Hypothesis Testing: Types, Tests & Decision Rules

TAKEAWAYS:

• Hypothesis testing is the process of making data-driven decisions by comparing sample statistics to population parameters using null and alternative hypotheses.
• Key steps include formulating hypotheses, selecting a test statistic, determining significance level (α), and making a decision (reject/fail to reject H₀).
• Common tests include Z-test (large samples), t-test (small samples), Chi-square (categorical data), and ANOVA (multiple groups).
• Type I (false positive) and Type II (false negative) errors guide risk management in business decisions.
• Real-world applications include A/B testing in eSewa’s app updates, market segmentation by Daraz, and credit risk assessment by Nabil Bank.
• The p-value and critical value approaches are two methods to evaluate hypothesis test results.

1. What is Hypothesis Testing?

Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It helps researchers answer questions like:

• "Does the new marketing campaign increase sales?"
• "Is there a significant difference in customer satisfaction between two product versions?"
• "Does employee training improve productivity?"

Key Definitions

2. Steps in Hypothesis Testing

flowchart TD
    A["1. Formulate Hypotheses"] --> B["2. Choose Significance Level (α)"]
    B --> C["3. Select Test Statistic"]
    C --> D["4. Collect & Analyze Data"]
    D --> E["5. Calculate Test Statistic"]
    E --> F["6. Determine p-value or Compare to Critical Value"]
    F --> G["7. Make Decision (Reject/Fail to Reject *H₀*)"]
    G --> H["8. Draw Conclusion"]

Step-by-Step Worked Example: Daraz’s A/B Test

Scenario: Daraz wants to test if a new checkout button color (green vs. red) increases conversion rates.

• Population: All Daraz users in Nepal.
• Sample: 1,000 users randomly assigned to two groups.
• Hypotheses:
  • H₀: μ_red = μ_green (no difference in conversion rates).
  • H₁: μ_red ≠ μ_green (conversion rates differ).

Data:

• Red button group: 12% conversion (n₁ = 500).
• Green button group: 14% conversion (n₂ = 500).

Test: Two-sample Z-test (since sample sizes are large). Calculation:

1. Calculate pooled standard deviation (s_p).
2. Compute Z-statistic: $$Z=\frac{({\bar{X}}_1-{\bar{X}}_2)}{\sqrt{s_p^2\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}$$
3. Compare Z to critical value (Z = ±1.96 for α = 0.05) or find p-value.

Result: Z = 2.10 > 1.96 → Reject H₀. Conclusion: The green button significantly improves conversion rates (p < 0.05).

3. Types of Hypothesis Tests

4. Errors in Hypothesis Testing

Two types of errors can occur:

mindmap
  root((Errors in Hypothesis Testing))
    Type I Error["False Positive\n(α error)\nReject *H₀* when true"]
      Example["NEPSE approves a stock IPO that later fails."]
      Cost["Wasted resources, lost investor trust."]
    Type II Error["False Negative\n(β error)\nFail to reject *H₀* when false"]
      Example["Nabil Bank rejects a low-risk loan applicant."]
      Cost["Missed business opportunities."]
    Trade-off["α ↑ → β ↓\nα ↓ → β ↑"]

Real-World Impact:

• Type I Error (False Alarm): WhatsApp banning a user’s account for "suspicious activity" when they’re innocent.
• Type II Error (Missed Opportunity): Google not detecting a bug in an app update because the test sample was too small.

5. Decision Rules: p-value vs. Critical Value

Worked Example: Ncell’s Customer Satisfaction Survey Question: Does Ncell’s new customer service training improve satisfaction scores?

• H₀: μ_before = μ_after (no improvement).
• H₁: μ_after > μ_before (one-tailed test).
• Sample: 40 customers before/after training.
• Test: Paired t-test (same customers surveyed twice).
• Result: t = 2.5, p = 0.01 < 0.05 → Reject H₀. Conclusion: Training significantly improved satisfaction (p < 0.05).

6. Hypothesis Testing in Business Research

Applications in Nepali Companies

Case Study: Himalayan Java’s Market Expansion

Problem: Himalayan Java wants to test if organic coffee sales differ by region (Kathmandu vs. Pokhara). Hypotheses:

• H₀: μ_Kathmandu = μ_Pokhara.
• H₁: μ_Kathmandu ≠ μ_Pokhara.

Data:

• Kathmandu (n = 100): Mean sales = $500, σ = $50.
• Pokhara (n = 80): Mean sales = $450, σ = $40.

Test: Two-sample t-test (unequal variances). Calculation: $$t=\frac{(500-450)}{\sqrt{\frac{50^2}{100}+\frac{40^2}{80}}}=3.16$$ Critical t-value (df = 178, α = 0.05): ±1.97. Decision: |3.16| > 1.97 → Reject H₀. Conclusion: Sales differ significantly (p < 0.05). Action: Targeted marketing in Pokhara.

7. Common Mistakes to Avoid

1. Ignoring Assumptions: Using a t-test when data is not normally distributed.
2. Incorrect Hypothesis Formulation: Testing H₀: "Sales increase" (should be H₀: "Sales do not increase").
3. P-hacking: Adjusting α or sample size to force significance.
4. Overlooking Effect Size: A significant p-value doesn’t always mean a practical difference (e.g., 1% vs. 0.9% conversion rates).
5. Multiple Testing: Running 10 tests increases Type I error risk (use Bonferroni correction).

## In the Real World

1. eSewa’s Fraud Detection

   • Idea Used: Chi-square test for categorical data.
   • How: eSewa tests if transaction patterns (time, amount) differ between fraudulent and legitimate users. A significant Chi-square result triggers alerts.
   • Example: If fraudsters use transactions > $500 at night more often (p < 0.05), eSewa flags such transactions for manual review.

2. Nabil Bank’s Loan Approval

   • Idea Used: Logistic Regression (Chi-square-based).
   • How: The bank tests whether factors like income, credit score, and employment status predict loan defaults. A rejected H₀ (e.g., "Credit score doesn’t matter") leads to stricter approval criteria.
   • Example: Data shows applicants with scores < 600 default 40% of the time (p < 0.001), so Nabil Bank raises the minimum score to 650.

3. Daraz’s Dynamic Pricing

   • Idea Used: ANOVA for multi-group comparisons.
   • How: Daraz tests if product prices should vary by region (Kathmandu vs. rural areas). If ANOVA shows significant differences (p < 0.05), prices are adjusted dynamically.
   • Example: A laptop sells for $800 in Kathmandu but $750 in Pokhara (F = 5.2, p = 0.02), so Daraz sets regional price tiers.

4. Pathao’s Driver Ratings

   • Idea Used: Correlation analysis (Pearson’s r).
   • How: Pathao tests if driver ratings correlate with ride duration or cancellation rates. A strong negative correlation (r = -0.7, p < 0.05) might lead to bonuses for high-rated drivers.
   • Example: Drivers with >4.5 ratings have 20% fewer cancellations (p = 0.01), so Pathao promotes them.

5. NEPSE’s Investor Sentiment

   • Idea Used: Z-test for proportions.
   • How: NEPSE tests if investor confidence differs before/after policy changes. A rejected H₀ (e.g., "Confidence is unchanged") triggers communication strategies.
   • Example: 60% of investors were bullish before a policy change vs. 70% after (Z = 2.5, p = 0.01), indicating improved sentiment.

## Exam Tip

How This Unit is Examined in PU (Pokhara University):

1. Theoretical Questions (30%):

   • Define H₀, H₁, p-value, and Type I/II errors.
   • Differentiate between parametric (Z, t) and non-parametric (Chi-square) tests.
   • Explain when to use one-tailed vs. two-tailed tests.

2. Problem-Solving (50%):

   • Given: Hypotheses, sample data, and significance level.
   • Do:
     • Identify the correct test (Z, t, Chi-square, ANOVA).
     • Calculate test statistic (show formulas).
     • Compare to critical value or find p-value.
     • State decision (reject/fail to reject H₀) and conclusion.
   • Example Question:

     "A sample of 50 Ncell users has an average call drop rate of 3% (σ = 0.5). Test at α = 0.05 if drops exceed the industry standard of 2%."

3. Case Studies (20%):

   • Apply hypothesis testing to real business scenarios (e.g., bank loan defaults, e-commerce sales).
   • Tip: Always link your answer to business decisions (e.g., "Reject H₀ → Launch the campaign").

Common Pitfalls in Exams:

• Forgetting to state assumptions (e.g., normality, independence).
• Misinterpreting one-tailed vs. two-tailed tests (e.g., using Z = ±1.645 for one-tailed).
• Incorrectly calculating degrees of freedom (e.g., t-test df = n - 1, ANOVA df = groups - 1).
• Ignoring effect size: Even if p < 0.05, ask if the difference is meaningful (e.g., 51% vs. 50% conversion).

Quick Revision Checklist:

Final Note: Hypothesis testing is the bridge between data and decision-making. Master it, and you’ll ace business research—and help companies like Nabil Bank, Daraz, and NTC make data-driven choices!