In biostatistics, statistical tests help determine whether study results are due to actual effects or random variation. Three important concepts that guide interpretation of test results are the power of test, the p-value, and confidence intervals. These concepts allow researchers to understand the strength of evidence, the probability of error, and the precision of their estimates.
Power of Test
The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. In simple terms, it measures a test’s ability to detect a true difference or effect.
Definition
Power = 1 – β
Here, β is the probability of a Type II error (failing to detect a true effect). Thus, higher power means lower chance of missing a real difference.
Why Power Matters
- Acknowledges the sensitivity of a statistical test.
- Ensures that important differences are not overlooked.
- Guides sample size determination in research planning.
- Helps evaluate reliability of non-significant results.
Factors Affecting Power
- Sample size: Larger sample → higher power.
- Effect size: Larger differences are easier to detect.
- Significance level (α): Increasing α increases power but risk of Type I error.
- Variability: Higher variability lowers power.
- Study design: Paired designs often yield higher power.
P-Value
The p-value is a statistical measure that indicates the probability of observing the obtained results, or more extreme results, if the null hypothesis is true. It helps determine whether results are statistically significant.
Interpretation
A small p-value suggests that the observed data is unlikely under the null hypothesis.
If p ≤ 0.05: Reject the null hypothesis (significant).
If p > 0.05: Fail to reject the null hypothesis (not significant).
Key Points About P-Value
- Does NOT indicate the size or importance of an effect.
- Does NOT measure the probability that the null hypothesis is true.
- Must be interpreted along with sample size and effect size.
- Influenced by variability and study design.
Examples
- p = 0.03 → Significant (effect likely exists).
- p = 0.20 → Not significant (insufficient evidence to reject H₀).
Statistical Estimation and Confidence Intervals
A confidence interval (CI) provides a range of values within which the true population parameter is likely to lie. It offers more information than a single estimate such as the mean.
Definition
A 95% confidence interval means that if the same study were repeated many times, approximately 95% of the calculated intervals would contain the true population value.
Example
Mean systolic blood pressure difference = 6 mmHg (95% CI: 2 to 10 mmHg). This means the true difference likely lies between 2 and 10.
Formula (for mean)
CI = Mean ± Z × (SD / √n)
- Z = 1.96 for 95% CI
- Z = 2.58 for 99% CI
Importance of Confidence Intervals
- Indicate precision of an estimate (narrow CI = high precision).
- Help interpret clinical importance, not just statistical significance.
- Show both direction and magnitude of effect.
Relationship Between P-Value and Confidence Interval
- If the 95% CI does not include 0 (for mean difference), the p-value will be < 0.05.
- CI provides additional context not offered by p-value alone.
- P-value shows significance, CI shows precision.
Putting It All Together
When interpreting research results:
- The p-value tells whether the effect is statistically significant.
- The confidence interval shows the likely size and direction of the effect.
- The power indicates whether the study had a reasonable chance of detecting the effect.
Detailed Notes:
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