Statistical Thinking Notes

Introduction to Statistics

  • Learning Objectives

    • Understand the three meanings of "statistics".

    • Differentiate variable types and be aware of systematic bias and stochasticity.

    • Recognize that statistical tests model reality.

  • Statistics vs Mathematics

    • Statistics uses mathematical principles but is not equivalent to mathematics.

Types of Data in Statistics

  • Categorical Data

    • Descriptive: Examples include gender, ethnicity.

  • Ordinal Data

    • Ranked order: Examples include pain scales or disease severity.

  • Numerical Data

    • Discrete: Countable values (e.g., number of individuals).

    • Continuous: Measured (e.g., height, weight).

    • Interval: Meaningful differences but no true zero (e.g., temperature).

    • Ratio: True zero exists (e.g., height in cm).

Stochasticity and Systematic Bias

  • Definitions

    • Stochasticity: Random variation affecting outcomes; observed as error in statistics.

    • Systematic Bias: Consistent deviation in measurement (e.g., scale readings).

  • Modeling Reality

    • Every biological variable includes stochastic elements; a statistical model reflects this.

    • Importance of ensuring model assumptions are met to validate conclusions.

Characteristics of Statistical Thinking

  • Data collection must align with hypothesis-driven research questions.

  • Use statistical methods to extract meaningful conclusions from complex data.

  • Understand that data analysis is informed by theoretical considerations (modeling relationships).

Good vs Bad Research Questions

  • Good questions should allow for complex data analysis and hypothesis testing:

    • Example of a good question: "How does childhood obesity correlate with academic performance in elementary school children?"

  • Avoid overly broad or overly narrow questions that do not guide meaningful research.

Misconceptions About Statistics

  • Statistics cannot 'prove' anything; they indicate likelihoods based on data.

  • Misunderstandings around P-values: A threshold does not guarantee truth.

  • Data always needs an appropriate analysis method, no matter the calculation ease.

Final Notes

  • Emphasis on the necessity of understanding statistics in healthcare, emphasizing involvement in evidence-based medicine.

  • Statistical literacy is crucial for interpreting and validating research in biological and health sciences.