2 Sample Tests Continued (meditation and caffeine)

Efficacy of Vaccines for HIV and AIDS

• Experimental Design Overview

  • Participants: Approximately 14,000 volunteers

  • Group Division:

    • Half received the placebo (control group)

    • Half received the vaccine (treatment group)

  • Data Collected:

    • Number of infections in both groups to compare efficacy.

• Statistical Procedure

  • Sample Proportions Calculated:

    • Each group’s infection rates were computed as proportions.

  • Two-Sample Z-Test:

    • Null Hypothesis (H0): The vaccine does not work; infection rates are equal.

    • Alternative Hypothesis (H1): Vaccinated group has a lower infection rate than the placebo group.

Effect of Caffeine on Athletic Performance

• Research Question

  • Does caffeine improve cardiovascular athletic performance (running, cycling, swimming)?

  • Focus: Improvements in endurance and speed.

• Discussion Points:

  • General consensus: Caffeine might enhance performance through increased alertness and endurance.

  • Potential for drawbacks such as post-caffeine crashes impacting performance.

Experimental Design for Caffeine Study

• Case Study:

  • Subject: A retired doctor with a rowing background.

  • Design: Self-experimentation with only one participant.

  • Control and Treatment:

    • Comparison between caffeinated and decaffeinated pills (i.e., vitamin C pills).

  • Blinding:

    • Subject unaware of whether he received caffeine or placebo to avoid bias.

    • Randomization by his wife choosing the treatment before each session.

• Data Collection:

  • Measurement of distance rowed in one hour under both conditions.

Results Analysis of Caffeine Study

• Findings Representation:

  • Data visualized as distance over time.

  • Key Observations:

    • Caffeinated sessions showed a significantly greater average distance covered compared to uncaffeinated ones.

• Statistical Analysis Steps:

  • Measures of central tendency (sample means) and variability (standard deviations) calculated for both conditions.

  • Question posed: Is there a statistically significant difference?

• Statistical Tests Used:

  • Two-Sample T-Test:

    • Null Hypothesis: Mean distance rowed caffeinated = mean distance rowed uncaffeinated.

    • T-test statistic calculated with a result indicating strong evidence against the null hypothesis (T = 5.83, P < 0.000001).

• Conclusion:

  • Strong evidence that caffeine enhances rowing performance.

  • Result implications: Despite the personal nature of the experiment, it indicates potential benefits of caffeine for athletic performance.

Limits of the Study and Further Considerations

• Experimental Limitations:

  • Individual variation: Results based on one person's data limit generalizability.

  • Alternative designs, like a matched pairs approach, could be explored for further validation – alternating caffeine and placebo treatments each week.

Two-Sample Proportion Z-Test for Empathy Study

• Research Question:

  • Does meditation improve empathy?

• Experimental Setup:

  • 39 participants split into treatment (20 taught to meditate) and control (19 wait-listed).

• Empathy Measurement:

  • Participants' willingness to give up their chair for a person on crutches as an empathy proxy.

• Results:

  • 50% of meditators offered seats vs. 16% of non-meditators.

  • Null Hypothesis: No difference in proportions of those offering seats in both groups.

• Statistical Analysis:

  • Two-proportion z-test conducted to determine significance of results.

  • Result: Statistically significant with a clear implication that meditation may enhance empathy.

  • Consideration of small sample sizes may limit broader applicability.

Summary of Statistical Procedures

• Emphasize the dual relationship between hypothesis testing and confidence intervals.

• Understand that rejecting the null hypothesis indicates strong evidence for an effect (caffeine and empathy enhancement), even if sample sizes are constrained.