## Thursday, August 22, 2013

### Salaries for Professor, Instructor and Graduate Assistant - an IPEDS derivation

** If you are using Microsoft Internet Explorer or Google Chrom browser, you would not be able to read the formulas in this article. These formulas were written in MathML, a W3C standard, and can be viewed in FireFox.

For the 2012-13 IPEDS (Integrated Postsecondary Education Data System) data collection year, National Center for Education Statistics (NCES) changed the information it collected through its Human Resource component. This change in data collection dictates how the average salary for Full-Time instructional Faculty can be calculated.

This article intended to provide a comparison of the new and the old way of calculating the average salary. The discussion is intentionally simplified in order to demonstrate the conceptual differences.

Prior to 2012-13 data collection, headcount numbers and salary outlays were collected for faculty with 9- or 10-month contract and 11- or 12-month contract for each gender and rank. So, for each gender and rank, there are basically 4 numbers: Total Salary Outlay for faculty with 9- or 10-month contract (S9), Total Headcount for faculty with 9- or 10-month contract (H9), Total Salary Outlay for faculty with 11- or 12-month contract (S11), and Total Headcount for faculty with 11- or 12-month contract (H11). The suggested way (by NCES) to calculate the annual 9-month average salary for each gender-rank combination is given by:

$\frac{{S}_{9}+\frac{9}{11}{S}_{11}}{{H}_{9}+{H}_{11}}$

, which, in essence, is the average of the monthly salary times 9.

Beginning 2012-13 data collection year, for each gender-rank combination, 5 numbers are collected: the Total Headcount for faculty with 9-month contract (H9), the Total Headcount for faculty with 10-month contract (H10), the Total Headcount for faculty with 11-month contract (H11), the Total Headcount for faculty with 12-month contract (H12), and the Total Salary Outlay for faculty with all four contract length (S9+S10+S11+S12). The suggested way (by NCES) to calculate the annual 9-month average salary for each gender-rank combination is given by:

$\frac{{S}_{9}+{S}_{10}+{S}_{11}+{S}_{12}}{9{H}_{9}+10{H}_{10}+11{H}_{11}+12{H}_{12}}x9$

, which, in essence, is the total salary outlay distributed into the total number of manpower-month.

Logically, the methodology changes begged the explanation of the differences between these two methods.

For simplicity, case with only 9-month and 11-month faculties are considered. Under this condition, the 2012-13 method reduced to:

$\frac{{S}_{9}+{S}_{11}}{9{H}_{9}+11{H}_{11}}x9$.

By carrying out the difference of the new and old methods, we arrived at:

$\frac{\frac{2}{11}{S}_{11}-\frac{2}{9}x\left(\frac{{S}_{9}+\frac{9}{11}{S}_{11}}{{H}_{9}+{H}_{11}}\right)x{H}_{11}}{9{H}_{9}+11{H}_{11}}x9$.

The difference indicates if the new number is higher or lower than the old number and by how much. The value represented by the parenthesis is that of the old method - the average monthly salary times 9 month. By multiplying it by two over nine and times the number of faculty with 11-month contract, the result represents the amount of money needed to bring the 11-month faculties' average salary to that of the old method for the two months (9-11). The leading term in the numerator indicates the two month allocation from the total salary outlay for the 11-month faculties. The net value of the numerator is, therefore, the amount of money that can be used the raise or lower the value of the new method apart from the average monthly salary of the old method. By solving the inequality equation:

$\frac{2}{11}{S}_{11}-\frac{2}{9}x\left(\frac{{S}_{9}+\frac{9}{11}{S}_{11}}{{H}_{9}+{H}_{11}}\right)x{H}_{11}>0$

, it can be proofed that higher monthly salary for the 11-month faculties would result in higher value for the 2012-13 formula than the older formula and the reverse is also true.

By consideration above and by making the same assumption NCES had made in the past (i.e. assuming all faculty with 9- or 10-month contracts are actually 9-month contract and that all faculty with 11- or 12-month contract are actually 11-month contract), it is possible to apply the new method to the pre 2012-13 data with predictable discrepancy.

Even though NCES had used the 9- and 11-month assumption in the past, the new 2012-13 data can be used to gauge if that assumption is a valid one. For example, the 2012-13 data revealed that majority of Nebraska's colleges are either have 9-month contracts or 12-month contracts. There are some 10-month contracts, but the 11-month contracts are nearly none. With these observation, the following formulas is a better estimate for the pre 2012-13 data:

At the same time, by discounting the minorities, the following formula can be applied to all years:
$\frac{{S}_{9}+{S}_{12}}{9{H}_{9}+12{H}_{12}}x9$

This would show the effects and differences caused by the new formula and also provide a ( reasonably ) compatible trend from the past to current.

#### 1 comment:

Ashley Smith said...
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