M09.02.06 Confidence Interval
Confidence intervals (CIs) are essential in statistical analysis, especially in clinical and epidemiological studies, to estimate the range within which the true population value likely lies, based on a sample.
Key Concepts of Confidence Intervals
Definition
A confidence interval provides a range that estimates the population parameter (such as a mean or relative risk) based on sample data. It specifies how far above or below the sample-based estimate the true population value may lie within a specified confidence level (e.g., 95% or 99%).
Formula:
Components of Confidence Interval Calculation
- Study Result: This could be the mean, relative risk, or another measure from the sample.
- Z-Score: Reflects the desired confidence level.
- 95% confidence level:
(often rounded to 2)
- 99% confidence level:
(rounded to 2.5)
- 95% confidence level:
- Standard Error (SE): Estimates the variability between samples; it is calculated as
where SD is the standard deviation and ‘n’ is the sample size. A smaller SE indicates a more precise study.
Confidence Interval Calculation Example
Imagine 100 ninth-grade students took an exam, and the results show:
- Mean score (
) = 65%
- Standard Deviation (SD) = 15
- Sample size (N) = 100
- Z-score for a 95% confidence interval = 2
Calculation:
Standard Error:
Confidence Interval:
The 95% confidence interval is 62 to 68. Thus, we are 95% confident that the mean score for the population of ninth-graders will fall within this range.
Confidence Intervals in Clinical Trials
When interpreting confidence intervals in clinical trials, overlapping intervals between groups imply no significant difference.
Example Interpretation with Relative Risk (RR)
| Relative Risk | Confidence Interval | Interpretation |
|---|---|---|
| 1.77 | (1.22 – 2.45) | Statistically significant (increased risk) |
| 1.63 | (0.85 – 2.46) | Not statistically significant |
| 0.78 | (0.56 – 0.94) | Statistically significant (decreased risk) |
Points to Remember
- Confidence Interval: Expresses a range within which the true population parameter likely falls.
- Standard Error: Reflects the precision of the sample estimate; influenced by sample size and variability.
- Interpretation of Confidence Intervals:
- A 95% confidence interval is common in medical research.
- Overlapping CIs between groups suggest no statistically significant difference.
- For RR or odds ratios, if the CI includes 1.0, the effect is not statistically significant.
Bibliography
- Sullivan, L. M. (2020). Essentials of Biostatistics in Public Health. Jones & Bartlett Learning.
- Dawson, B., & Trapp, R. G. (2021). Basic and Clinical Biostatistics. McGraw Hill.
- Rosner, B. (2015). Fundamentals of Biostatistics. Cengage Learning.