A pharmaceutical company is testing a new drug claimed to lower cholesterol levels. The lead researcher believes the drug is effective and designs a clinical trial. Here are the details:
1. 200 participants with high cholesterol are randomly divided into two groups of 100 each.
2. Group A receives the new drug, Group B receives a placebo.
3. Cholesterol levels are measured before and after a 30-day treatment period.
4. The researcher considers the treatment effective if there’s a statistically significant difference (p < 0.05) between the groups.
Results:
– Group A (Drug): Mean cholesterol reduction of 15 mg/dL, standard deviation 8 mg/dL
– Group B (Placebo): Mean cholesterol reduction of 12 mg/dL, standard deviation 7 mg/dL
The lead researcher concludes that the drug is effective in lowering cholesterol.
1. T-test for statistical significance:
Null hypothesis (H₀): There is no difference between the drug and placebo groups.
Alternative hypothesis (H₁): There is a difference between the drug and placebo groups.
t = (x̄₁ – x̄₂) / √(s₁²/n₁ + s₂²/n₂)
Where:
x̄₁ = 15, x̄₂ = 12 (mean reductions)
s₁ = 8, s₂ = 7 (standard deviations)
n₁ = n₂ = 100 (sample sizes)
t = (15 – 12) / √((8²/100) + (7²/100))
t = 3 / √(0.64 + 0.49)
t = 3 / √1.13
t = 3 / 1.063
t ≈ 2.82
Degrees of freedom: df = n₁ + n₂ – 2 = 198
The critical t-value for df=198 and α=0.05 (two-tailed) is approximately 1.97.
Since 2.82 > 1.97, we reject the null hypothesis. The difference is statistically significant at the 0.05 level.
2. 95% Confidence Interval:
CI = (x̄₁ – x̄₂) ± t₀.₀₂₅ * √(s₁²/n₁ + s₂²/n₂)
Where t₀.₀₂₅ for df=198 ≈ 1.97
CI = (15 – 12) ± 1.97 * √(8²/100 + 7²/100)
CI = 3 ± 1.97 * 1.063
CI = 3 ± 2.09
CI = (0.91, 5.09)
We can be 95% confident that the true difference in mean cholesterol reduction between the drug and placebo groups is between 0.91 and 5.09 mg/dL.
3. Potential sources of confirmation bias:
– The lead researcher’s prior belief in the drug’s effectiveness may influence study design or interpretation.
– Only positive results (cholesterol reduction) are being measured.
– The statistical threshold (p < 0.05) is arbitrary and may lead to over-interpretation of marginal results.
– Potential selective reporting of outcomes that confirm the hypothesis.
4. Improvements to study design:
– Use a double-blind design where neither participants nor researchers know who receives the drug or placebo.
– Pre-register the study protocol and analysis plan.
– Include multiple outcome measures beyond just cholesterol reduction.
– Use a larger sample size to increase statistical power.
– Consider a longer treatment period to assess long-term effects.
– Include an active control group with a known cholesterol-lowering drug.
5. Ethical implications:
– Confirmation bias can lead to overestimation of drug benefits and underestimation of risks.
– It may result in ineffective or potentially harmful treatments being approved.
– Biased research wastes resources and may misdirect future research efforts.
– It can erode public trust in medical research and healthcare recommendations.
– There’s an ethical obligation to design and conduct studies that prioritize patient safety and scientific integrity over desired outcomes.
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