Statistics for FRCS

Types of Data

  1. Continuous Variables (Ratio, Integer Data)
    • Example: Age, Distance, or Hours Spent Revising
    • Characteristics:
      • Zero is the origin and values are independent of units.
      • Tend to be quantitative.
      • May or may not be parametric in distribution.
  2. Categorical Variables (Nominal, Ordinal Data)
    • Example: Race, Gender, Category in a Classification System
    • Characteristics:
      • Typically non-numerical variables.
      • Tend to be qualitative.
      • Are non-parametric.

Distribution of Data

  1. Parametric Data
    • Normally distributed, forming a Gaussian bell-shaped curve.
    • Mode, mean, and median are the same.
  2. Non-Parametric Data
    • Most data are skewed.
    • The median or mode is used to assess central tendency, not the mean.

Measures of Spread/Variability

  1. Interquartile Range
    • Describes deviation or spread from the mean, grouping data into quarters (25%).
  2. Standard Deviation (SD)
    • Describes deviation of individual values from the mean.
    • Used in normal distribution:
      • 68% of values within 1 SD, 95% within 2 SDs, 99% within 3 SDs.
  3. Variance
    • SD squared, representing spread from the mean when the mean is the central tendency.
  4. Confidence Interval
    • Describes measurement accuracy, typically a 95% confidence interval.
    • A small confidence interval means all values are close to central tendency (mean, mode, or median).

P-Values, Errors, and Power Analysis

Null Hypothesis

  • Assumes that an observed difference occurred by chance. Studies aim to reject the null hypothesis to prove observed differences.

P-Value

  • Probability that the difference was not due to chance. Usually set to less than 5% (0.05).

Bonferroni Adjustment

  • Used when multiple variables are tested. It reduces the P-value and the chance of Type 1 errors.

Types of Errors

  1. Type 1 (Alpha) Error
    • False positives: Rejecting the null hypothesis when it is actually true.
    • Can be reduced by lowering the P-value but increases the risk of Type 2 errors.
  2. Type 2 (Beta) Error
    • False negatives: Accepting the null hypothesis when it is actually false.
    • Common in orthopedics and can be minimized by increasing the sample size.

Study Power and Power Analysis

  • Study Power is 1 minus the Type 2 error rate, usually 0.8 (80%).
  • Power Analysis can be performed prior to the study to determine the required sample size or post hoc to validate the significance of findings.

Study Design

  1. Retrospective, Prospective, Cross-Sectional, or Longitudinal:
    • Cross-sectional: Examines a group at one time point.
    • Longitudinal: Follows patients over time.
  2. Observational vs. Experimental:
    • Observational: No alteration made, only observation.
    • Experimental: A maneuver is applied, followed by analysis.

Study Types and Hierarchy

  1. Level 1
    • Randomized Controlled Trials (RCT), Meta-analyses of RCTs, Systematic Reviews of Level 1 studies.
  2. Level 2
    • Poor quality RCTs (No blinding, <80% follow-up), Meta-analyses of non-RCT studies, etc.
  3. Level 3
    • Retrospective comparative studies, case control studies with historical controls.
  4. Level 4
    • Case series (no control group).
  5. Level 5
    • Expert opinion.

Tests to Analyze Data

Parametric Tests

  1. Unpaired Student T-Test: Compares the mean between two independent, normally distributed groups.
  2. ANOVA (Analysis of One-Way Variance): Used when multiple observations are made or categories are tested.

Non-Parametric Tests

  1. Chi-Squared: Analyzes differences between two groups of categorical variables.
  2. Mann-Whitney U: Non-parametric test for discrete data like gender.
  3. Fisher’s Exact Test: Used when sample size is small (n < 5).

Epidemiologic Tests

  1. Screening: Testing a large population for a disease of low prevalence. WHO Criteria for screening include the importance of the disease, known incidence, and treatment availability.

  2. Incidence: Number of new diagnoses in a defined population.

  3. Prevalence: Number of people with a condition at a given time (snapshot).

Sensitivity and Specificity

  1. Sensitivity: Percentage of true positives (TP / TP + FN).
  2. Specificity: Percentage of true negatives (TN / TN + FP).

Correlation Tests

  • Pearson’s Correlation: For parametric data.
  • Spearman’s Rank Correlation: For non-parametric data.

Survival Analysis

  1. Actuarial Method: Survival calculated at set times (e.g., annually).
  2. Kaplan-Meier Method: Survival recalculated each time there is a failure.

Survivorship Analysis for Joints

  • Based on the total number of joints followed, failures, and censored patients.
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