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When we are not concerned with the magnitude of the two variables under discussion, we consider
- a)Rank correlation coefficient
- b)Product moment correlation coefficient
- c)Coefficient of concurrent deviation
- d)(a) Or (b) but not (c)
Correct answer is option 'C'. Can you explain this answer?
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When we are not concerned with the magnitude of the two variables unde...
Coefficient of concurrent deviation
The coefficient of concurrent deviation is a measure of the degree of agreement between two sets of measurements. It is used when we are not concerned with the magnitude of the two variables under discussion.
Formula
The formula for the coefficient of concurrent deviation is:
r = ∑ Dxy / √(∑ Dx^2) √(∑ Dy^2)
Where:
Dxy = the deviation of the ith observation of X from its mean multiplied by the deviation of the ith observation of Y from its mean
Dx = the deviation of the ith observation of X from its mean
Dy = the deviation of the ith observation of Y from its mean
Interpretation
The coefficient of concurrent deviation ranges from -1 to +1. A value of +1 indicates perfect agreement, while a value of -1 indicates perfect disagreement. A value of 0 indicates no agreement or disagreement.
Example
Suppose we want to measure the agreement between two sets of measurements of the same variable, taken by two different observers. We have the following data:
Observer 1: 10, 12, 15, 18, 20
Observer 2: 8, 13, 16, 17, 21
We first calculate the mean and deviation of each set of measurements:
Observer 1: Mean = 15, Deviation = -5, -3, 0, 3, 5
Observer 2: Mean = 15, Deviation = -7, -2, 1, 2, 6
Then we calculate the coefficient of concurrent deviation:
r = (-5*-7) + (-3*-2) + (0*1) + (3*2) + (5*6) / √((-5)^2 + (-3)^2 + 0^2 + 3^2 + 5^2) √((-7)^2 + (-2)^2 + 1^2 + 2^2 + 6^2)
r = 28 / √59 √70
r = 0.53
This indicates a moderate degree of agreement between the two observers.
The coefficient of concurrent deviation is a measure of the degree of agreement between two sets of measurements. It is used when we are not concerned with the magnitude of the two variables under discussion.
Formula
The formula for the coefficient of concurrent deviation is:
r = ∑ Dxy / √(∑ Dx^2) √(∑ Dy^2)
Where:
Dxy = the deviation of the ith observation of X from its mean multiplied by the deviation of the ith observation of Y from its mean
Dx = the deviation of the ith observation of X from its mean
Dy = the deviation of the ith observation of Y from its mean
Interpretation
The coefficient of concurrent deviation ranges from -1 to +1. A value of +1 indicates perfect agreement, while a value of -1 indicates perfect disagreement. A value of 0 indicates no agreement or disagreement.
Example
Suppose we want to measure the agreement between two sets of measurements of the same variable, taken by two different observers. We have the following data:
Observer 1: 10, 12, 15, 18, 20
Observer 2: 8, 13, 16, 17, 21
We first calculate the mean and deviation of each set of measurements:
Observer 1: Mean = 15, Deviation = -5, -3, 0, 3, 5
Observer 2: Mean = 15, Deviation = -7, -2, 1, 2, 6
Then we calculate the coefficient of concurrent deviation:
r = (-5*-7) + (-3*-2) + (0*1) + (3*2) + (5*6) / √((-5)^2 + (-3)^2 + 0^2 + 3^2 + 5^2) √((-7)^2 + (-2)^2 + 1^2 + 2^2 + 6^2)
r = 28 / √59 √70
r = 0.53
This indicates a moderate degree of agreement between the two observers.
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When we are not concerned with the magnitude of the two variables under discussion, we considera)Rank correlation coefficientb)Product moment correlation coefficientc)Coefficient of concurrent deviationd)(a) Or (b) but not (c)Correct answer is option 'C'. Can you explain this answer?
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