Choosing the Right Test
Master the decision-making process for selecting the appropriate hypothesis test
Lesson Objectives
By the end of this lesson, you will be able to:
- Ask the right questions to identify which hypothesis test to use
- Use a decision flowchart to systematically choose tests
- Distinguish between all hypothesis tests from Modules 8 and 9
- Avoid common mistakes in test selection
- Confidently select the correct test for any scenario
1. The Big Picture: All Hypothesis Tests
You've now learned SEVEN different hypothesis tests across Modules 8 and 9. Here's the complete summary:
| Test Name | What It Tests | Test Statistic | Key Identifier |
|---|---|---|---|
| One-sample z-test (mean) | One population mean (σ known) | z | Known σ, one group |
| One-sample t-test (mean) | One population mean (σ unknown) | t | Unknown σ, one group |
| One-sample z-test (proportion) | One population proportion | z | Proportion, one group |
| Two-sample t-test (independent) | Two population means (independent) | t | Two separate groups, means |
| Paired t-test | Mean difference (dependent samples) | t | Same subjects twice or matched pairs |
| Two-sample z-test (proportions) | Two population proportions | z | Two groups, proportions/percentages |
2. Decision Flowchart
Hypothesis Test Decision Flowchart
If testing a MEAN:
NO → One-sample t-test
PAIRED → Paired t-test
If testing a PROPORTION:
One-sample z-test for proportion
Two-sample z-test for proportions
3. Key Decision Questions
Question 1: Mean or Proportion?
- Mean (μ): Average, mean, typical value, measurements on a continuous scale
- Examples: average height, mean test score, average income, mean blood pressure
- Proportion (p): Percentage, proportion, rate, probability of success, fraction
- Examples: proportion who pass, percentage defective, cure rate, voter support
Question 2: One Sample or Two Samples?
- One sample: Comparing sample data to a known population value or claim
- Example: "The average height is claimed to be 5'8". Does our sample support this?"
- Two samples: Comparing two groups or populations
- Example: "Is the average height of men different from women?"
Question 3 (For Two Samples - Means): Independent or Paired?
- Independent: Two completely separate, unrelated groups
- Example: Group A receives treatment, Group B receives placebo (different people)
- Paired (Dependent): Same subjects measured twice OR matched pairs
- Example: Blood pressure before and after medication (same people)
- Example: Twins, one in each group (matched pairs)
Question 4 (For One Sample - Mean): Is σ Known?
- σ known: Use z-test (rare in practice)
- σ unknown: Use t-test (most common)
4. Practice Scenarios: Identify the Test
Scenario 1
A teacher claims that the average test score in her class is 75. You randomly sample 30 students and find x̄ = 78, s = 8. Test the claim.
Reasoning:
- Testing a mean (average test score)
- One sample (one class)
- σ unknown (we have s, not σ)
Test: H₀: μ = 75, Hₐ: μ ≠ 75
Scenario 2
A pharmaceutical company tests if Drug A lowers cholesterol more than Drug B. They give Drug A to 40 patients and Drug B to 35 different patients, measuring cholesterol after treatment.
Reasoning:
- Testing means (cholesterol levels)
- Two samples (Drug A group and Drug B group)
- Independent (different patients in each group)
Test: H₀: μ₁ = μ₂, Hₐ: μ₁ < μ₂ (or μ₁ ≠ μ₂)
Scenario 3
A weight loss program measures the weight of 25 participants before and after an 8-week program. Does the program result in significant weight loss?
Reasoning:
- Testing means (weight)
- Two measurements (before and after)
- SAME participants measured twice → PAIRED!
Test: Calculate d = Before - After for each person, then test H₀: μd = 0, Hₐ: μd > 0
Scenario 4
A quality control manager claims that no more than 5% of products are defective. A random sample of 200 products finds 15 defective items. Test the claim.
Reasoning:
- Testing a proportion (percentage defective)
- One sample (one group of products)
- Comparing to a claimed value (5% or p₀ = 0.05)
Test: H₀: p = 0.05, Hₐ: p > 0.05 (right-tailed)
Scenario 5
A researcher wants to know if men and women differ in support for a policy. She surveys 300 men (180 support) and 250 women (165 support).
Reasoning:
- Testing proportions (support vs. not support)
- Two samples (men and women)
- Independent groups (different people)
Test: H₀: p₁ = p₂, Hₐ: p₁ ≠ p₂ (two-tailed)
Scenario 6
Researchers measure reading speed for 12 children before and after a speed-reading intervention. Does the intervention improve reading speed?
Reasoning:
- Testing means (reading speed)
- Before and after measurements
- SAME 12 children measured twice → PAIRED!
Test: Calculate d = After - Before, test H₀: μd = 0, Hₐ: μd > 0
5. Common Mistakes and How to Avoid Them
Mistake #1: Using Independent Test for Paired Data
Wrong: Testing before/after data with a two-sample t-test
Right: Use a paired t-test whenever the same subjects are measured twice
Why it matters: Using the wrong test loses statistical power and can lead to incorrect conclusions!
Mistake #2: Confusing Proportions with Means
Wrong: Using a t-test when comparing percentages
Right: Percentages, rates, and proportions require z-tests
Tip: If the data is categorical (yes/no, success/failure), it's a proportion!
Mistake #3: Not Checking Conditions
Wrong: Blindly applying a test without verifying assumptions
Right: Always check sample size, normality, and independence conditions
Why it matters: Violating conditions can make your results invalid!
Mistake #4: Using z-test When σ is Unknown
Wrong: Using a z-test for means when you only have sample standard deviation s
Right: Use t-test when σ is unknown (which is almost always!)
Tip: If the problem gives you s (not σ), use a t-test!
6. Quick Reference Summary
| Scenario | Test to Use | Quick Check |
|---|---|---|
| One group, testing a mean, σ unknown | One-sample t-test | Have x̄, s, n → compare to μ₀ |
| One group, testing a proportion | One-sample z-test (proportion) | Have p̂, n → compare to p₀ |
| Two different groups, comparing means | Independent two-sample t-test | Two separate groups, x̄₁ vs x̄₂ |
| Same subjects twice OR matched pairs, comparing means | Paired t-test | Before/after or twins → calculate differences |
| Two groups, comparing proportions | Two-sample z-test (proportions) | p̂₁ vs p̂₂, use pooled proportion |
Final Practice: Test Your Skills
Challenge 1: A company tests two ad campaigns. They show Ad A to 500 random customers and Ad B to 450 different random customers. They measure the proportion who make a purchase. Which test?
Challenge 2: A researcher tests if a meditation app reduces anxiety. She measures anxiety scores for 30 people before using the app and again after 4 weeks of use. Which test?
Challenge 3: A factory claims the average widget weight is 50 grams. You sample 40 widgets and find x̄ = 48.5, s = 3.2. Which test?
Key Takeaways
- Always start by identifying: mean or proportion?
- Then ask: one sample or two?
- For two samples with means: independent or paired?
- For one sample with means: is σ known? (Almost always NO → use t-test)
- Paired data = same subjects twice or matched pairs → MUST use paired t-test
- Proportions/percentages → use z-tests
- Practice with many scenarios until test selection becomes automatic!