Misconception Heatmap
Top 3 misconceptions per topic, shaded by % of students
| Topic | Misconception 1 | Misconception 2 | Misconception 3 |
|---|---|---|---|
| Hypothesis Testing | Thinks p-value is probability H₀ is true 67% | Confuses α with p-value 45% | Rejects H₀ when p > α 28% |
| t-test vs z-test | Uses z-test when σ unknown 58% | Ignores sample size threshold 42% | Applies z-test to small samples 31% |
| Confidence Intervals | Thinks 95% CI means 95% chance μ is in interval 71% | Confuses CI width with confidence level 38% | Ignores sample size effect on width 25% |
| Type I & II Errors | Swaps Type I and Type II definitions 52% | Thinks reducing α always better 44% | Ignores power in study design 36% |
| Central Limit Theorem | Thinks CLT applies to any sample size 48% | Confuses σ with σ/√n 55% | Applies CLT to non-independent samples 22% |
| Normal Distribution | Assumes all data is normally distributed 41% | Misreads z-score direction 33% | Forgets to standardize before lookup 29% |
38% of students have not yet demonstrated reliable reasoning on hypothesis testing.
Top gap: interpreting p-value as P(H₀ is true), affecting 67% of the cohort
At-risk students
Top Stuck Points
2-min interventions
Interpreting p-value as P(H₀ is true)
Quick poll: 'What does p=0.03 mean?' then show the 3 common wrong answers before the correct frequentist definition.
Using z-test when σ is unknown
Draw the decision tree on the board: 'Do you know σ?' → No → t-test. Takes 90 seconds.
Confusing CI interpretation (95% chance μ is in interval)
Simulate 20 CIs live in R/Excel. Show ~19 contain μ. 'The interval is random, not μ.'
Rejecting H₀ when p > α
Show an underpowered study where a real effect exists but p > α. Ask: 'Is H₀ true here?' Students see that failing to reject ≠ accepting H₀, it means insufficient evidence.
Swapping Type I and Type II error definitions
Use the courtroom analogy: Type I = convicting innocent (α), Type II = freeing guilty (β).
Based on 33 active students this week. Students may appear in multiple stuck points.
Students Needing Attention
12 of 47 students flagged. Click any row to see their misconceptions.
| Student | Hypothesis Testing | t-test vs z-test | P-values | Confidence Intervals | Type I/II Errors | Normal Dist. | Avg ▼ |
|---|---|---|---|---|---|---|---|
| Avery Brown | 35% | ||||||
| Taylor Kim | 38% | ||||||
| Jamie Lee | 41% | ||||||
| Alex Chen | 45% | ||||||
| Morgan Davis | 58% | ||||||
| Jordan Park | 62% | ||||||
| Quinn Garcia | 69% | ||||||
| Casey Williams | 74% | ||||||
| Sam Johnson | 82% | ||||||
| Drew Martinez | 85% | ||||||
| Maria Santos | 88% | ||||||
| Riley Thompson | 91% |
Showing 12 students flagged for attention out of 47 enrolled