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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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Most Upvoted Answer
When we are not concerned with the magnitude of the two variables unde...
Explanation:
When we are not concerned with the magnitude of the two variables under discussion, we consider the coefficient of concurrent deviation.
Coefficient of Concurrent Deviation:
The coefficient of concurrent deviation is a measure of association between two variables when we are not concerned with their magnitudes. It is also known as the coefficient of coincidence or the coefficient of agreement. It is denoted by rcd and is defined as:
rcd = (ΣDxy² / ΣDxy)
Where Dxy = Sign of (X - Mx) × Sign of (Y - My)
Mx and My are the medians of X and Y respectively.
Properties of Coefficient of Concurrent Deviation:
1. It is a pure number and has no unit of measurement.
2. It lies between -1 and +1.
3. Its sign indicates the direction of association. If rcd is positive, the association is direct, and if it is negative, the association is inverse.
4. It is insensitive to the magnitude of the variables under consideration.
Example:
Suppose we want to measure the association between the gender of a person and their political preference (Republican or Democrat). We do not care about the magnitude of the variables, only whether they are the same or different. We can calculate the coefficient of concurrent deviation as follows:
Gender Political Preference Dxy Dxy²
Male Republican +1 1
Male Democrat -1 1
Female Republican -1 1
Female Democrat +1 1
ΣDxy = 0
ΣDxy² = 4
rcd = (ΣDxy² / ΣDxy) = undefined (division by zero)
In this case, the coefficient of concurrent deviation is undefined because the denominator is zero. This happens when there is perfect agreement or disagreement between the variables.
When we are not concerned with the magnitude of the two variables under discussion, we consider the coefficient of concurrent deviation.
Coefficient of Concurrent Deviation:
The coefficient of concurrent deviation is a measure of association between two variables when we are not concerned with their magnitudes. It is also known as the coefficient of coincidence or the coefficient of agreement. It is denoted by rcd and is defined as:
rcd = (ΣDxy² / ΣDxy)
Where Dxy = Sign of (X - Mx) × Sign of (Y - My)
Mx and My are the medians of X and Y respectively.
Properties of Coefficient of Concurrent Deviation:
1. It is a pure number and has no unit of measurement.
2. It lies between -1 and +1.
3. Its sign indicates the direction of association. If rcd is positive, the association is direct, and if it is negative, the association is inverse.
4. It is insensitive to the magnitude of the variables under consideration.
Example:
Suppose we want to measure the association between the gender of a person and their political preference (Republican or Democrat). We do not care about the magnitude of the variables, only whether they are the same or different. We can calculate the coefficient of concurrent deviation as follows:
Gender Political Preference Dxy Dxy²
Male Republican +1 1
Male Democrat -1 1
Female Republican -1 1
Female Democrat +1 1
ΣDxy = 0
ΣDxy² = 4
rcd = (ΣDxy² / ΣDxy) = undefined (division by zero)
In this case, the coefficient of concurrent deviation is undefined because the denominator is zero. This happens when there is perfect agreement or disagreement between the variables.
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When we are not concerned with the magnitude of the two variables unde...
A very simple and casual method of finding correlation when we are not serious about the magnitude of the two variables is the application of concurrent deviation
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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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