# Statistics - Reliability Coefficient

A measure of the accuracy of a test or measuring instrument obtained by measuring the same individuals twice and computing the correlation of the two sets of measures.

Reliability Coefficient is defined and given by the following function:

## Formula

${Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ - Sum\ of\ Variance)}{Total Variance})}$

Where −

• ${N}$ = Number of Tasks

### Example

Problem Statement:

An undertaking was experienced with three Persons (P) and they are assigned with three distinct Tasks (T). Discover the Reliability Coefficient?

P0-T0 = 10
P1-T0 = 20
P0-T1 = 30
P1-T1 = 40
P0-T2 = 50
P1-T2 = 60


Solution:

Given, Number of Students (P) = 3 Number of Tasks (N) = 3. To Find, Reliability Coefficient, follow the steps as following:

### Step 1

Give us a chance to first figure the average score of the persons and their tasks

The average score of Task (T0) = 10 + 20/2 = 15
The average score of Task (T1) = 30 + 40/2 = 35
The average score of Task (T2) = 50 + 60/2 = 55


### Step 2

Next, figure the variance for:

Variance of P0-T0 and P1-T0:
Variance = square (10-15) + square (20-15)/2 = 25
Variance of P0-T1 and P1-T1:
Variance = square (30-35) + square (40-35)/2 = 25
Variance of P0-T2 and P1-T2:
Variance = square (50-55) + square (50-55)/2 = 25


### Step 3

Presently, figure the individual variance of P0-T0 and P1-T0, P0-T1 and P1-T1, P0-T2 and P1-T2. To ascertain the individual variance value, we ought to include all the above computed change values.

Total of Individual Variance = 25+25+25=75

### Step 4

Compute the Total change

Variance= square ((P0-T0)
- normal score of Person 0)
= square (10-15) = 25
Variance= square ((P1-T0)
- normal score of Person 0)
= square (20-15) = 25
Variance= square ((P0-T1)
- normal score of Person 1)
= square (30-35) = 25
Variance= square ((P1-T1)
- normal score of Person 1)
= square (40-35) = 25
Variance= square ((P0-T2)
- normal score of Person 2)
= square (50-55) = 25
Variance= square ((P1-T2)
- normal score of Person 2)
= square (60-55) = 25


Now, include every one of the qualities and figure the aggregate change

Total Variance= 25+25+25+25+25+25 = 150

### Step 5

At last, substitute the qualities in the underneath offered equation to discover

${Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ - Sum\ of\ Variance)}{Total Variance}) \\[7pt] = \frac{3}{(3-1)} \times \frac{(150-75)}{150} \\[7pt] = 0.75 }$