Historical Context
“Post Hoc” originates from the Latin phrase “Post hoc, ergo propter hoc,” which translates to “After this, therefore because of this.” This term has been a significant point of discussion in philosophy and logic due to its implications on causation and correlation.
Types/Categories
1. Post Hoc Fallacy
- Definition: A logical fallacy that assumes that if one event happens after another, then the first event must be the cause of the second.
- Example: Assuming that a rooster crowing causes the sun to rise because the crowing happens before the sunrise.
2. Post Hoc Tests in Statistics
- Definition: Statistical analyses performed after an experiment to find patterns or relationships that were not specified before the data was seen.
- Examples: Tukey’s HSD, Scheffé’s Test, and Bonferroni correction.
Key Events
-
Philosophical Discussions (Ancient Greece):
- Early philosophers like Aristotle discussed causation and the fallacies associated with it.
-
Development of Post Hoc Tests (20th Century):
- The development of statistical methods for multiple comparison testing emerged in the mid-20th century, refining data interpretation methods.
Detailed Explanations
Philosophical Implications
The “Post Hoc” fallacy is a logical misstep that conflates correlation with causation. It is crucial to distinguish that just because one event follows another, it doesn’t imply the first caused the second.
Statistical Analysis
Post hoc analyses are used to test the reliability of findings after an experiment. They involve multiple comparison methods to minimize the probability of Type I errors (false positives).
Mathematical Formulas/Models
Mermaid diagrams are helpful for visualizing post hoc comparisons.
graph TD
A[Experiment]
B[Post Hoc Tests]
C[Tukey's HSD]
D[Scheffé's Test]
E[Bonferroni Correction]
A --> B
B --> C
B --> D
B --> E
Importance
Understanding the post hoc fallacy and using post hoc statistical tests appropriately is crucial for interpreting experimental data correctly. It prevents drawing erroneous conclusions from mere sequential events and aids in scientific rigor.
Applicability
- Research: To validate the significance of experiment results.
- Medicine: To evaluate the efficacy of treatments post-trials.
- Economics: For analyzing trends post-policy implementations.
Examples
- Medical Research: Using post hoc tests to determine if different dosages of a drug have distinct effects.
- Educational Studies: Analyzing student performance across various teaching methods.
Considerations
- False Positives: Be cautious of inflated error rates when performing multiple comparisons.
- Confounding Variables: Ensure proper controls to avoid misleading correlations.
Related Terms with Definitions
- Correlation vs. Causation: The concept that correlation between two variables does not imply one causes the other.
- Type I Error: Incorrect rejection of a true null hypothesis (false positive).
- Causality: The relationship between cause and effect.
Comparisons
- Post Hoc vs. Pre Hoc: Pre hoc analyses are planned before data collection, while post hoc tests are conducted after seeing the data.
- Causal Inference vs. Correlation Analysis: Causal inference focuses on causation, whereas correlation analysis identifies relationships without assuming causality.
Interesting Facts
- The phrase “Post hoc, ergo propter hoc” has been debated for centuries in philosophical circles, underscoring the human tendency to find patterns and causal relationships.
Inspirational Stories
- John Snow: The father of modern epidemiology used a form of post hoc analysis to identify the source of a cholera outbreak in London in the 1850s, saving countless lives.
Famous Quotes
- “Correlation does not imply causation.” - Many Researchers
Proverbs and Clichés
- “Don’t put the cart before the horse.” - Emphasizes logical sequence over mere temporal order.
Expressions
- “After this, therefore because of this.” - Translation of “Post hoc, ergo propter hoc.”
Jargon and Slang
- “Post Hoc Analysis”: Often used in research to refer to retrospective analysis after seeing the data.
FAQs
**Q1: What is a post hoc fallacy?**
**Q2: How is post hoc used in statistics?**
**Q3: What are some common post hoc tests?**
References
- Aristotle. “Physics.”
- John Snow. “On the Mode of Communication of Cholera.” (1855)
- Tukey, J.W. (1953). “The Problem of Multiple Comparisons.”
Summary
Post hoc, signifying “after the event,” has vital applications in logic and statistics. While it offers valuable insights post-experimentation, care must be taken to avoid logical fallacies and erroneous conclusions. Understanding its proper use ensures robust and reliable data interpretation, crucial across various fields, from medical research to economics.
