MATH 1106 · Probability and Statistics: Hypothesis Testing

Led by Ronald Fisher Simulacrum

The p-value, significance levels, Type I and II errors, one- and two-sample tests, matched pairs, and why the replication crisis is Fisher's legacy misapplied.

1. Module 1

   The Logic of Hypothesis Testing

   Led by Ronald Fisher Simulacrum

   The question

   "The p-value is the probability that the null hypothesis is true." This is wrong. What does the p-value actually measure — and why can a hypothesis be falsified but never finally verified?

   Outcome

   The student can state hypotheses, explain the p-value correctly, and describe the Type I/II error trade-off.

   Sub-units

   1. ○ 1.1 Hypothesis Formulation Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   The Test Statistic and One-Sample Tests

   Led by Ronald Fisher Simulacrum

   The question

   Mean lifetime 487 hours (claimed: 500), SD 42, n = 36. Compute the test statistic and p-value. Reject at α = 0.05? And what does "fail to reject" actually mean?

   Outcome

   The student can conduct one-sample z-tests and t-tests and interpret the result correctly.

   Sub-units

   1. ○ 2.1 One-Sample Test Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Two-Sample Tests: Difference of Means and Proportions

   Led by Ronald Fisher Simulacrum

   The question

   Group B scores 4 points higher than Group A. The difference is statistically significant (p = 0.03). Is it educationally important? What is the distinction — and what additional information resolves it?

   Outcome

   The student can conduct two-sample tests and construct confidence intervals for differences.

   Sub-units

   1. ○ 3.1 Two-Sample Test Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   Matched Pairs and Testing Proportions

   Led by Ronald Fisher Simulacrum

   The question

   Ten runners, before and after a training programme. Two-sample t-test or matched-pair? The matched-pair is more powerful here. Why — and what does it find?

   Outcome

   The student can identify matched-pair situations and conduct the matched-pair t-test.

   Sub-units

   1. ○ 4.1 Matched-Pair Test Open this unit → ✓ ↻
   Open this module → Print certificate of completion
5. Module 5

   The p-Value Controversy and the Limits of Significance Testing

   Led by Ronald Fisher Simulacrum

   The question

   A p-value of 0.049 and 0.051 are essentially the same evidence. The field treats them as publish vs discard. Choose a replication failure and analyse what it reveals about the misuse of significance testing.

   Outcome

   The student can explain p-hacking, publication bias, and the conditions for a well-powered, reliable study.

   Sub-units

   1. ○ 5.1 Final Essay: The Misuse of Significance Open this unit → ✓ ↻
   Open this module → Print certificate of completion