Method for statistical comparison of occupations by skill sets and other relevant attributes
A method and system for measuring transferability of workers between and among occupations by means of the mathematical relationships between those occupations' key attributes, as defined by publicly available data on the competencies required as specified by a complete catalog of U.S. occupations known as O*NET. This method provides a concise, informative measurement for comparing the relative requirements of Abilities, Skills, Knowledge, and other relevant attributes of occupations, enabling users to gauge the feasibility of transferring workers from one occupation to another.
1. A method for computing a correlation coefficient for a pair of occupations as an indication of transferability of workers between the occupations comprising:
providing a computer to perform computations;
selecting the pair of occupations;
for each occupation in a set of occupations:
entering into a matrix or database a set of scores for a selected individual worker attribute for an occupation, the set of scores for each attribute being one or more sets S k consisting of N k scores, where S k x j (j=1, 2, . . . N k );
computing, with the computer, a product of an Importance score and a Level score for the attribute to produce a composite attribute value;
entering the composite attribute value into the matrix;
computing the difference between the computed product for each attribute between any pair of occupations;
computing the sums of all differences between the computed product for each attribute between any pair of occupations to equal the total difference;
entering the total difference value into the matrix;
accessing, with the computer, data in the matrix;
computing, with the computer, a correlation coefficient for the pair of occupations by correlating the composite attribute value for the pair of occupations by the following formula:
Correl
(
X
,
Y
)
=
∑
i
N
k
{
(
x
i
-
μ
x
)
(
y
i
-
μ
y
)
}
[
∑
i
N
k
(
x
i
-
μ
x
)
2
∑
i
N
k
(
y
i
-
μ
y
)
2
]
wherein: X and Y represent two vectors in a set, S k , of scores for the x th and y th occupations in a set of occupations; where both x and y run from 1 to N, where N is the number of occupations in the set of occupations and x and y are composite attribute values assigned to each occupation; k is a value indicating a Level assigned to an individual worker attribute; x i a X; y i a Y; i=1, 2, . . . N k ;
μ
x
=
∑
i
N
k
{
x
i
}
N
k
is the mean value of the X vector and
μ
xy
=
∑
i
N
k
{
y
i
}
N
k
is the mean value of the Y vector normalizing the correlation coefficients on a scale of 1 to 100;
adjusting the normalized correlation coefficients by
producing a ratio whereof the numerator is calculated as the sum of the differences between the members of each pair of the composite Level-Importance scores for two selected occupations, the two selected occupations being a source occupation and a destination occupation, for which the composite Level-Importance scores for the destination occupation exceed the composite Level-Importance scores for the source occupation, and the denominator is calculated as the raw sum of the composite Level-Importance scores of the destination occupation; and
adjusting the correlation coefficients, with the computer, for each composite attribute by averaging it with the produced ratios; and
producing a report of the correlation coefficients for all pairs of occupations in the set to indicate transferability of workers, indicated by a value of the correlation coefficients, between the occupations,
wherein a mathematical summary of Level values of work relevant attributes of the individual worker are compiled and adjusted based on multiple occupations that the individual worker performed.
2. A method for computing a correlation coefficient for a pair of occupations as an indication of transferability of workers between the occupations comprising:
providing a computer to perform computations;
selecting the pair of occupations;
for each occupation in a set of occupations:
entering into a matrix or database a set of scores for a selected individual worker attribute for an occupation, the set of scores for each attribute being one or more sets S k consisting of N k scores, where S k x j (j=1, 2, . . . N k );
computing, with the computer, a product of an Importance score and a Level score for the attribute to produce a composite attribute value;
entering the composite attribute value into the matrix;
computing the difference between the computed product for each attribute between any pair of occupations;
computing the sums of all differences between the computed product for each attribute between any pair of occupations to equal the total difference;
entering the total difference value into the matrix;
accessing, with the computer, data in the matrix;
computing, with the computer, a correlation coefficient for the pair of occupations by correlating the composite attribute value for the pair of occupations by the following formula:
Correl
(
X
,
Y
)
=
∑
i
N
k
{
(
x
i
-
μ
x
)
(
y
i
-
μ
y
)
}
[
∑
i
N
k
(
x
i
-
μ
x
)
2
∑
i
N
k
(
y
i
-
μ
y
)
2
]
wherein: X and Y represent two vectors in a set, S k , of scores for the x th and y th occupations in a set of occupations; where both x and y run from 1 to N, where N is the number of occupations in the set of occupations and x and y are composite attribute values assigned to each occupation; k is a value indicating a Level assigned to an individual worker attribute; x i a X; y i a Y; i=1, 2, . . . N k ;
μ
x
=
∑
i
N
k
{
x
i
}
N
k
is the mean value of the X vector and
μ
xy
=
∑
i
N
k
{
y
i
}
N
k
is the mean value of the Y vector normalizing the correlation coefficients on a scale of 1 to 100;
adjusting the normalized correlation coefficients by
producing a ratio whereof the numerator is calculated as the sum of the differences between the members of each pair of the composite Level-Importance scores for two selected occupations, the two selected occupations being a source occupation and a destination occupation, for which the composite Level-Importance scores for the destination occupation exceed the composite Level-Importance scores for the source occupation, and the denominator is calculated as the raw sum of the composite Level-Importance scores of the destination occupation; and
adjusting the correlation coefficients, with the computer, for each composite attribute by averaging it with the produced ratios; and
producing a report of the correlation coefficients for all pairs of occupations in the set to indicate transferability of workers, indicated by a value of the correlation coefficients, between the occupations,
wherein a Level value for each element of each occupation may be adjusted based on a length of time the worker worked in the occupation, and by a period of time since the worker last actively performed the occupation to reflect the degree to which the attribute can be assumed still to characterize the individual worker.
3. A method for computing a correlation coefficient for a pair of occupations as an indication of transferability of workers between the occupations comprising:
providing a computer to perform computations;
selecting the pair of occupations;
for each occupation in a set of occupations:
entering into a matrix or database a set of scores for a selected individual worker attribute for an occupation, the set of scores for each attribute being one or more sets Sk consisting of N k scores, where S k ˜xj (j=1, 2, . . . N k );
computing, with the computer, a product of an Importance score and a Level score for the attribute to produce a composite attribute value;
entering the composite attribute value into the matrix;
computing the difference between the computed product for each attribute between any pair of occupations;
computing the sums of all differences between the computed product for each attribute between any pair of occupations to equal the total difference;
entering the total difference value into the matrix;
accessing, with the computer, data in the matrix;
computing, with the computer, a correlation coefficient for the pair of occupations by correlating the composite attribute value for the pair of occupations by the following formula:
Correl
(
X
,
Y
)
=
∑
i
N
k
{
(
x
i
-
μ
x
)
(
y
i
-
μ
y
)
}
[
∑
i
N
k
(
x
i
-
μ
x
)
2
∑
i
N
k
(
y
i
-
μ
y
)
2
]
wherein: X and Y represent two vectors in a set, S k , of scores for the x th and y th occupations in a set of occupations; where both x and y run from 1 to N, where N is the number of occupations in the set of occupations and x and y are composite attribute values assigned to each occupation; k is a value indicating a level assigned to an individual worker attribute; x i a X; y i a Y; i=1, 2, . . . N k ;
μ
x
=
∑
i
N
k
{
x
i
}
N
k
is the mean value of the X vector and
μ
xy
=
∑
i
N
k
{
y
i
}
N
k
is the mean value of the Y vector;
normalizing the correlation coefficients on a scale of 1 to 100;
adjusting the normalized correlation coefficients by
producing a ratio whereof the numerator is calculated as the sum of the differences between the members of each pair of the composite level-importance scores for two selected occupations, the two selected occupations being a source occupation and a destination occupation, for which the composite level-importance scores for the destination occupation exceed the composite level-importance scores for the source occupation, and the denominator is calculated as the raw sum of the composite level-importance scores of the destination occupation; and
adjusting the correlation coefficients, with the computer, for each composite attribute by averaging it with the produced ratios; and
producing a report of the correlation coefficients for all pairs of occupations in the set to indicate transferability of workers, indicated by a value of the correlation coefficients, between the occupations wherein a mathematical summary of numerical values of the work-relevant attributes of a given population of workers is created and, systematically compared with that of another population of workers.