Practical versus Statistical Significance In clinical trials for treatment of a skin disorder, 642 of 2105 patients receiving the current standard treatment were cured of the disorder and 697 of 2115 patients receiving a new proposed treatment were cured of the disorder.
b. Do you think that the difference in success rates is practically significant? What factors might influence your decision?

Verified step by step guidance

1. First, calculate the success rates (proportions) for each treatment group. For the current standard treatment, the success rate is \(\hat{p}_1 = \frac{642}{2105}\). For the new proposed treatment, the success rate is \(\hat{p}_2 = \frac{697}{2115}\).
2. Next, find the difference in success rates between the two treatments: \(\hat{p}_2 - \hat{p}_1\). This gives a measure of how much better or worse the new treatment performed compared to the standard one.
3. Consider the concept of practical significance, which asks whether the observed difference is large enough to matter in a real-world or clinical context, beyond just being statistically significant.
4. Reflect on factors that might influence practical significance, such as the size of the difference in success rates, the severity of the skin disorder, potential side effects, cost, ease of treatment, and patient preferences.
5. Finally, think about the clinical implications: even a small difference might be important if the new treatment is safer or cheaper, or a larger difference might be needed to justify switching treatments if the new one is more expensive or has more side effects.

Key Concepts

Statistical Significance

Statistical significance measures whether an observed effect, like the difference in cure rates, is likely due to chance or represents a real difference. It is often assessed using hypothesis tests and p-values, which help determine if the new treatment's success rate differs meaningfully from the standard treatment.

Practical Significance

Practical significance considers whether the size of the observed effect is large enough to have real-world importance or impact. Even if a difference is statistically significant, it may not be meaningful in clinical practice if the improvement is too small to affect patient outcomes or decision-making.

Factors Influencing Practical Significance

Factors such as the magnitude of the difference in cure rates, side effects, cost, patient quality of life, and treatment feasibility influence practical significance. These considerations help determine if adopting the new treatment is beneficial beyond just statistical results.