# Methodology

Unlike other online compensation sites, Compensation Interactive (CI) only uses actual data from our own surveys and data collected from this web site.  We review and approve all data before adding it to our database.

Compensation Interactive “averages” are means, that is, the equivalent to summing all the values and dividing by how many there are. The 50th percentile is the median.

## Weighting by time:

As data continuously enters CI, the information in older data becomes less relevant.  To capture the importance of recent data, new data begins with a weight of 1, and older data is re-weighted only 90% of its previous weight every month after it entered, and removed completely after 13 months.  Thus, for example, data that is three months old is re-weighted by 90% three times, giving a weight of 1 x .9 x .9 x .9 = .729.

For example, assume that we want to “average” three values by this method.  One value, 300, is new, one value, 200, is three-months old, and one value, 100 is 16-months old.  The 300 has a weight of 1, the 200 has a weight of .729, and the 16-month old 100 has been discarded a month ago.

Time-weighted average = (Sum of each value x its weight) / (Sum of the weights)

 Value Weight Value x Weight 300 1 300.0 200 .729 145.8 100 discarded – Sum 1.729 445.8

Time-weighted average = (sum of each value x its weight) / (sum of the weights)

= 445.8 / 1.729

= 257.8

Thus the recent 300 figures importantly in the average, the 200 less so, and the 100 not at all.  This procedure is similar to exponential smoothing used in forecasting.

## Total Cash Calculation Formula:

Average total cash for each company is:

(Average base x Number of employees) + (Average bonus x Number of bonus earners)÷Number of Employees

Employees who are eligible but did not receive a bonus are excluded from the number receiving and average Annual Bonus columns and from the “Average bonus x Number of bonus earners” calculation in the formula above. Long-term incentive compensation is not included.

## Sufficient Data

Compensation Interactive displays actual results for a position only if five or more companies report data for it. For positions with less than five companies reporting, Compensation Interactive calculates the report with multipliers created from the database.

## Percentiles

Percentiles in Compensation Interactive match the results that would be provided by the default percentile choice in Microsoft Excel. Thus the minimum value is labeled 0%, the maximum value is 100% and linear interpolation between the two nearest values is used for percentiles without an exact match. For example, consider an array with six values and the percentiles matching each:

 Value Percentile 5 0% 8 20% 9 40% 12 60% 14 80% 17 100%

The estimated 50th percentile would be halfway between the 40th and 60th percentile, or halfway between nine and 12, equal to 10.5 (This matches the traditional choice of median in a data set with an even number of values — average the two middle values).

To estimate a percentile with linear interpolation, use the known percentiles just below and above the desired percentile and the values matching those two percentiles.  Suppose we wished to estimate the 35th percentile from our six values above.

Desired Percentile, DP, is 35.

The percentile below, Pb, is 20, with value below, Vb, of 8.

The percentile above, Pa, is 40, with value above, Va, of 9.

Compute the desired value, DV  =  Vb + (DP-Pb)/(Pa-Pb) x (Va-Vb)

In our case, DV  =  8 + ( 35 – 20 ) / ( 40 – 20 ) x ( 9 – 8 )  =  8 + 15 / 20 x 1 =  8 + .75  =  8.75 as estimated 35th percentile.

Similarly, for instance, the estimated 75th percentile would be 13.5.