basics 1 -probability, event, outcome space, construct and content validity
Page 1: Introduction to Biostatistics
Basic concepts: Probability, events, outcome space, construct validity, content validity
Page 2: Key Concepts
Key concepts introduced in the class:
Probability, odds (including odds ratio)
Event and outcome space
Construct validity
Content validity
Page 3: Insight on Agreement
Humorous understanding of statistics:
Probability of all statisticians agreeing on something is very low.
Page 4: Understanding Probability
Probability is defined as:
Relative frequency of an event occurring in the long run.
Notations:
P(x) = 0: event x will not occur.
P(x) = 1: event x will occur.
P(not x) = 1 – P(x).
The course focuses on frequentist framework compared to Bayesian.
Page 5: Bayesian Statistics Overview
Frequentist definition:
Chance as relative frequency in the long run.
Bayesian definition:
Conditional probability based on data and prior beliefs.
Example: Probability of HIV infection.
More advanced topics included later on count data.
Page 6: Odds and Related Concepts
Definition of Odds:
Odds = probability of event happening divided by probability of event not happening.
Formula: Odds = P(x) / (1 – P(x))
Alternative: P(x) = Odds / (1 + Odds)
Page 7: Odds Ratio Calculation
Example of odds for hypertension:
Obese: 14/7 = 2
Non-obese: 12/27 ≈ 0.444
Odds Ratio (OR) = 2 / 0.444 = 4.505.
Interpretation: Obese individuals have 4.5 times the odds of hypertension.
Page 8: Defining Events
Probability as relative frequency requires:
Clear definition of the event/outcome.
Understanding of possible outcomes (outcome space).
Discussion topics include:
Events like Fukushima, AIDS, Covid-19 rates, and climate change.
Page 9: Fukushima Event Discussion
Relevant figures and data involved in events.
Page 10: Understanding an AIDS Victim
Definitions and clarifications:
Death due to HIV infection and related health issues.
Challenges in defining and attributing causality.
Reference: Revised Surveillance Case Definition for HIV Infection.
Page 11: Covid-19 Infection Rate Concerns
Key considerations include:
Who and what we count.
Test sensitivity and specificity issues.
Reporting methods (day, week, area).
Uncertainty estimation inherent in numbers.
Page 12: Global Climate Change Complexity
Questions to explore:
Definition of climate and evidence for climate change.
Temperature considerations, geographical disparities, global warming impacts.
Page 13: From Abstract Concepts to Concrete Definitions
Steps to define constructs:
Conceptual definition: Clarifying what you mean.
Operational definition: How variables are defined and measured.
Page 14: Construct Validity Focus
Construct validity refers to:
Whether variables accurately represent the construct of interest.
Examples include health indicators and global temperature metrics.
Page 15: Issues of Low Construct Validity
Importance of gathering authentic data on constructs.
Low construct validity cannot be resolved with mathematical adjustments.
If too low, research validity is compromised.
Page 16: Quote on Construct Validity
"It is not just incorrect; it is not even wrong." - Wolfgang Pauli.
Page 17: Example of Mismeasure
S.J. Gould's example on cranial capacity and intelligence:
Misconception: Skull volume equated to intellectual capacity.
Page 18: Content Validity Considerations
Content validity evaluates:
Completeness of variables in relation to the construct of interest.
Focuses on whether variables collectively cover relevant aspects of the research question (RQ).