Calculate the Standard Deviation Index (SDI) to assess the accuracy of test results relative to a control mean. Essential for statistical analysis and laboratory quality control.
Calculate the Standard Deviation Index (SDI) to assess the accuracy of your test results.
The Standard Deviation Index (SDI) is a statistical tool used to assess the accuracy and precision of a test result relative to a control or peer group mean. It quantifies the number of standard deviations a test result is from the control mean, providing valuable insight into the performance of analytical methods in laboratory settings and other testing environments.
The SDI is calculated using the following formula:
Where:
To compute the SDI:
Suppose:
Calculation:
An SDI of 1.0 indicates the test result is one standard deviation above the control mean.
SDI between -1 and +1: Acceptable performance.
Test results are within one standard deviation of the control mean, indicating good alignment with expected values. No action is typically required.
SDI between -2 and -1 or between +1 and +2: Warning range.
Results are acceptable but should be monitored. This range suggests potential deviation from the norm that may require attention. Investigate possible causes and consider retesting.
SDI less than -2 or greater than +2: Unacceptable performance.
Investigation is required to identify and correct issues. Results in this range indicate significant deviation from expected values and may signify systemic problems in the testing process or instrumentation. Immediate corrective actions are recommended.
In clinical laboratories, the SDI is crucial for:
Industries use SDI to:
Researchers apply SDI to:
The concept of the Standard Deviation Index evolved from the need for standardized methods to assess laboratory performance. With the advent of proficiency testing programs in the mid-20th century, laboratories required quantitative measures to compare results. The SDI became a fundamental tool, providing a straightforward way to evaluate accuracy relative to peer group data.
Prominent figures in statistics, such as Ronald Fisher and Walter Shewhart, contributed to the development of statistical quality control methods that underpin the use of indexes like the SDI. Their work laid the foundation for modern quality assurance practices in various industries.
1' Calculate SDI in Excel
2' Assume Test Result in cell A2, Control Mean in B2, Standard Deviation in C2
3= (A2 - B2) / C2
41def calculate_sdi(test_result, control_mean, standard_deviation):
2 return (test_result - control_mean) / standard_deviation
3
4## Example usage
5test_result = 102
6control_mean = 100
7standard_deviation = 2
8
9sdi = calculate_sdi(test_result, control_mean, standard_deviation)
10print(f"SDI: {sdi}")
111calculate_sdi <- function(test_result, control_mean, standard_deviation) {
2 (test_result - control_mean) / standard_deviation
3}
4
5## Example usage
6test_result <- 102
7control_mean <- 100
8standard_deviation <- 2
9
10sdi <- calculate_sdi(test_result, control_mean, standard_deviation)
11cat("SDI:", sdi, "\n")
121% Calculate SDI in MATLAB
2test_result = 102;
3control_mean = 100;
4standard_deviation = 2;
5
6sdi = (test_result - control_mean) / standard_deviation;
7disp(['SDI: ', num2str(sdi)]);
81function calculateSDI(testResult, controlMean, standardDeviation) {
2 return (testResult - controlMean) / standardDeviation;
3}
4
5// Example usage
6const testResult = 102;
7const controlMean = 100;
8const standardDeviation = 2;
9
10const sdi = calculateSDI(testResult, controlMean, standardDeviation);
11console.log(`SDI: ${sdi}`);
121public class SDICalculator {
2 public static void main(String[] args) {
3 double testResult = 102;
4 double controlMean = 100;
5 double standardDeviation = 2;
6
7 double sdi = (testResult - controlMean) / standardDeviation;
8 System.out.println("SDI: " + sdi);
9 }
10}
111#include <iostream>
2
3int main() {
4 double testResult = 102;
5 double controlMean = 100;
6 double standardDeviation = 2;
7
8 double sdi = (testResult - controlMean) / standardDeviation;
9 std::cout << "SDI: " << sdi << std::endl;
10
11 return 0;
12}
131using System;
2
3class Program
4{
5 static void Main()
6 {
7 double testResult = 102;
8 double controlMean = 100;
9 double standardDeviation = 2;
10
11 double sdi = (testResult - controlMean) / standardDeviation;
12 Console.WriteLine("SDI: " + sdi);
13 }
14}
151<?php
2$testResult = 102;
3$controlMean = 100;
4$standardDeviation = 2;
5
6$sdi = ($testResult - $controlMean) / $standardDeviation;
7echo "SDI: " . $sdi;
8?>
91test_result = 102
2control_mean = 100
3standard_deviation = 2
4
5sdi = (test_result - control_mean) / standard_deviation
6puts "SDI: #{sdi}"
71package main
2
3import "fmt"
4
5func main() {
6 testResult := 102.0
7 controlMean := 100.0
8 standardDeviation := 2.0
9
10 sdi := (testResult - controlMean) / standardDeviation
11 fmt.Printf("SDI: %.2f\n", sdi)
12}
131let testResult = 102.0
2let controlMean = 100.0
3let standardDeviation = 2.0
4
5let sdi = (testResult - controlMean) / standardDeviation
6print("SDI: \(sdi)")
7An SVG diagram illustrating the SDI and its interpretation ranges.