Part c
Using the data provided in part (b), evaluate the effect size by calculating Cohen’s d for the paired differences.
Assessing Statistical Power and Effect Sizes
A researcher is analyzing the effectiveness of a new drug using a two-sample T test. The study requires comparing minor effect sizes under different clinical conditions. The researcher must also determine the sample size needed to detect these effects while controlling for Type I and Type II errors. (a) Compare the interpretation of small, medium, […]
Designing a High-Power Statistical Study
You are tasked with designing a study to test a new drug using a one-sample Z test. The goal is to detect a clinically meaningful effect while controlling the type I and type II error rates. (a) Specify a desired power level for the study and justify your choice in a clinical trial context. (b) […]
Graphical Analysis of Effect Size on Type II Error
A pharmaceutical company is conducting a clinical trial for a new drug intended to reduce systolic blood pressure. The null hypothesis (H₀) states that the drug has no effect on blood pressure. The alternative hypothesis (H₁) states that the drug reduces blood pressure. A one-tailed Z-test is chosen to determine if there is statistically significant […]
Part b
Derive the formula and solve for the minimum sample size \(n\) required to achieve a power of 80% given an effect size of 0.5 and a known standard deviation of 1.
Interpreting Statistical and Practical Significance
Explain the difference between statistical significance and practical significance in the context of hypothesis testing. In your explanation, discuss the role of the p-value and why a result that is statistically significant may not necessarily be practically significant.