Study Guide
Nonparametric statistics
Undergraduate materials for Density and smoothing: Comparison to parametric alternatives.
What this standard means
- Comparison to parametric alternatives
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Define population, sample, and parameter of interest 2. Check assumptions before applying a test 3. Interpret results in context, not just numerically
_See printable PDF for diagram._
Common misconceptions
Address these early. Name the misconception, show a correct model, then have students retry a short item.
- P-hacking or misreading confidence intervals — watch for this when practicing comparison to parametric alternatives; pause, model the correct approach, then retry.
- Confusing correlation with causation — watch for this when practicing comparison to parametric alternatives; pause, model the correct approach, then retry.
- Using wrong distribution for the data type — watch for this when practicing comparison to parametric alternatives; pause, model the correct approach, then retry.
Quick checks
Use as 2–5 minute formative checks mid-lesson. Students should finish independently.
1. In 1–2 minutes: complete one straightforward item aligned to Comparison to parametric alternatives. 2. True or false (and fix if false): a common statement about comparison to parametric alternatives. 3. Write or show one example that correctly demonstrates comparison to parametric alternatives.
Exit tickets
End-of-lesson evidence of learning. Collect, sort into got-it / almost / reteach, and plan the next day.
1. Exit ticket: Solve one item for Comparison to parametric alternatives and circle the strategy you used. 2. Exit ticket: In one sentence, what does comparison to parametric alternatives mean? Give a tiny example.
Challenge problems
Stretch tasks for students ready for more complexity after core practice.
1. Challenge: Create a multi-step problem that requires comparison to parametric alternatives, then solve it. 2. Challenge: Find and correct the error in a flawed solution related to Comparison to parametric alternatives. Explain the fix.
Enrichment questions
Open-ended extensions that deepen understanding and connections across standards.
1. Enrichment: How does Comparison to parametric alternatives connect to an earlier or later standard in Density and smoothing? 2. Enrichment: Invent a real-world scenario where comparison to parametric alternatives matters and explain the math.
Math talk prompts
Use for turn-and-talk, whole-class discussion, or written reflection.
- How would you explain comparison to parametric alternatives to a classmate?
- What model or strategy helps most with Comparison to parametric alternatives?
- Where might someone go wrong on this standard, and how would you help them?
Vocabulary review
Revisit these terms with examples, non-examples, and student-friendly definitions.
- comparison to parametric alternatives — the focus skill for Comparison to parametric alternatives
- standard — what students should know and be able to do (Comparison to parametric alternatives)
- domain — Density and smoothing
- explain — describe reasoning with words, models, or equations
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Comparison to parametric alternatives.
- [ ] Selects appropriate statistical methods
- [ ] Computes and interprets estimates and tests
- [ ] Communicates uncertainty clearly
Materials for this standard
- Practice Problems — 20 printable sets (computational and word problems)
- Word Problems — 20 word-only sets plus 10 difficulty-tier sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors