Statistical tests
Types of Variables
Qualitative
Nominal/Categorical: Multiple categories without a specific order (e.g., Yes/No)
Ordinal: Multiple categories with a specific order (e.g. Low/Medium/High risk)
Quantitative
Discrete: Countable values (e.g., Number of people in a family)
Continuous: Measurable values with no limit (e.g., Height, Weight, Blood Pressure)
Statistical Tests
Fisher’s Exact Test
Compares two variables, used for categorical data
Applicable when sample size is small (less than 10 in a cell)
Chi-Squared Test
Assesses goodness of fit or independence of categorical variables
Suitable for variables with more than two categories
Mann-Whitney U Test (Wilcoxon Rank-Sum Test)
Compares medians between two groups
Non-parametric test
Kruskal-Wallis Test
Compares medians across more than two groups
Non-parametric test
T-Tests
Compares means between two groups
Types
Paired: Same group at different times
Independent: Different groups
One-Sample: Compares a group mean to a standard value
To check if two populations are different from one another, perform a two-tailed t test
To check if one population mean is greater than or less than the other, perform a one-tailed t test
Parametric test
ANOVA
Compares means across more than two groups
One-Way: One independent variable
Two-Way: Two independent variables
Parametric test
Spearman’s and Pearson’s Correlation
Spearman’s: Non-parametric, used for ranked data
Pearson’s: Parametric, used for continuous data
Measures correlation between variables
Statistical Concepts
Stem-and-Leaf Plots: Represent actual data points
Randomisation: Can be stratified based on specific patient characteristics
Type 1 Error: Incorrectly rejecting a true null hypothesis (false positive)
Type 2 Error: Failing to reject a false null hypothesis (false negative)
Risk Measures
Absolute Risk (AR): Numer of events divided by number of people in a group
Absolute Risk Reduction (ARR): AR (control) minus AR (treatment) groups
Relative Risk (RR): Ratio of AR in treatment to control group
Relative Risk Reduction (RRR): Proportional reduction in risk = ARR divided by AR(control)
Number Needed to Treat (NNT): Number of patients needed to treat to prevent one event = 1 divided by ARR
Number Needed to Harm (NNH): Number of patients needed to harm one person 1 divided by (AR treatment minus AR control)
Odds Ratio (OR): Odds of an event in the exposed divided by odd in non-exposed group
Hazard Ratio (HR): Risk of an event occurring in the exposed group divided by non-exposed group
Significance and Errors
Confidence Interval (CI): If CI includes 1 (for RR, OR, HR) or 0 (for absolute differences), there is no significant difference
Minimal Clinically Important Difference (MCID): The smallest effect that is meaningful in clinical practice
Power and Sample Size
Power = 1 minus (β) = Likelihood of detecting a true difference
Alpha (α): Probability of Type 1 error, commonly set at 0.05 (5%)
Beta (β): Probability of Type 2 error, typically set at 0.1-0.2 (10-20%)
Power Calculation Factors
Baseline Incidence: Rare events require a larger sample size
Population Variance: Higher variance increases sample size needed
Treatment Effect Size: Smaller effect sizes require more participants
Alpha: Lower alpha reduces Type 1 error but may require more participants
Beta: Lower beta increases power but also requires a larger sample size
References
Statistics at Square One, Ninth Edition, T D V Swinscow, Revised by M J Campbell, 1997. BMJ https://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one
https://www.statstest.com/choose-your-test/