Briefly summarize the experimental design for deciding whether a proposed treatment should go on for further study. Note where independence came into play. If you were more conservative and reject the treatment only if the probability that it is 30% effective is less than .05 what does the math tell you about whether you would more than 14 patients or fewer than 14 patients?
The experimental design for deciding whether a proposed treatment should go on for further study typically follows a randomized controlled trial (RCT) approach. Here is a summary of the experimental design:
1. Study Sample: A sample of patients with a particular condition or disease is selected randomly or through a specific recruitment process. It is important that the sample is representative of the target population.
2. Random Assignment: The selected patients are randomly assigned into two groups: the treatment group and the control group. Random assignment ensures that each patient has an equal chance of being assigned to either group, which helps to control for any potential confounding variables.
3. Treatment Administration: The treatment group receives the proposed treatment, while the control group receives either a placebo or an alternative treatment (standard care). The treatment administration should be double-blinded, meaning both the patients and the researchers are unaware of who is receiving the treatment and who is not, to minimize bias.
4. Outcome Measurement: The effectiveness of the treatment is measured by comparing the outcomes between the treatment and control groups. The outcome measures might include specific health indicators, symptom improvement, or overall survival rates.
5. Statistical Analysis: Statistical analysis is conducted to determine if the treatment has a significant effect. Independence plays a crucial role in the analysis, particularly in hypothesis testing. Independence assumes that the outcomes of each patient in the sample are not influenced by the outcomes of others in the same study.
Now, let's address the second part of your question. Assuming you are more conservative and want to reject the treatment only if the probability that it is 30% effective is less than 0.05 (or 5%), we can use statistical calculations.
To determine the number of patients required in the study, we need to conduct a power analysis. The power analysis is used to estimate the sample size needed to detect a certain effect size with a desired level of statistical power.
Suppose you want to detect an effect size of 0.3 (30% effectiveness) with a power of 0.95 (95%) and a significance level of 0.05 (5%). You can use statistical software or power analysis calculators to estimate the sample size needed, which will provide the number of patients required.
However, based on your question, we need to consider the reverse scenario. If you want more than 14 patients or fewer than 14 patients, we need to interpret this from a different perspective.
If the sample size is less than 14, it means there is insufficient statistical power to adequately detect a significant effect or confidently reject the null hypothesis. This could result in a higher probability of committing a Type II error (false negative) and potentially missing a genuinely effective treatment.
On the other hand, if the sample size is more than 14, it suggests a larger sample, which can provide greater statistical power to detect a significant effect and reduce the likelihood of making a Type II error. Therefore, having more than 14 patients would be preferable for obtaining more reliable conclusions.
In summary, the experimental design involves random assignment of patients into treatment and control groups, administering the proposed treatment, and measuring outcomes to assess effectiveness. Independence is necessary in statistical analysis. If your threshold for treatment effectiveness is 30%, having more than 14 patients is recommended for obtaining reliable results.