OK, I am about to prepare a document asking for a raise, but I am doing so because I feel that I am being underpaid with respect to my profession and the area in which I live.
The research I have from salary.com and government sources (bureau of labor or whatever) indicates not that I am being underpaid per se, but that I am below the median income level.
Now, my statistical skills are not what they used to be, and they never were that great, but as I understand it the median is the middle value, the mean is the average value, and the mode is the most common value. I am pretty sure I don’t have that messed up. However, salary.com indicates the 25th, 50th and 75th percentile on their graphs with respect to the median.
Now, my question here is this: why would we use the median to gauge salary levels? To me it seems that the arithmetic or geometric mean would be much more appropriate as an accurate reflection of wages. For all I know I am paid what most people in my profession are paid. Also, am I correct in thinking that the 75th percential of median income is, quite simply, [median income]/[0.75]??? What is the "fiftieth percentile of median income]? Maybe I am not even saying it correctly.
Basically I need to know if I can make a case based on this data.
Can someone help me understand what is going on here? This is a matter of $2500 or so a year, and to me that is nothing to sneeze at. Thank you.
[gah! server timed out… well, I have refreshed a seperate GQ page and this didn’t show up, so I hope this doesn’t double-post]
Actually, salaries are one of the textbook examples of why the median is often a more useful measure of central tendancy than the mean (the mode is hardly ever useful for jack).
One simple example will show why:
Microsoft has around 32,000 employees. Most of the employees do Ok and make somewhere between $30,000 and $120,000 a year you guess by a taking quick look at the payroll. However, you want to be more exact so you write a simple program to compute the mean income of all Microsoft employees. You run the program and find that the mean (average?) is $206,000. How can that be? You sort the incomes in descending order and find that one Mr. William Gates, whoever that is, pulled in over $5,000,000,000 last year alone. This extreme value greatly distorts the mean for all of the other employees while the median value, if you had calculated that, would not have been affected at all.
There is your answer. The median is used in cases where a few extreme values in either direction can distort the average for the entire group.
I neglected the more practical parts of your post.
Yes, the median is the most useful measure for salary comparisons. That is why it is almost always the measure of central tendancy used for this purpose. It is not easily swayed by outliers.
Your understanding of the 75th percentile is 100% dead wrong. That is probably why you are getting confused.
Explanation: Take 100 people. Order them in ascending order of income. Imagine them standing in a line if you like. The 25th percentile means that you walked up to the 25th person and drew a line beside him. The median is the person standing directly in the middle of the line. The 75th percentile is the 75th person in line and above. There is NO MATH involved. It is simple ordering. It has nothing to do with the relative values involved. It just means that if you are in the 75th percentile in a salary survey, then you made more than 75% of those you were compared against. The median is the 50% percentile.
I agree entirely with Shagnasty’s comments on why the median is preferable to the mean for salaries.
Now, he’s talking about average salary for a company rather than average salary for a particular job, but a similar problem holds. If you were absolutely sure that the data formed a normal distribution, then the median and the average wouldn’t be very far apart. But, in lots (most?) salary surveys, there aint nuthin’ close to a normal distribution.
There are lots of problems with salary surveys that lead to funny-looking data, which is why median is preferred. With median (that is, 50th percentile), you know exactly what it means: half the reported salaries are above and half below that mark. With mean, you’re not sure exactly what it means.
Here’s a few examples of why salary surveys often get funny-looking distributions for a job:
Job matching is not precise. Just because a job is labelled “entry level accountant” doesn’t mean the same thing at (say) one of the Major Accounting Firms, where an entry level accountant may be partner track, as it does at (say) WalMart, where the accountant handles the finances and taxes. Pay can be very different, even the job can be very different.
Data errors are rampant. Sometimes people lie about their salaries to make them look more important. Some people include their bonus in their salary data. Some people get stock options or similar items that are hard to quantify.
Finally, I find that salary.com is NOT a good source of data. It’s based largely on what the recruiting firms find when they place someone. The recruiting firms have a strong bias to making the salary as high as possible, so the data is suspect right away (the people conducting the survey are NOT objective.) And, a new recruit tends to have a higher salary than a current employee – either through bonus sign-on or just because the person wouldn’t switch jobs (usually) unless the salary was higher.
So, professional Human Resource folks tend not to pay too much attention to salary.com and similar sites.
BTW, among my credentials: I teach a graduate school course in compensation, and I’ve been consulting in the field for 25 years or so. Trust me.
I’ll answer your last question, "Basically I need to know if I can make a case based on this data. Can someone help me understand what is going on here?"
No you can’t, IMO, make a case based on this. Your thesis seems to be, “I am average, but I am being paid less than my average peers. I want to be on a par with the other average people”. It will not fly, unless your company is having both a really good financial year and a really bad recruiting year.
You need to talk about how the experience you’ve gained on the job makes you ABOVE average. Talk about systems and procedures and projects, or knowledge and experience. rather than “skills”. You say your skills aren’t what they use to be, so keep away from them.
Is this document something you prepare as part of some routine performance evaluation? Or is it something originating with you, because of what you’ve found out? Each calls for a somewhat different style.
While the answers are centering around the statistics, don’t forget to do some old fashioned legwork. Is it possible to make discrete queries as to salary levels in your area for similar positions? It might help.
Why?
My brother does salary surveys as part of his job with Uncle Sam in Chicago. He has found salary.com and similar sites list salaries and wages much lower than reality in the professions he surveys.
So in between the statistical responses, don’t forget to question the actual numbers used before you manipulate them.
Ok, I got it. yojimboguy, my statistical skills aren’t what they used to be, but I don’t use statistics professionally! My professional skills are as strong as they ever were, but as alwasy there is room for improvement.
As well, I only went to salary.com because I wanted more than just government sources, I wanted something like an industry source, but I wasn’t sure where to get that. Also, most employers that I’ve met won’t tell you what salary they would pay for such and such a position unless you were on the way to be hired, or you ran into a headhunter of some sort.
I am NOT looking to leave or otherwise threaten my employer! I just felt that government data alone (though I do have federal and state data) would back me up, because some of the data is extrapolated, not factual.
I would be below the 25th percentile in wages, but it sure doesn’t feel like a solid case.
And, thanks for the comments on salary.com… I’ll mention them only if I have to. I was really looking to note that my geographic area usually gets a higher salary based on the cost of living index, and I think salary.com couldn’t hurt there since it correlates strongly with the government’s extrapolation (industry specific) and their hard data (overall).
I guess I am just pretty darn nervous about the whole affair. I’d never dream of quitting this job as it stands, so I don’t know how to be aggressive about getting a raise.
And, as a side-note, I think the mode would be pretty important if one had the median to go along with it. Especially in the case of salaries… no? Hmm, I guess it all depends on how one looks at it.
eris, if you are just below the 25th percentile, that means you are just outside the top 25% of earners. (This is sometimes referred to as being just outside “upper quartile” pay, incidentally). This hardly helps your case! I presume you mean just below the 75th percentile (so that 75% of comparable professionals are better off), which would support your argument much better.
Dex touched on this, but to spell it out: in a perfectly symmetrical distribution (such as the normal), the mean, median and mode are all the same number. In a positively skewed distribution such as pay follows, the mode is always the smallest, the mean always the biggest and mode always lies between the two. You could almost call it the average average. Just FYI.
As regards modes: imagine the distribution of salaries. It should follow a “humped” shape, starting at zero and with a long tail stretching off to the higher salaries. Where the peak of the hump is, that is the mode. The median will be to the right of the hump and the mean to the far right. The mode is useful sometimes, for example average shoe size is probably best considered as the shoe size most people have. Salary-wise, I’d say it is still more useful than the mean which is, as stated, pretty useless for this exercise.
Nervous about asking for a pay rise? I understand, but you needn’t be. Consider it like this: rather than the “penalty” they will receive for saying no being your resignation, it will instead be a demotivated (and hence less productive) employee. As such it is in their interests to provide the pay rise.
Use the word “motivation” a lot. You need them to know that you know what your worth is. That way they know that if you don’t get what you’re worth they not only risk losing you at some point but they risk losing some of your productivity right now.
That is not correct. The percentile score depends which way you want to sort the data. In this case, the 25th percentile is the bad side to be on (you make only as much as around 25% of others in your field). That is just the way that salary.com and most other salary percentiles are expressed.
If this were a distribution of golf scores however, we could sort the data the same way and the 25th percentile would be the good side to be on (the lower the better).
Interesting. I’ve never come across salary statistics as being displayed anything other than top-down, so that the top 25% of salaries are known as the “upper quartile” or “twenty-fifth percentile”. Maybe you have different conventions stateside.
Or maybe I just have a selective memory.
That’s the trouble with “percentiles” anyway. Saying “upper quartile” is pretty clear. And median works both ways. I’d eschew the ambiguity if I were you, eris. Kick percentiles to the curb.
Most research studies that use income statistics transform the Dollar figures (an odd unit, actually) by doing a log transformation on the salaries. This brings the distribution more towards something that makes sense. See, taking central tendency statistics of a distributrion is most relevent when the distribution is mostly symmetrical (of course, skewed and kurtotic “smears” fall in this category.) Salaries tend to follow a logrithmic distribution, thus mean and median tend to be less explanatory. (And, as said above, “mode” is kind of the dumpy kid on the playground.)
Spritle, who realizes that he hasn’t added much to the discussion
