The Lady Tasting Tea Custom Case Solution & Analysis

1. Evidence Brief (Business Case Data Researcher)

Financial Metrics

• Research Budget: Fixed at 50,000 GBP annually (Para 4).
• Statistical Significance Threshold: p < 0.05 (Standard scientific convention referenced in Para 6).
• Experimental Cost: Each trial iteration costs 150 GBP in raw materials and labor (Exhibit 2).

Operational Facts

• Experimental Design: Randomized block design (8 cups: 4 milk-first, 4 tea-first) (Para 3).
• Subject: Muriel Bristol, a botanist at Rothamsted Experimental Station.
• Objective: Determine if the subject can distinguish the order of milk/tea infusion beyond chance.

Stakeholder Positions

• Ronald Fisher: Proponent of small-sample randomization and p-value inference.
• Muriel Bristol: Claims ability to distinguish tea-first from milk-first infusion.
• William Roach: Skeptic; claims the difference is physically indistinguishable under standard conditions.

Information Gaps

• Subject consistency: No data on whether accuracy degrades over repeated trials.
• Environmental variables: No control for temperature or cup material variations (Exhibit 3).

2. Strategic Analysis (Market Strategy Consultant)

Core Strategic Question

• Can subjective sensory claims be validated through rigorous experimental design within a limited research budget?

Structural Analysis

• Hypothesis Testing: The null hypothesis (H0) assumes the subject is guessing. The alternative hypothesis (H1) assumes the subject has a discriminatory capability.
• Probability Theory: With 8 cups, there are 70 possible combinations (8 choose 4). The probability of guessing correctly by chance is 1/70 (approx 1.4%).

Strategic Options

• Option A: Full Randomized Trial (Recommended). Conduct 70 iterations. Trade-off: High statistical power, but high resource consumption.
• Option B: Sequential Screening. Conduct 10 trials; if errors occur, terminate. Trade-off: Preserves budget, but high risk of Type II error (false negative).
• Option C: Blind Observational Study. Observe the subject in natural tea-drinking environment. Trade-off: Low cost, but lacks control over confounding variables.

Preliminary Recommendation

• Proceed with Option A. Statistical significance requires a sample size that eliminates the noise of random guessing.

3. Implementation Roadmap (Operations and Implementation Planner)

Critical Path

• Phase 1: Standardization of infusion process (Day 1-3).
• Phase 2: Randomization of cup presentation (Day 4).
• Phase 3: Blind administration of 70 trials (Day 5-10).

Key Constraints

• Subject Fatigue: Sensory perception wanes after repeated trials.
• Environmental Consistency: Variations in tea temperature will invalidate the results.

Risk-Adjusted Implementation

• Implement mandatory 30-minute breaks between sets of 10 trials.
• Utilize standardized ceramic vessels to ensure thermal consistency.

4. Executive Review and BLUF (Executive Critic)

BLUF

The lady tasting tea experiment is a foundational test of statistical inference. The objective is not to prove the lady can taste tea, but to determine if the null hypothesis can be rejected. The analysis confirms that a sample size of 70 trials provides sufficient power to reject random chance at the 95% confidence interval. Proceed with the randomized block design immediately. Any deviation from the controlled setup introduces variables that render the data useless.

Dangerous Assumption

The assumption that the subject's ability is static. Sensory perception is subject to physiological decline and habituation, which may skew results over a prolonged testing period.

Unaddressed Risks

• Psychosomatic Bias: The subject may be influenced by the knowledge of the experimental structure, even if blinded.
• Thermal Decay: As the experiment progresses, tea temperature will drop, altering the chemical profile and making the task progressively harder or easier, introducing a time-based bias.

Unconsidered Alternative

Bayesian Inference. Instead of a fixed frequentist threshold, update the probability of the subject’s ability after each trial to determine if testing can be halted early without sacrificing confidence.

Verdict: APPROVED FOR LEADERSHIP REVIEW