median = (130+132)/2 = 131.0 mmHg. With n=10 (even), the median is the average of the 5th and 6th values. It is less affected by the outlier.
Range = 165 − 120 = 45 mmHg. Min = 120, Max = 165.
Q1 = 126, Q3 = 138, IQR = 12 mmHg. The middle 50% of readings span only 12 mmHg, showing that the 165 value is genuinely atypical.
SD ≈ 13.2 mmHg. Computed from the deviations of each value from the mean. The 165 value inflates the SD considerably.
Takeaway: When one patient has an unusually high reading (165 mmHg here), the median and IQR give a more representative picture of the typical patient than the mean and SD alone. This is exactly why skewed clinical data — such as length of stay or C-reactive protein — are routinely summarised with medians.
Inferential Statistics in Medical Research
Researchers rarely have access to entire populations. A clinical trial enrolls hundreds of patients, not all people who might ever take the drug. Inferential statistics provides methods to reason from a sample back to the population it came from, while being transparent about the uncertainty that process introduces.
Descriptive statistics describe the sample at hand (e.g., "the mean reduction in blood pressure in our trial was 8 mmHg"). Inferential statistics use that sample to draw conclusions about a broader population (e.g., "we estimate the true average reduction is between 4 and 12 mmHg"). The confidence interval is the inferential tool; the sample mean is descriptive.
The core concepts of inferential statistics are the standard error (how much a sample statistic would vary across repeated samples of the same size from the same population), the confidence interval (a range of plausible values for the population parameter), and the p-value (the probability of observing a result at least as extreme as the one obtained, if the null hypothesis were true). These are covered in depth in the inferential statistics section of this site.
Common Statistical Methods in Medical Research
Method selection depends on the research question, variable types, number of groups, independence of observations, sample size, and study design. The table below covers the most common methods. It is a guide, not an algorithm — complex studies often need specialist statistical advice.
| Research question | Outcome type | Common method | Key considerations |
|---|---|---|---|
| Compare one mean to a reference | Continuous | One-sample t-test | SD must be estimated from sample |
| Compare two independent means | Continuous | Welch/independent t-test | Welch preferred when SDs differ |
| Compare paired measurements | Continuous | Paired t-test | Observations must be linked (same patient, before/after) |
| Compare 3+ group means | Continuous | One-way ANOVA | Requires post-hoc testing if significant |
| Compare two categorical distributions | Categorical | Chi-square test | Expected counts ≥5 in each cell |
| Small cell counts (categorical) | Categorical | Fisher's exact test | Use when any expected count <5 |
| Compare two ordinal / non-normal groups | Ordinal / skewed continuous | Mann-Whitney U | Tests difference in distributions, not necessarily medians |
| Compare paired ordinal / non-normal | Ordinal / skewed continuous | Wilcoxon signed-rank | Paired observations required |
| Compare 3+ non-normal independent groups | Ordinal / skewed continuous | Kruskal-Wallis | Non-parametric extension of ANOVA |
| Measure linear association | Two continuous variables | Pearson correlation | Assumes linear relationship; sensitive to outliers |
| Measure monotonic association | Ordinal or non-normal continuous | Spearman correlation | Rank-based; more robust |
| Predict continuous outcome from predictors | Continuous | Linear regression | Check linearity, independence, constant variance |
| Predict binary outcome (disease yes/no) | Binary | Logistic regression | Produces odds ratios; check for separation |
| Predict count outcome | Count | Poisson or negative binomial regression | Check for overdispersion |
| Analyse time to event | Time-to-event | Kaplan-Meier, Cox regression | Handles censored observations |
| Analyse clustered / repeated observations | Any | Mixed-effects models | Required when patients contribute multiple readings |
A continuous outcome does not automatically call for a t-test. Paired data require paired methods. Clustered data (e.g., patients nested within hospitals) require multilevel models. Repeated measurements within the same patient violate the independence assumption of many standard tests. Always consider the study design first.
Hypothesis Testing in Medical Research
Hypothesis testing formalises the question "could this result be due to chance?" It requires researchers to commit to assumptions before seeing the data, which reduces the risk of post-hoc rationalisation.
The framework
The null hypothesis (H₀) is the default position — usually that there is no difference, no association, or no effect. The alternative hypothesis (H₁) is what the researcher is investigating. The test statistic summarises how far the sample result is from what H₀ predicts, measured in units of standard error. The p-value is the probability of observing a test statistic at least as extreme as the one calculated, if H₀ were true.
A p-value of 0.03 does not mean there is a 3% chance the null hypothesis is correct. It means that if H₀ were true, there is a 3% probability of observing data this extreme or more extreme. This distinction matters: the p-value is a property of the data given H₀, not a probability statement about H₀ itself.
Does a new antihypertensive reduce systolic blood pressure more than the control?
H₀: The mean SBP reduction is equal in both groups (μ₁ − μ₂ = 0). H₁: The new drug produces a greater mean reduction (μ₁ − μ₂ > 0). We use a one-sided alternative because we are specifically testing whether the new drug is better.
α = 0.05. Set before data collection.
Observed results (hypothetical): Treatment group: mean reduction = 12 mmHg, SD = 8, n = 80. Control group: mean reduction = 7 mmHg, SD = 9, n = 80.
Mean difference = 12 − 7 = 5 mmHg. 95% CI for the difference: approximately 2.3 to 7.7 mmHg (hypothetical). Welch t-test p ≈ 0.001.
Decision: p = 0.001 < α = 0.05. Reject H₀. The data are inconsistent with no difference at the 5% significance level.
Interpretation: The new drug was associated with a 5 mmHg greater mean reduction in SBP (95% CI: 2.3 to 7.7 mmHg, p ≈ 0.001) compared with the control. Whether a 5 mmHg difference is clinically meaningful depends on the patient population, existing therapies, side-effect profile, and cost — questions that statistics alone cannot answer.
Effect Size in Medical Research
A p-value tells you whether an effect is statistically distinguishable from zero. It does not tell you how large that effect is. Effect size fills that gap. Researchers should routinely report both.
| Effect size measure | Typical use | What it expresses |
|---|---|---|
| Mean difference | Continuous outcome, two groups | Raw units (e.g., mmHg, kg) |
| Cohen's d | Standardised continuous outcome | Difference in SD units; allows cross-study comparison |
| Risk difference (RD) | Binary outcome | Absolute difference in event probabilities |
| Relative risk (RR) | Binary outcome (cohort studies, RCTs) | Ratio of event probabilities |
| Odds ratio (OR) | Binary outcome (case-control studies, logistic regression) | Ratio of event odds |
| Hazard ratio (HR) | Time-to-event outcome | Ratio of instantaneous event rates between groups |
| Pearson r | Association between two continuous variables | Direction and strength of linear association (−1 to +1) |
A large sample can produce a tiny, statistically significant effect that is irrelevant to clinical practice. A small sample might produce a clinically important difference that fails to reach statistical significance simply because there were too few patients. Neither situation is handled well by reporting only the p-value.
Confidence Intervals in Medical Research
A confidence interval (CI) communicates both the estimated effect and the precision of that estimate. It is a range of values computed from the sample data using a method that, across repeated identical studies, would capture the true population value a specified percentage of the time.
If you ran 100 identical studies and computed a 95% CI from each, approximately 95 of those intervals would contain the true population value. For any single study, the interval either contains the true value or it does not. A wider interval means less precision; a narrower interval means more. Width is driven by sample size and variability.
Consider a hypothetical example: Treatment A reduces systolic blood pressure by an estimated 6 mmHg compared with treatment B, with a 95% CI of 2 to 10 mmHg. This tells you the estimated effect is 6 mmHg, but values anywhere from 2 to 10 mmHg are consistent with the data at this level of certainty. The entire interval lies above zero, which is consistent with concluding that A performs better. If the interval had spanned −1 to 13 mmHg, the data would also be consistent with no difference — or even a small disadvantage — and the conclusion would be far less certain.
Risk, Odds, and Association Measures
Cohort studies, case-control studies, and clinical trials each produce different measures of association for binary outcomes. Understanding which measure applies — and what it means — is essential for reading medical literature.
Definitions
Risk (or probability) is the proportion of a group that experiences the outcome: risk = events / total. Odds is the ratio of those who experience the event to those who do not: odds = events / non-events. When the event is rare, risk and odds are numerically similar. When the event is common, they diverge considerably, and an odds ratio can substantially overstate the relative risk.
Exposure and Disease Outcome
| Disease present | Disease absent | Total | |
|---|---|---|---|
| Exposed | 40 | 160 | 200 |
| Unexposed | 20 | 180 | 200 |
| Total | 60 | 340 | 400 |
Risk (exposed) = 40/200 = 0.20 (20%)
Risk (unexposed) = 20/200 = 0.10 (10%)
Risk difference (RD) = 0.20 − 0.10 = 0.10 (10 percentage points). Ten more people per 100 exposed develop disease compared with unexposed.
Relative risk (RR) = 0.20 / 0.10 = 2.0. The exposed group has twice the risk of the unexposed group.
Odds (exposed) = 40/160 = 0.25. Odds (unexposed) = 20/180 ≈ 0.111. Odds ratio (OR) = 0.25 / 0.111 ≈ 2.25. Note: the OR exceeds the RR because the outcome is not rare (10% in unexposed). When the outcome is rare (<10%), the OR approximates the RR closely.
Association does not establish causation. These numbers describe a statistical relationship in this hypothetical dataset. A causal interpretation requires ruling out confounding, reverse causation, and bias through study design and analysis, not through the numbers themselves.
Diagnostic Test Statistics
When a clinical test produces a positive or negative result, four possible outcomes exist relative to the patient's true disease status. Statistical measures of diagnostic accuracy quantify how well the test performs across each type of outcome.
| Disease present (D+) | Disease absent (D−) | |
|---|---|---|
| Test positive (T+) | True Positive (TP) | False Positive (FP) |
| Test negative (T−) | False Negative (FN) | True Negative (TN) |
A screening test evaluated in 500 hypothetical patients
Results: TP = 90, FP = 15, FN = 10, TN = 385
Sensitivity = 90 / (90+10) = 90/100 = 0.90 (90%). The test correctly identifies 90% of patients who actually have the disease.
Specificity = 385 / (385+15) = 385/400 = 0.9625 (96.25%). The test correctly rules out disease in 96.25% of those who do not have it.
PPV = 90 / (90+15) = 90/105 ≈ 0.857 (85.7%). A positive test result corresponds to true disease in about 86% of cases — given this population's disease prevalence.
NPV = 385 / (385+10) = 385/395 ≈ 0.975 (97.5%). A negative result means the patient is disease-free in about 97.5% of cases.
Important: PPV and NPV depend on the disease prevalence in the tested population. The same test applied to a low-prevalence population will have a lower PPV (more false positives relative to true positives), even if sensitivity and specificity remain constant. Sensitivity and specificity are intrinsic test properties; predictive values are context-dependent. For more on these concepts, see the sensitivity and specificity guide.
Regression in Medical Research
Linear regression
Linear regression models the relationship between a continuous outcome and one or more predictor variables. In medical research, a typical application might predict systolic blood pressure from age, BMI, and physical activity level. Each coefficient in the model represents the estimated change in the outcome for a one-unit increase in that predictor, holding all others constant.
Y = outcome variableβ₀ = interceptβ₁…βₖ = coefficientsX₁…Xₖ = predictorsε = residual errorLogistic regression
Logistic regression is used when the outcome is binary — for example, whether a patient was readmitted within 30 days, whether treatment produced a response, or whether a patient developed a complication. It models the log-odds of the outcome as a linear function of the predictors. The results are reported as odds ratios with confidence intervals. An odds ratio greater than 1 indicates a higher odds of the outcome in the predictor group; less than 1 indicates lower odds.
Logistic regression produces odds ratios. When the outcome is common (say, more than 10% of participants), odds ratios can substantially overestimate the corresponding risk ratio. Some researchers use modified Poisson regression or other approaches to estimate risk ratios directly from binary outcomes when this distinction matters.
Both linear and logistic regression can adjust for confounders — variables that are associated with both the predictor of interest and the outcome. Adjusted coefficients and odds ratios represent the association between a predictor and outcome after accounting for those confounders. However, statistical adjustment cannot remove bias from unmeasured confounders, and it does not by itself establish a causal relationship. For more detail on regression methods, see the multiple linear regression and logistic regression pages.
Survival Analysis in Medical Research
Many medical outcomes are not simply yes/no at a single point in time — they involve how long it takes for something to happen. Time to death, time to relapse, time to hospital readmission, or time to first adverse event are all time-to-event outcomes. Ordinary regression methods are not suitable for these data because many participants will not have experienced the event by the time the study ends — a situation called censoring.
The Kaplan-Meier curve is the standard tool for visualising survival over time. It estimates the probability of surviving (or remaining event-free) at each point in time, accounting for censored observations. The median survival time is the time at which 50% of participants have experienced the event.
The Cox proportional hazards model is the most widely used method for comparing survival between groups while adjusting for covariates. It produces a hazard ratio (HR). An HR of 0.70 means the event rate in the treatment group is 30% lower than in the comparison group at any given time point (under the proportional hazards assumption). Like the odds ratio, the hazard ratio is a ratio — not a risk difference — so the absolute clinical importance depends on the baseline hazard as well.
Statistics in Clinical Trials
Randomised controlled trials are the gold standard for evaluating treatment effects. Statistical methods appear at every stage.
Sample size planning
Before a trial starts, statisticians calculate the number of participants needed to detect a specified effect size at a given power (typically 80% or 90%) and significance level. An underpowered trial can miss a real effect; an overpowered one wastes resources and exposes excess patients to an experimental treatment.
Randomisation and allocation
Random allocation creates treatment groups that are comparable at baseline on both measured and unmeasured factors. Statistical analysis of baseline characteristics confirms balance and identifies any chance imbalances to be accounted for in the analysis.
Primary outcome analysis
The primary analysis compares the pre-specified primary outcome between arms, using the statistical test specified in the protocol. The analysis is typically intention-to-treat: all randomised participants are included in the group to which they were allocated, regardless of whether they actually received the treatment.
Effect estimation and uncertainty
The treatment effect is reported as a point estimate (mean difference, risk ratio, hazard ratio) with a confidence interval. Both the direction and the width of the interval inform clinical interpretation.
Missing data and sensitivity analyses
Participants drop out of trials. The missing-data mechanism matters: if dropout is related to the outcome (missing not at random), simple complete-case analysis can introduce bias. Multiple imputation, sensitivity analyses, and pattern-mixture models are commonly used approaches.
Confounding and Bias
A confounder is a variable that is associated with both the exposure and the outcome but does not lie on the causal path between them. If smoking is a confounder of an apparent relationship between coffee drinking and lung cancer — because smokers also drink more coffee — a raw comparison of coffee drinkers and non-drinkers will overstate any association between coffee and cancer. Statistical adjustment for confounders (through stratification, multivariable regression, or propensity score methods) attempts to produce estimates that more closely reflect the true exposure-outcome relationship.
Distinguish confounders from mediators (variables that lie on the causal path — adjusting for them removes the very effect you want to measure) and effect modifiers (variables that change the magnitude or direction of the exposure-outcome relationship in different subgroups). Misidentifying one for the other leads to incorrect analytical choices.
- Selection bias: Participants who join the study differ systematically from those who do not, or from those who drop out.
- Information / measurement bias: Exposure or outcome is measured differently between groups (differential misclassification).
- Recall bias: Cases and controls remember past exposures differently (common in retrospective studies).
- Attrition bias: Dropout is related to the treatment or outcome, producing an unrepresentative sample at follow-up.
- Publication bias: Studies with statistically significant results are more likely to be published, distorting the literature.
Statistical methods can reduce the impact of confounding under specific assumptions, but they cannot fix problems created by study design. No amount of regression adjustment compensates for a fundamentally biased comparison.
Complete Medical Research Example
The following walkthrough illustrates how statistical methods connect to form a complete analysis. All numbers are hypothetical and are used purely for teaching purposes.
Does a dietary intervention reduce LDL cholesterol more than standard care?
Research question: In adults with mildly elevated LDL cholesterol, does a structured dietary programme reduce LDL more than standard care advice over 12 weeks?
Design and sample: Randomised controlled trial. Intervention group (n=100) and control group (n=100). Allocation by computer-generated random numbers.
Descriptive statistics (baseline — hypothetical): Intervention: mean age 52 years (SD 11), mean baseline LDL 3.9 mmol/L (SD 0.5). Control: mean age 51 years (SD 12), mean baseline LDL 3.8 mmol/L (SD 0.6). Groups appear balanced at baseline.
Primary outcome — mean change in LDL (hypothetical): Intervention: −0.55 mmol/L (SD 0.38). Control: −0.18 mmol/L (SD 0.40). Mean difference = −0.37 mmol/L.
Hypothesis test: Two-sample Welch t-test. t ≈ 6.7 (df ≈ 198). p < 0.001. The mean difference is statistically significant at α = 0.05.
Effect size and CI: Mean difference = −0.37 mmol/L (95% CI: −0.48 to −0.26 mmol/L). The entire interval is below zero, consistent with a genuine benefit of the intervention.
Regression adjustment for baseline LDL: After adjusting for baseline LDL (ANCOVA), the estimated treatment effect was −0.36 mmol/L (95% CI: −0.47 to −0.25 mmol/L), consistent with the unadjusted result. Adjustment reduced the residual variance and slightly narrowed the CI.
Limitations: Open-label design (participants knew their group assignment). 12-week follow-up is short. Results apply to the population enrolled; generalisability to other age groups, ethnicities, or LDL levels requires caution. These are all considerations beyond the statistical analysis itself.
The dietary intervention was associated with a statistically significant and clinically plausible reduction in LDL cholesterol of 0.37 mmol/L (95% CI: 0.26 to 0.48 mmol/L) compared with standard care over 12 weeks. All numbers in this example are hypothetical and serve only as a teaching illustration.
Statistical vs Clinical Significance
One of the most important concepts in medical statistics is the difference between a result that is statistically significant and one that is clinically meaningful. They are not the same, and confusing them leads to poor medical decisions.
Effect size, the width of the confidence interval, the baseline risk of the outcome, the side-effect profile, patient preferences, and treatment cost all enter clinical decisions. Statistics informs those decisions; it does not replace them.
Common Mistakes in Medical Statistics
Treating p < 0.05 as proof
A p-value below the threshold indicates the data are inconsistent with H₀ at that level — not that the effect is real, large, or important.
Ignoring effect size
Reporting only the p-value obscures whether the observed difference is large enough to matter clinically.
Ignoring confidence intervals
A point estimate without a CI hides the precision — or lack of it — behind every statistical estimate.
Confusing correlation with causation
Two variables that move together are not necessarily causally related. Study design, not statistical analysis, determines whether causal language is justified.
Treating odds ratios as risk ratios
When outcomes are common, the odds ratio overestimates the relative risk. This error inflates perceived treatment benefits in many published studies.
Using the wrong statistical test
Applying a paired test to independent data (or vice versa), or using a parametric test on heavily skewed data without checking assumptions, produces incorrect p-values.
Ignoring repeated measurements
When the same patient contributes multiple observations, those observations are not independent. Standard tests that assume independence produce artificially narrow confidence intervals.
Ignoring missing data
Dropping participants with missing values (complete-case analysis) is only valid if the data are missing completely at random — an assumption that is rarely verified.
Over-interpreting subgroup analyses
Testing many subgroups without pre-specifying them inflates the false-positive rate. A nominally significant subgroup finding requires external replication before drawing clinical conclusions.
Non-significance does not mean no effect
Failure to reject H₀ is not evidence that H₀ is true — especially in underpowered studies. The correct language is "fail to reject H₀," not "the treatment has no effect."
Using mean for skewed data
Hospital length of stay, cost, and many laboratory values are right-skewed. Reporting the mean is misleading; the median and IQR are more informative for these variables.
Overfitting regression models
Adding more predictors than the data can support produces models that describe the sample well but generalise poorly to new patients. A rule of thumb is at least 10 events per predictor in logistic regression, though this is a simplification.
How to Choose a Statistical Test
Test selection follows from the research question, not just the data type. The decision tree below provides a starting framework. Complex study designs — clustered samples, repeated measures, multilevel data, time-varying exposures — often require methods not captured by a simple flowchart.
Statistical Test Decision Framework
Statistical test selection depends on the research question and study design, not only on whether data appear "normal." Consult a statistician when designing studies with complex sampling schemes, repeated measurements, or multilevel data structures.
How to Report Statistical Results
Clear statistical reporting allows readers to assess the evidence, reproduce the analysis, and apply results appropriately. The examples below show professional reporting formats for common estimates.
| Statistic | Recommended format | Hypothetical example |
|---|---|---|
| Continuous variable (approx. symmetric) | Mean ± SD or Mean (SD) | Baseline SBP: 138 ± 14 mmHg |
| Continuous variable (skewed) | Median [IQR] | LOS: 4 [2–8] days |
| Binary outcome | n (%) or proportion (95% CI) | Adverse events: 14 (7.0%), 95% CI: 3.9–11.4% |
| Mean difference | MD (95% CI), p-value | MD −5.2 mmHg (95% CI: −8.1 to −2.3), p = 0.001 |
| Risk ratio | RR (95% CI), p-value | RR 0.72 (95% CI: 0.55–0.94), p = 0.014 |
| Odds ratio | OR (95% CI), p-value | OR 0.65 (95% CI: 0.44–0.97), p = 0.036 |
| Hazard ratio | HR (95% CI), p-value | HR 0.78 (95% CI: 0.62–0.98), p = 0.033 |
All numerical examples above are hypothetical. Medical journals typically follow reporting guidelines such as CONSORT (for clinical trials), STROBE (for observational studies), or TRIPOD (for prediction models). These guidelines specify which statistics must be reported and how.
Interactive Medical Statistics Calculators
Medical Statistics Calculator
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Enter counts from a 2×2 diagnostic accuracy table.
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Statistical Software for Medical Research
| Software | Typical medical uses | Notes |
|---|---|---|
| R | Clinical trial analysis, survival analysis, epidemiology, bioinformatics, meta-analysis | Free, open-source, extensive package ecosystem (survival, lme4, meta) |
| Python | Data wrangling, machine learning on health data, health informatics | Free; statsmodels and lifelines for statistical modelling |
| SPSS | Clinical and social science research, survey analysis | Commercial; menu-driven interface; widely used in clinical settings |
| Stata | Epidemiology, health economics, clinical trials, panel data | Commercial; widely used in public health research |
| SAS | Pharmaceutical clinical trials, regulatory submissions | Commercial; preferred in FDA-regulated drug development |
| Excel | Basic descriptive statistics, simple charts | Not suitable for complex regression, survival analysis, or large datasets |
Medical Statistics Glossary
- Biostatistics
- The application of statistical methods to biological, medical, and public health research, including study design and analysis.
- Confounder
- A variable associated with both exposure and outcome that distorts the apparent exposure-outcome relationship if not accounted for.
- Confidence Interval
- A range of values, computed from the sample, that would contain the true population parameter in a specified proportion of repeated samples.
- Effect Size
- A quantitative measure of the magnitude of an association or difference, independent of sample size.
- Hazard Ratio
- The ratio of the instantaneous event rate in one group to another at any given time; produced by Cox proportional hazards regression.
- Hypothesis Testing
- A formal procedure for deciding whether sample data are inconsistent with a null hypothesis, using a test statistic and a p-value.
- Intention-to-Treat
- An analysis principle that includes all randomised participants in the group to which they were assigned, regardless of protocol adherence.
- IQR
- Interquartile range — the difference between the 75th and 25th percentiles; a robust measure of spread for skewed data.
- Odds Ratio
- The ratio of the odds of an event in one group to the odds in another; produced by logistic regression and case-control studies.
- P-value
- The probability of observing a test statistic at least as extreme as the one obtained, given that the null hypothesis is true.
- Relative Risk
- The ratio of the probability of an outcome in the exposed group to the probability in the unexposed group.
- Sensitivity
- The proportion of truly diseased individuals correctly identified by a test as positive (TP / (TP + FN)).
- Specificity
- The proportion of truly disease-free individuals correctly identified by a test as negative (TN / (TN + FP)).
- Standard Error
- The estimated standard deviation of a sample statistic (e.g., the sample mean) across hypothetical repeated samples.
- Statistical Power
- The probability that a test correctly rejects a false null hypothesis (1 − β); depends on sample size, effect size, and α.
- Type I Error
- Rejecting a true null hypothesis (false positive). Its probability is controlled by the significance level α.
- Type II Error
- Failing to reject a false null hypothesis (false negative). Its probability is β; power = 1 − β.
- Survival Analysis
- Statistical methods for analysing time-to-event data, accounting for censored observations.
Frequently Asked Questions
Statistics in medical research is the application of mathematical methods to collect, summarise, analyse, and interpret health data. It provides the tools researchers need to compare treatments, estimate the size of effects with appropriate uncertainty, test hypotheses, evaluate diagnostic tests, and communicate evidence reliably to clinicians and policymakers.
Biostatistics is statistics applied specifically to biological and health-related sciences. It covers study design, sample size calculation, clinical trial analysis, survival analysis, epidemiological methods, and the regulatory statistics required for drug approval. The term is used across academic public health, pharmaceutical research, and clinical trial organisations.
A p-value is the probability of observing results at least as extreme as those in the study data, assuming the null hypothesis (typically "no effect" or "no difference") is true. A p-value of 0.04 means there is a 4% probability of seeing this result — or a more extreme one — if the null hypothesis were correct. It is not the probability that the null hypothesis is true, and a low p-value is not proof that a treatment works.
A 95% CI is a range of values computed using a method that, in repeated identical studies, would capture the true population parameter 95% of the time. For a single study, the interval either contains the true value or it does not. Wider intervals indicate less precision (smaller samples or more variability); narrower intervals indicate more precision. The CI conveys both the estimated effect and the uncertainty around it.
Relative risk (risk ratio) is the ratio of the probability of an event in the exposed group to the probability in the unexposed group. The odds ratio is the ratio of the odds (events / non-events) in each group. When events are rare (less than ~10% in the unexposed group), the two are numerically similar. When events are common, the odds ratio is farther from 1.0 than the risk ratio and can misleadingly suggest a larger effect. Case-control studies must use odds ratios; cohort studies and RCTs can directly estimate risk ratios.
No. Statistical significance means the observed result is unlikely under the null hypothesis at the chosen significance threshold. It says nothing about whether the effect is real in a causal sense, whether it is clinically important, whether it will replicate, or whether the study was free from bias. Effect size, confidence intervals, study design quality, replication, and clinical context all contribute to conclusions about whether a treatment is effective.
It depends on the outcome type and study design. For continuous outcomes in independent groups (e.g., blood pressure in a treated vs control arm), the Welch t-test is standard. For paired data (the same patients before and after treatment), the paired t-test applies. For binary outcomes (e.g., readmission yes/no), the chi-square test or a risk ratio analysis is appropriate. For non-normal or ordinal outcomes, Mann-Whitney U is an alternative. See the test selection section above for a fuller framework.
Sensitivity is the proportion of patients with the disease who test positive (true positive rate). Specificity is the proportion without the disease who test negative (true negative rate). A highly sensitive test misses few cases; a highly specific test produces few false alarms. For screening programmes, high sensitivity is often prioritised. For confirmatory tests, high specificity matters more. Positive and negative predictive values depend on prevalence and change across different populations even if sensitivity and specificity stay constant.
Logistic regression is used when the outcome variable is binary — for example, disease yes/no, hospital readmission yes/no, or treatment response yes/no. It models the log-odds of the outcome as a function of one or more predictor variables and produces adjusted odds ratios with confidence intervals. It is appropriate for both cross-sectional, cohort, and case-control data, and for confounding adjustment in clinical studies.
Survival analysis is used when the outcome of interest is the time until a specific event — death, relapse, discharge, complication, or readmission. It handles censored data: participants who leave the study without experiencing the event contribute the follow-up time they provided, rather than being dropped. Kaplan-Meier curves visualise the estimated survival function over time. The Cox proportional hazards model compares event rates between groups while adjusting for covariates, producing hazard ratios.