Medical Statistics

Types of data

Categorical

Nominal: categories without order, such as blood group.

Ordinal: categories with a meaningful order, such as a clinical grade.

Numerical

Discrete: count data.

Continuous: measurements that can take values across a range.

Describing a distribution

Central tendency

• mean
• median
• mode

The mean is sensitive to extreme values. The median is often more representative for skewed data.

Spread

• standard deviation for approximately normally distributed data
• interquartile range for skewed data
• range is easy to understand but strongly influenced by extremes

Normal distribution

In an ideal normal distribution:

• about 68% of observations lie within 1 standard deviation of the mean
• about 95% lie within 2 standard deviations

Orthopaedic data are frequently skewed, so normality should not be assumed.

Hypothesis testing

Null hypothesis

Usually states that there is no difference or association.

P value

The p value is the probability of observing data at least as extreme as those obtained, assuming the null hypothesis and statistical model are correct.

It is not the probability that the null hypothesis is true.

The null hypothesis usually states that there is no difference or association. A p value is the probability of obtaining data at least as extreme as those observed, assuming the null hypothesis and model assumptions are correct.

It is not:

• the probability that the null hypothesis is true
• the probability that the result happened by chance
• a measure of the size or clinical importance of the effect

Type I and Type II error

• Type I error: false-positive conclusion
• Type II error: false-negative conclusion

Power is the probability of detecting a real effect of a specified size and equals 1 minus the type II error rate.

Confidence interval

A confidence interval describes the range of values compatible with the data under the statistical model.

A narrow confidence interval indicates greater precision than a wide interval.

Statistical significance versus clinical importance

A very small effect can be statistically significant in a large study. A clinically important effect can fail to reach statistical significance in an underpowered study.

Always consider:

• effect size
• confidence interval
• patient relevance
• study quality

Diagnostic tests

Sensitivity = proportion of diseased patients who test positive.

Specificity = proportion of non-diseased patients who test negative.

Positive and negative predictive values depend strongly on disease prevalence.

Sensitivity is the probability that a test is positive when disease is present.

Specificity is the probability that a test is negative when disease is absent.

Positive and negative predictive values depend strongly on disease prevalence.

Likelihood ratios are useful because they describe how much a test result changes the odds of disease and are less directly dependent on prevalence.

Correlation and regression

Correlation measures the strength of association between variables. Correlation does not prove causation.

Regression models can estimate the relationship between an outcome and one or more predictors while adjusting for other measured variables.

Parametric and non-parametric tests

Parametric tests make assumptions about the distribution of data and model residuals. Non-parametric tests are useful when those assumptions are unsuitable, particularly for ordinal or markedly skewed data.

Viva principle

Explain the clinical meaning of the statistic rather than giving only a formula.

Describing data

Choose summary measures according to data distribution.

For approximately symmetric continuous data, mean and standard deviation are useful. For skewed data, median and interquartile range usually describe the centre and spread more appropriately.

Categorical data are described using counts and proportions.

Sampling and uncertainty

A sample estimate varies from sample to sample. The standard error describes uncertainty around an estimate and decreases as sample size increases.

A confidence interval expresses a range of values compatible with the observed data under the statistical model. It is usually more informative than a p value alone because it shows both direction and precision.

Errors and power

A type I error is a false positive.

A type II error is a false negative.

Power is the probability of detecting a specified true effect and depends on sample size, variability, effect size and significance threshold.

Correlation and agreement

Correlation measures association, not agreement. Two methods can correlate strongly while differing systematically.

Agreement between measurements may be better assessed using methods such as Bland-Altman analysis or appropriate reliability statistics depending on the data type.

Regression

Regression models estimate the relationship between an outcome and one or more predictors while allowing adjustment for confounders.

Linear regression is commonly used for continuous outcomes; logistic regression for binary outcomes; survival models for time-to-event data.

Adjustment reduces confounding only for variables that have been adequately measured and modelled.

Survival analysis

Kaplan-Meier methods estimate time-to-event probability while accounting for censoring. In arthroplasty, revision can be treated as the event, but competing events such as death complicate interpretation in older populations.

Number needed to treat

NNT is the inverse of absolute risk reduction. It is meaningful only with a defined outcome, time horizon and patient population.

FRCS synthesis

Statistics should answer a clinical question. Translate every result into:

• size of effect
• precision
• probability of bias
• clinical relevance
• applicability

That demonstrates understanding beyond formula recall.