Normal Distribution and Standard Deviation
In a normal distribution curve, two standard deviations (SD) from the mean would include approximately 95% of all values. 1
Understanding the Normal Distribution
The normal distribution (also called Gaussian distribution) is a symmetric, bell-shaped curve that is fundamental to statistical analysis in medicine and science. When data follows this distribution, we can make precise statistical inferences using standard deviations.
Key Properties of Standard Deviations in Normal Distribution:
- One SD (±1 SD): Encompasses approximately 68% of all values 1, 2
- Two SD (±2 SD): Encompasses approximately 95% of all values 1
- Three SD (±3 SD): Encompasses approximately 99.7% of all values 1
Clinical and Statistical Significance
The use of two standard deviations (±2 SD) as a reference interval is the standard approach recommended by multiple professional organizations, including:
- The European Association for the Study of the Liver
- The American Association for Clinical Chemistry
- The European Association of Cardiovascular Imaging 1
This approach creates a balance between identifying truly abnormal values while minimizing false positives. Using ±2 SD ensures that approximately 5% of healthy individuals will have values outside the reference range (2.5% on each end) 1.
Why Not Other SD Ranges?
- ±1 SD (68%): Too restrictive, leading to excessive false positives 1
- ±3 SD (99.7%): Too inclusive, potentially missing clinically significant deviations 1
Applications in Medical Research and Practice
When establishing reference intervals for laboratory tests or other clinical measurements, the ±2 SD approach is considered standard practice 1. This ensures that:
- Reference ranges are statistically sound
- Approximately 95% of healthy individuals fall within the normal range
- Values outside this range warrant further investigation
Special Considerations
For asymmetrically distributed data, percentile-based approaches may be more appropriate, typically using the 2.5th and 97.5th percentiles 1, which would still capture approximately 95% of the values but account for the non-normal distribution.
Understanding the properties of the normal distribution and standard deviation is essential for proper interpretation of clinical data, establishing reference ranges, and making evidence-based clinical decisions.