🧪 Ronald Fisher: The p‑value Rebel

Philosophy: Evidence, not decisions

Fisher believed statistics should help scientists measure evidence against a null hypothesis.

Key ideas

• The null hypothesis is a straw man you try to poke holes in.
• The p‑value measures how incompatible the data are with the null.
• You never “accept” the null — you simply fail to find evidence against it.
• No fixed rules. No rigid thresholds.
• Statistics is about learning, not making yes/no decisions.

Fisher’s vibe:

The scientist as a detective, gathering clues and weighing evidence.

⚔️ Jerzy Neyman & Egon Pearson: The Decision‑Theorists

Philosophy: Decisions, not evidence

Neyman and Pearson believed statistics should guide actions, not beliefs.

Key ideas

• You must choose between two hypotheses:
  
• You control long‑run error rates:
  Type I error (false positive)
  Type II error (false negative)
• You choose a fixed α (significance level) before collecting data.
• You define critical regions and make binary decisions:
• Reject
• Fail to reject

Neyman–Pearson vibe:

The statistician as a quality‑control officer: strict rules, long‑run guarantees, no interpretation.

💥 Why They Fought

Fisher thought Neyman–Pearson’s approach was:

• too rigid
• too mechanical
• too focused on long‑run behavior instead of the actual experiment
• philosophically misguided

Neyman thought Fisher’s p‑values were:

• subjective
• inconsistent
• lacking clear decision rules
• too dependent on interpretation

They respected each other’s brilliance but fundamentally disagreed on what statistics is for.

🧩 The Modern Mess: We Use Both

Here’s the twist:
Modern hypothesis testing is a Frankenstein hybrid of both philosophies.

We use:

• Fisher’s p‑values
• Neyman–Pearson’s α levels, Type I/II errors, and decision rules

But these ideas don’t actually fit together perfectly.

Example of the hybrid:

• Compute a p‑value (Fisher)
• Compare it to a pre‑chosen α (Neyman–Pearson)
• Make a binary decision (Neyman–Pearson)
• Then interpret the p‑value as “strength of evidence” (Fisher)

It’s like mixing oil and water — but we’ve been doing it for 80 years.

🎨 A Simple Analogy

Fisher = a thermometer

Tells you how hot the evidence is.

Neyman–Pearson = a fire alarm

If the temperature crosses a threshold, the alarm goes off.

We now use the thermometer to decide when to trigger the fire alarm.
Fisher would roll his eyes. Neyman would sigh.

📚 A Quick Side‑by‑Side

Feature	Fisher	Neyman–Pearson
Purpose	Measure evidence	Make decisions
Key tool	p‑value	Critical values, α, β
Hypotheses	Only	and
Interpretation	Continuous evidence	Binary decision
Accept ?	Never	Yes (implicitly)
Error control	None	Type I & II errors
Philosophy	Inductive inference	Long‑run frequency control

🎯 Why This Matters for Students

Understanding the Fisher–Neyman battle helps students see:

• why hypothesis testing feels contradictory
• why p‑values are often misinterpreted
• why “statistical significance” is not the same as evidence
• why modern statistics is moving toward effect sizes, confidence intervals, and Bayesian methods

It’s not that students are confused — it’s that the system itself is a compromise between two incompatible worldviews.