The Clinical Study Power Calculator helps researchers determine the statistical power of a clinical study. Statistical power measures the likelihood of detecting a true effect when it exists, reducing the risk of false-negative results (Type II errors). This calculator assists in optimizing study design by considering factors like sample size, effect size, and significance level. It ensures that studies are adequately powered to yield reliable and actionable results.
Formula of Clinical Study Power Calculator
The general formula for calculating power is:
Power = P(Z > Zα - Zβ)
Where:
Zα: The Z-score corresponding to the significance level (α).
Zβ: The Z-score corresponding to the desired power (1 - β).
P(Z > Zα - Zβ): The probability of a Z-score being greater than the difference between Zα and Zβ.
Specific Formulas for Different Study Designs
Two-Sample t-test:
Power = P(t > tα - δ√(2/n))
Where:
tα: The t-critical value for the given significance level and degrees of freedom.
δ: The standardized effect size (difference in means divided by the pooled standard deviation).
n: The sample size per group.
One-Sample t-test:
Power = P(t > tα - δ√n)
Where:
tα: The t-critical value for the given significance level and degrees of freedom.
δ: The standardized effect size.
n: The sample size.
Pre-Calculated Metrics for Common Scenarios
| Study Design | Effect Size (δ) | Sample Size (n) | Power (1 - β) |
|---|---|---|---|
| Two-Sample t-test | 0.5 | 50 | 0.80 (80%) |
| Two-Sample t-test | 0.8 | 30 | 0.90 (90%) |
| One-Sample t-test | 0.5 | 60 | 0.85 (85%) |
This table provides insights into the relationships between sample size, effect size, and power for typical clinical studies.
Example of Clinical Study Power Calculator
Scenario:
A researcher is conducting a two-sample t-test with the following parameters:
- Effect size (δ): 0.5
- Sample size per group (n): 50
- Significance level (α): 0.05
Solution:
Using the formula:
Power = P(t > tα - δ√(2/n))
- Determine tα for α = 0.05 (commonly 1.96 for large sample sizes).
- Calculate δ√(2/n):
δ√(2/n) = 0.5√(2/50) = 0.141. - Subtract δ√(2/n) from tα:
tα - δ√(2/n) = 1.96 - 0.141 = 1.819. - Find the probability P(t > 1.819), yielding approximately 0.80 (80% power).
This calculation shows that the study has an 80% chance of detecting a true effect of the specified size.
Most Common FAQs
Statistical power ensures that studies are capable of detecting true effects, reducing the risk of false-negative results and enabling confident conclusions about interventions or treatments.
The power depends on the sample size, effect size, significance level (α), and study design. Larger sample sizes and higher effect sizes typically increase power.
Yes, the calculator can be applied to any research requiring statistical analysis, including non-clinical fields like social sciences or business analytics.