Ordered to Calculate a Percentile from a Median Figure

Life for compensation specialists would be much easier if management stopped playing at being pay practice experts.  Witness a common dilemma faced by a hapless HR manager: 

We pay our Technical Staff at the 60th percentile of the market.  I have the survey’s min and max but must calculate the 60th%ile from the typical 50th%ile.

What is a total rewards professional to do, when commanded to make an impossible calculation?

Knowledge of the fundamental mathematical principles applicable to pay surveys might help avoid this problem in the future.  As explained in detail in professional discussions about percentiles, you must possess all the underlying observations to rank them in order to display the 60th%ile.  You can’t identify the data point where 60% of the elements fall below and 40% of the observations remain above it, unless you have all the underlying data point observation elements to stack up in a rank-ordered sequence. 

The survey provider must share all the data responses or should otherwise report where the 60th%ile point falls.  You can't calculate it from survey summaries that lack specific detailed facts.  Without each of those observation elements in each survey, it is impossible for you to pay at the 60th%ile of the market unless your survey REPORTS where that point lies.  Rather than guess where a different percentILE stands, it makes more sense to simply change your structure policy to pay a certain percentAGE above the mean average or median.  The 60th%ile might be 1% above it or 30% above it*.  You can't know exactly where it is without having all the observations in hand.  If top management bristles at a suggestion that their policy is deficient and should be changed, you could carefully explain that a reasonable estimate is the next best option. 

It might be possible to make credible guesses about where the 60^th%ile lies in a particular occupation’s ranked scale of values; but such projections can’t be accurate with any degree of precision and will vary by job, too.  Some clever comp pros make maximum use of the metrics they DO have, like the median (50th%ile) and the 75th percentile, for example.  Simply splitting the difference betwen those two will produce a "generously well above average" policy target without even trying to claim what percentile that guesstimate represents.  Using the midpoint between two known percentiles is both practical and defensible.

Here are real numbers.  Drawing from an extremely robust dataset encompassing the majority of workers in America, the 60^th%ile for a receptionist is less than 2% above the average and almost 4% above the median.  Comparable differentials for the 60^th%ile for an accountant are approximately 1% higher. Computing the midpoint between the median and the 75th%ile yields a number that stays very close to the 65th%ile. 

None of those comparisons are adjusted for industry, location or responsibility level; neither size nor profitablity are statistically predictable pay factors for those benchmark jobs.  The spreads cited above won’t necessarily apply to a small survey.  Any percentile break point for different jobs in your particular kind of enterprise in your principal location will probably be different, too.  Nevertheless, as long as you clearly define your assumptions (i.e. splitting the difference from known values) when making projections, you should be fairly safe from serious criticism.  Strong disagreements can be referred to math professors who can mediate the matter as experts or fight the statistical battle for you. 

The pay distribution intervals found in even the most robust survey observation samples are not consistent, constant or symmetrical and thus are very unresponsive to formulistic prediction.  So any guess will (not "might") produce errors.  When the correct answer is impossible because you lack the real data required for precise accuracy, all you can do is apply a SWAG. 

What do you think?

*From these analyses, paying 10% above the norm produces a number ranging from the 74^th percentile  to the 82^nd  percentile.  The rank relationships vary by job, by location and by comparison norm standard (average or median).

E. James (Jim) Brennan is Senior Associate of ERI Economic Research Institute, the premier publisher of interactive pay and living-cost surveys. After over 40 years in HR corporate and consulting roles throughout the U.S. and Canada, he’s pretty much been there done that (articles, books, speeches, seminars, radio/TV, advisory posts, in-trial expert witness stuff, etc.), serves on the Advisory Board of the Compensation and Benefits Review and will express his opinion on almost anything.

Creative Commons image "Numbers and Finance" by reynermedia, courtesy of seniorliving.org

Comments

[Trevor Norcross]

Hi Jim,
Nice post. Having managed comp surveys early in my career the data behind the curtain is interesting.

If you have an executive that does not understand how the math works and is not willing to spend the money to have the survey vendor create a special cut of data than all you can do is create an educated swag. Your post gives everyone a better perspective on how to do it.

[E. James (Jim) Brennan]

Thanks, Trevor. Hope the tips prove helpful, because we really need to know a bit about survey statistics to respond effectively to some compensation challenges.

[Jacque Vilet]

Good to pass on the details. Even if CEOs aren't usually interested in details it's good to have them just in case.

[E. James (Jim) Brennan]

The only time the CEO will ask for a detailed explanation of some issue is when you don't have it available. Isn't that one of Murphy's Laws, Jacque?

For the same reason, when I created court expert witness testimony repots, I always prepared for the toughest questions I could think of, realizing that the opposing expert was likely smarter than I was. If a challenge occurred to me, a smarter person surely would raise it, too.

[Tony Bergmann-Porter]

All of this assumes that compensation is a science. i submit that it is at least as much an art.

[Dan Walter]

Hi Jim,

Excellent piece.

I am sure many readers would find it helpful to see some data curves for different positions. It often seems like many non-comp people believe that all positions result in either a standard bell curve or some sort of robotic pyramid progression.

Does ERI have some example of data curves for a variety of positions?

[Petr Vrabec]

When I need to calculate a position between known points, say Median and Q3, I call it "virtual percentile" to highlight it is not coming directly from the survey.

[Mark]

Just recently I prepared a look for examining and measuring for specific skills while positioning relative to the CR or to X% of the range. Following that process then adjusted the quartile payments to recognize the separate group(s) based on the targeted "rate" or position in range.

[Jim Johnson]

Jim, as usual, your comments are "spot on".

One option for those wanting to use the 60th %ile of the market is to request the 3rd party survey to provide it. This is an option in at least one major survey purveyor that caters to the high tech community.