Calculating position in range versus percentile data Posted:
03/23/2010 06:22am
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I have the 25th, median, and 75th percentiles. What formula would work in order to determine where our incumbent's base pay falls in relation to the percentiles. Example: The survey shows $47,446 (25th), $56,731 (median), and $65,914 (75th percentile). If our incumbent is making $64,295, how would I determine at what level we are paying in comparison to the market?

Calculating position in range versus percentile data Posted:
03/23/2010 06:32am

The only thing you can say with definity is that the salary of $64,295 falls between the median (50th percentile) and the 75th percentile of the market survey data.

The only way you can determine what the exact percentile of the salary is in the market survey is to (a) know the complete survey data and calculate the percentile, or (b) ask the survey company to provide you with that calculation.

In a previous post, Jim Brennan observed that you might be able to scientifically calculate such a number if your knew the surveyed data fell on a perfect normal bell curve, but survey data never falls in a perfect normal bell curve.

Calculating position in range versus percentile data Posted:
03/23/2010 06:44am
Revised: 03/23/2010 06:48am

I believe that you could say this, for example: Our incumbent's salary of $64,295 is13% above the market median of $56,731. As stated previously, you can't say at what percentile the incumbent's salary is at with the information you have. Which is more meaningful---the percentile or the difference in salaries?

Calculating position in range versus percentile data Posted:
03/23/2010 06:49am

For members who want to strengthen their knowledge about these kind of issues, check out WorldatWork's certification course T3 or GR2: Quantitative Methods.

Calculating position in range versus percentile data Posted:
03/23/2010 08:14am

If you are looking for immediate help with percentiles, may I suggest these resources:

A wokspan back to basics article on using survey statistics to determine employee compensation. It provides a good thumb nail description of common survey statistics that you might want to keep handy. http://www.worldatwork.org/waw/adimLink?id=16277&nonav=yes.

The following link is to a description of how percentiles are defined and calculated. Note that the most commonly used definition for compensation professionals is definition 2.

Calculating position in range versus percentile data Posted:
03/23/2010 08:38am

You are paying well above market (shown by the market index of 113%) and almost at the 75th percentile. But you have no way of knowing if your number falls at the 53rd%ile or at the 74th%ile. I'd guess that your number falls somewhere around the 72nd to 74th percentiles, but that's a SWAG assuming that there are a lot of observations with the typically skewed distribution for salaries.

Calculating position in range versus percentile data Posted:
03/30/2010 09:50am

(1 rating)

This is an interesting and relevant quote from a recent workspan article on this subject:

Another problem with the 75th-percentile approach is there is a commonly held belief that paying at the 75^{th} percentile is equivalent to paying about 10 percent above market. However, in the large IT survey mentioned earlier, while the author determined that the 75th percentile equaling 10 percent above median or mean was not far off the mark in many cases, this relationship held only in huge samples. As samples get smaller, the variations in the difference between the 75th percentile and the median or mean will magnify, making the percentile measure (i.e., distributional measure) an unreliable number for setting targets. Due to this variability in the 75th percentile number, a better way to pay a certain percentage above market is to adjust the market rates (medians or means) by that percentage to produce the targeted rates.

Calculating position in range versus percentile data Posted:
03/31/2010 07:41am
Revised: 03/31/2010 07:42am

I would agree with Paul's answer - That is the simpliest way to describe the incumbent's position relative to the market: between the 50th and 75th percentile.

Calculating position in range versus percentile data Posted:
03/31/2010 08:36am

Adding to Paul's comment, the other way could be giving the data point to the survey house and asking them to point percentrank for this incumbent. This will give you where exactly the employee falls. I have done this for several clients in my consulting days.

#2

Calculating position in range versus percentile data Posted:
11/21/2013 12:32pm

Can you help with more information on how to "scientifically" calculate an individual's market percentile position by assuming the survey data fell on a perfect normal bell distribution? A recent handout I obtained from a meeting has survey 25%,50%, 75% & 90%, an individual's compensation and a final calcuated market percentile position listed for the indivdual. I am trying to validate whether the market percentile position listed is correct or not and am having difficulty getting more information from the source of the handout. Thanks!

#1

Calculating position in range versus percentile data Posted:
11/21/2013 01:07pm

You can't do it without the raw data from the people who calcutated the the percentiles.

Calculating position in range versus percentile data Posted:
11/22/2013 12:26am

If your survey ranks all the entries from lowest to highest and all the intervals between observations are identical, it would be easy to extrapolate any specific percentile. If the survey includes a report of the percentile of a specific individual, that SHOULD be precisely correct as long as the surveyors had access to each individual observation so they could show the exact "rank" (in percentile terms) of each.

To extrapolate from the markers you showed in your last paragraph, the 80th %ile would probably fall approximately one-third of the distance between the 75th and the 80th percentile points, if the inter-observation intervals are identical. However, that never happens in real life, because pay suffers from heteroschedasticity http://www.statsmakemecry.com/smmctheblog/confusing-stats-terms-explained-heteroscedasticity-heteroske.html which means tightly clustered modes tend to appear at entry levels but values spread out at higher levels and become widely distributed, there are more cases below the average than above it, there are no zero observations but a few high-end outliers always exist... and other unique statistical properties, like positive kurtosis, skewed distributions, randomness and such apply, too.

If the survey TELLS you the percentile rank of a specific observation, it should be exactly correct; but if you try to extrapolate it, you will be making a guess and your estimate will probably have a bit of error to it. That said, an extrapolation from your example at the 80th percentile won't miss by too much, since the real 80th %ile will PROBABLY be closer to the 75th than to the 90th %ile (but three are no guarantees). On the other hand, trying to guess the 88th %ile or the 94th %ile accurately would most likely be very difficult, because the dispersion variation of higher ranking samples is much greater than at lower levels: the distance between the lowest and the next lowest tends to be much smaller than the distance between the second-highest and the very highest. You would need standard deviation statistics, too, for more refined estimates. Even then, pay does not follow the bell-shaped symmetrical parametric distribution underlying the definitions of reliability statistics, so you would still be estimating rather than identifying a true fact.

This would be an excellent question for a statistics professor. We have some, but I don't bother them on questions I think I can handle. Hope this helps. If not, try my expert co-worker chris.chasteen@erieri.com, who has his PhD in statistics and is also a member here. He can correct any errors of mine.

Calculating position in range versus percentile data Posted:
12/27/2013 06:45am

(1 rating)

Interesting discussion. One question I have (you can tell I am not a mathematics expert) is, what does the percentile positioning really matter? If the survey you are comparing against had one more (in a small sample) or several hundred more (in a large sample), the positioning of your datapoint would change. How does this compare against other surveys--are you looking at multiple sources?

Is this degree of precision truly helpful? My preference would be to use Jim's answer: "the individual is paid at 113% of the median." This information, combined with peer incumbent data, may be what is really needed to make a recommendation (if that is the point)?

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