##### Definition:

Reliability coefficient is used to compute the association of two set of values.

##### Example:

A project was undergone with three Persons (P) and they are allocated with three different Tasks (T). Find 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,

###### Step 1:

Let us first calculate the average score of the persons and their tasks,
The average score of Task (T_{0}) = 10 + 20 /2 = 15
The average score of Task (T_{1}) = 30 + 40 /2 = 35
The average score of Task (T_{2}) = 50 + 60 /2 = 55

###### Step 2:

Next, calculate 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:

Now, calculate the individual variance of P0- T0 and P1- T0,
P0- T1 and P1- T1, P0-T2 and P1-T2.
To calculate the individual variance value, we should add all the above calculated variance values.
i.e. Sum of Individual Variance = 25+25+25=75

###### Step 4:

Calculate the Total variance.
Variance= square ((P0- T0) - average score of Person 0)
= square (10-15)
= 25
Variance= square ((P1- T0) - average score of Person 0)
= square (20-15)
= 25
Variance= square ((P0- T1) - average score of Person1)
= square (30-35)
= 25
Variance= square ((P1- T1) - average score of Person1)
= square (40-35)
= 25
Variance= square ((P0- T2) - average score of Person2)
= square (50-55)
= 25
Variance= square ((P1- T2) - average score of Person2)
= square (60-55)
= 25
Now, add all the values and calculate the total variance,
Total Variance= 25+25+25+25+25+25 = 150

###### Step 5:

Finally, substitute the values in the below given formula to find Reliability Coefficient
RC = (N/(N-1)) * ( (Total Variance - Sum of Variance) / Total Variance)
= 3/ (3-1) * (150-75)/150
= 0.75