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Reliability Coefficient
Statistics - Repabipty Coefficient
A measure of the accuracy of a test or measuring instrument obtained by measuring the same inspaniduals twice and computing the correlation of the two sets of measures.
Repabipty Coefficient is defined and given by the following function:
Formula
${Repabipty Coefficient, RC = (frac{N}{(N-1)}) imes (frac{(Total Variance - Sum of Variance)}{Total Variance})}$
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 Repabipty 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, Repabipty 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 inspanidual variance of P0-T0 and P1-T0, P0-T1 and P1-T1, P0-T2 and P1-T2. To ascertain the inspanidual variance value, we ought to include all the above computed change values.
Total of Inspanidual 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 quapties and figure the aggregate change
Total Variance= 25+25+25+25+25+25 = 150
Step 5
At last, substitute the quapties in the underneath offered equation to discover
${Repabipty Coefficient, RC = (frac{N}{(N-1)}) imes (frac{(Total Variance - Sum of Variance)}{Total Variance}) \[7pt] = frac{3}{(3-1)} imes frac{(150-75)}{150} \[7pt] = 0.75 }$ Advertisements