Nit-Picking the Coverage? I Don't Think So
Justin Katz
Something jumps out about this isolated parenthetical "correction" in today's story about the state of the state address in the Providence Journal, by Katherine Gregg, Steve Peoples, and Cynthia Needham:
With respect to state workers, he said: “The average state employee earns $61,000 per year in salary with fringe benefits valued at another $34,000 (a total of $95,000) and a 35-hour work week. Bringing the health-care, pension benefits and work week into line with the private sector could save the state tens of millions per year. This will be the focal point of our contract negotiation with labor leadership.”
(A Journal analysis found that the median state employee salary was $46,600 as of last June.)
As I'm sure the professional journalists are aware, there's a difference between the average of a set of numbers and their median., and there are different circumstances during which each is more appropriate. I have a hard time believing, frankly, that the writers of both the speech and of the news article weren't very careful about which word they used.
If it is indeed the case that the average is 31% greater than the median, the implication would be that more than half of state workers make well above the that number. I'd have to do more research than I care to expend on this particular item to say for sure, but I'd wager that there are additional considerations (e.g., which jobs are counted) that make it inappropriate for the Projo to offer such a note unless it's willing to spend the column inches on a thorough explanation.
I'd like to see them both explain how they arrived at their numbers in more full fashion (or at least ensure they're both using the same set of data). But I don't see how we can cry foul on one party here without doing likewise on the other.
Justin says, "If it is indeed the case that the average is 31% greater than the median, the implication would be that more than half of state workers make well above the that number"
Hmmm? There's an extra word there, or something. Anyway, If the median is 46.6K, then exactly 1/2 of the workers make more than that amount, which is the definition of the median.
Averages (means) are skewed by extreme values. When there are such extreme values, the median is generally the better measure, but reporting BOTH mean and median tell us more about the distribution than either alone.
Generally (but not always) if a distribution has a higher mean than median, the distribution is "right skewed". In plain words, if the median is 46K and the mean is 63K, it is most likely that MOST workers are making less than the average, and a smallish number of high salaries are "well above that number". I wonder who they might be?
(For fun, find the mean and median of the series 40,40,40,50,120)
It's not that the median is "more accurate" than the mean, since they are different measures, but it seems pretty clear Carcieri's speech writers chose the average, rather than the median, because it inflates the number, makes state workers look wealthier, and makes it easier to take things (like a week of salary) away from them.
By the way, why is it OK to take a week's salary away from state workers, but not everyone else? It's not like they or their families are to blame for the deficit. Why not take the governor's and the state legislature's salaries instead?
Oh, and Justin...
I know this is terribly pedantic, but I also know you're a writer and would care and won't take offense. Isn't it "nit-picking"? (Nits being louse eggs, or louse larvae or something?)
LOL- Either I totally hallucinated "Knit Picking" or you changed it while I was writing the above comment (and thus before you had seen it).
Please feel free to delete this comment and the one above!
This is about the 8th time the Projo has "contradicted" the administrations "average" figure by using a "median" figure. I emailed every reporter who made this mistake. I even called Kathy Gregg and left an answer on her voicemail. After so many such "errors", it is clearly no coincidence.
Mike,
Thanks for the notice. I will be sure to call those reporters myself and tell them that the median is a perfectly valid measure, and is doubtless the better one under the circumstances.
They did the right thing, but I bet they know that already.
Yes, Chalkdust, I taught 6–8 grade math classes once upon a time, so I understand how means and medians work. Your argument is generally true, but in this case you're ignoring generalizations that one can reasonably make about the data: First, that there aren't any Bill Gateses in state government, making $1 billion per year, and second, that the half below the median don't deviate by all that much. Given those two assumptions, the half below the median are likely near it, leaving the half above the median higher than the mean.
Consider the series 20, 20, 40, 40, 40, 40, 46, 46, 46, 60, 70, 100, 100, 100, 100, 120. The average is 61.75, and the median is 46. To achieve the same average vs. median, you'd have to pull the higher numbers within a smaller range of deviation and compensate, as I said, with a Bill Gates or two at the top. (This factor becomes more powerful, I'd note, as the group becomes larger, and the group of state employees is pretty big.)
As to which measure is "the better one under the circumstances," I'd argue that the average is preferable in this context because we're more interested in their aggregate cost than individual comparisons (as in comparisons between, say, teachers and private-sector workers). Again, consider my hypothetical series: the sum of the numbers is 988. The sum if they were all the average would be... 988. The sum if they were all the median would be 736. To the point, you'd use the median if you intended to minimize the sense of the group's total salary expense.
For the record, my objection isn't to the Projo's using the median, but to its doing so in a manner that presents it as a correction when it is actually an alternative. Your assertion notwithstanding, it isn't a "doubtless" matter.
As to the nit/knit thing, among the various items on my multitasking list is looking at shirts, so yes, I did initially put up "knit-picking," but I changed it pretty soon thereafter.
Instead of arguing about statistical distributions, I dug up the projo article from July of 2007.
http://www.projo.com/news/content/STATE_EMPLOYEE_SALARIES_07-29-07_3G67LS2.241f5a1.html
Here's the breakdown
Total Employees: 16,106
Under 30K 1423 (8.8%)
Between 30K and 60K 9,908 (61.5%)
Between 60-100 4155 (25.8%)
Above $100K: 620 (3.9%)
Range: $1-$286,840 (2 people including the Gov's wife take $1/year. The URI basketball coach is the highest paid state employee).
Median Salary: $46.6
Mean Salary: $51.5
70% made less than the $60K that the Governor says is the average salary, but how did Carcieri got $61K as the mean? I can't believe the average state salary jumped $10K since July.
I realize I didn't respond to Justin's point. If you're interested in the aggregate cost, you'll report the aggregate cost. Averages don't help with this.
If you're interested in the question of whether state workers are paid too much, you'll report what workers make. The question is whether the mean or the median best represents that.
Carcieri used the mean because it makes it sound like the "average" worker makes a ton of money. However, if you realize that 70% of workers make less than Carcieri's number, you'll know that it's not a fair representation of the "average" state worker.
Justin,
Absolutely excellent explanation of average vs. median. Kind of reminds me of "their, they're, there" -- but they all sound alike, so what's it matter, right?. I guess the Projo writers never made it through 8th grade math.
Chalkdust,
Thank you for pointing out this gem:
"The URI basketball coach is the highest paid state employee."
I don't doubt it for a second. We certainly have our priorities straight.
Justin,
The State house employees for Pravda are not journalists or reporters but propagandists closely aligned with the unions and Democratic party. If you have a few minutes sometime take a look at Gregg's 'reporting' on the Smart Staffing contracts from last year. Pure propaganda! Think you'll find her spin on the 22% overhead particularly disingenuous and dirty. Gregg in particular has a long history of misinforming the reader by intentionally omitting relevant information from her articles. Sadly you can't trust a single thing written in Pravda these days. They don't even try to mask their agendas anymore. Just can't help but wonder if in their quiet moments the lack of journalistic integrity and standards they employ ever bothers them. Oh wait Pravda is a union shop isn't it? Means they have no integrity and no standards for quality work product.
Nevermind! lol
Chalkdust.
Your cite doesn't include overtime. I don't have the time right now to seek (or collect) comparable data for that, but in an "industry" in which workers often have shortened workweeks (e.g., 35 hours), overtime could be significant.
As to the current debate, it could be that Carcieri's analysis cut out folks who made nominal amounts ($1) and a college student who worked a half hour and made under $4. Your/the Projo's numbers include part-time, seasonal, basically all employees. A very good argument could be made that many of them can be excluded. (Although, if a significant number make around $50,000 for a 20-hour week, that would certainly be interesting.)
So, add in overtime, remove some of the peculiarities, and what do you have? I don't know... I'm out of blogging time this morning. But the point is that the Projo oversimplified things — essentially making a spun claim from the governor's opponents' side.
It's understandable that the governor wouldn't go into extended statistical detail in a verbal speech. It's poor reportage that the Journal would do the same.
Average vs median.
If you take the average compensation earned and multiply it by the number of workers, you will arrive at the actual total cost of the work force. If you take the median compensation and multiply by the number of state workers, you will fall short by quite a bit.
The ProJo wished to put forward a falsely lower number by "correcting" the Governor.
Welp, looks like they changed tack this morning, but still find the Guvs numbers too high:
In Tuesday’s speech, Carcieri said the average state employee works a 35-hour workweek and earns $61,000 per year. A separate Journal analysis found that the average state employee earned $51,400 last year.
Of course, as has been stated, the methodology of each party needs to be revealed or its just political he said/she said.
Will: At some schools, they argue that boosters contribute far more to the school than the school spends, so a winning team is worth it. I can't speak for URI.
Justin: I don't think the 2 $1/year workers make any difference, but you're right about overtime and part time workers being included. However, if you exclude those, you'll then have to include all part-time and overtime from any private sector wages you compare it to.
The Governor has a political agenda he's trying to achieve and he's going to present the numbers in the way most favorable to that agenda. I don't have a problem with him doing that, and I don't have a problem with the ProJo pointing out that the median is different. I agree that the Projo might have added a line to explain mean v. median to edify readers. Now the Governor's office can explain how they got an mean that is $10K higher than the projo, and why the mean is better than the median. Maybe we can get them to do a follow-up story.
Monique: What you say about the relationship between mean and median and total is correct, but it is not relevant to determining which is the best representation of the data, or which is a "false" representation". Skewness in income distributions is exactly why income is often, if not typically, reported in in terms of median. This is pretty standard stuff, and not really controversial.
There is nothing "false" about the Projo's reporting of the median income. In fact, it's a more telling figure than the Governor's use of average. Knowing both numbers is even better than knowing one or the other.
Marc-
I have a feeling the Projo "average" doesn't include either overtime or longevity. The governor's $95,000 figure is correct. If you take ALL compensation (overtime, pension, health care, longevity,, etc.), divide that by the number of FTE you will get to the $95,000 average.
Hell, we have prison guards in this state making $120,000 in pay alone, without benefits.
As to overtime, I believe (but can't say for certain) that many state employees (if not most) get overtime on a daily basis, i.e., if they work over seven hours in a particular day the overtime rate kicks in (unlike the real world in which overtime rates kick in once one works over 30 hours in a week).
Also, with the average workers in RI only making something in the $30's, without a pension and far less (if any) health care and other benefits - for a workweek that is about 15% longer than a state employee - then the discussions regarding mean vs. average pay for state employees becomes somewhat academic for it is inarguable that public sector compensation is grossly out of line with private sector compensation (which, being determined by the free market, tells us what positions are actually worth).
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I'd like to see them both explain how they arrived at their numbers in more full fashion (or at least ensure they're both using the same set of data). But I don't see how we can cry foul on one party here without doing likewise on the other.
Posted by: rhody at January 23, 2008 7:29 PMJustin says, "If it is indeed the case that the average is 31% greater than the median, the implication would be that more than half of state workers make well above the that number"
Hmmm? There's an extra word there, or something. Anyway, If the median is 46.6K, then exactly 1/2 of the workers make more than that amount, which is the definition of the median.
Averages (means) are skewed by extreme values. When there are such extreme values, the median is generally the better measure, but reporting BOTH mean and median tell us more about the distribution than either alone.
Generally (but not always) if a distribution has a higher mean than median, the distribution is "right skewed". In plain words, if the median is 46K and the mean is 63K, it is most likely that MOST workers are making less than the average, and a smallish number of high salaries are "well above that number". I wonder who they might be?
(For fun, find the mean and median of the series 40,40,40,50,120)
It's not that the median is "more accurate" than the mean, since they are different measures, but it seems pretty clear Carcieri's speech writers chose the average, rather than the median, because it inflates the number, makes state workers look wealthier, and makes it easier to take things (like a week of salary) away from them.
By the way, why is it OK to take a week's salary away from state workers, but not everyone else? It's not like they or their families are to blame for the deficit. Why not take the governor's and the state legislature's salaries instead?
Posted by: Chalkdust at January 23, 2008 9:33 PMOh, and Justin...
I know this is terribly pedantic, but I also know you're a writer and would care and won't take offense. Isn't it "nit-picking"? (Nits being louse eggs, or louse larvae or something?)
Posted by: chalkdust at January 23, 2008 9:37 PMLOL- Either I totally hallucinated "Knit Picking" or you changed it while I was writing the above comment (and thus before you had seen it).
Please feel free to delete this comment and the one above!
Posted by: chalkdust at January 23, 2008 9:40 PMThis is about the 8th time the Projo has "contradicted" the administrations "average" figure by using a "median" figure. I emailed every reporter who made this mistake. I even called Kathy Gregg and left an answer on her voicemail. After so many such "errors", it is clearly no coincidence.
Posted by: Mike at January 23, 2008 9:42 PMMike,
Thanks for the notice. I will be sure to call those reporters myself and tell them that the median is a perfectly valid measure, and is doubtless the better one under the circumstances.
They did the right thing, but I bet they know that already.
Posted by: chalkdust at January 23, 2008 9:46 PMYes, Chalkdust, I taught 6–8 grade math classes once upon a time, so I understand how means and medians work. Your argument is generally true, but in this case you're ignoring generalizations that one can reasonably make about the data: First, that there aren't any Bill Gateses in state government, making $1 billion per year, and second, that the half below the median don't deviate by all that much. Given those two assumptions, the half below the median are likely near it, leaving the half above the median higher than the mean.
Consider the series 20, 20, 40, 40, 40, 40, 46, 46, 46, 60, 70, 100, 100, 100, 100, 120. The average is 61.75, and the median is 46. To achieve the same average vs. median, you'd have to pull the higher numbers within a smaller range of deviation and compensate, as I said, with a Bill Gates or two at the top. (This factor becomes more powerful, I'd note, as the group becomes larger, and the group of state employees is pretty big.)
As to which measure is "the better one under the circumstances," I'd argue that the average is preferable in this context because we're more interested in their aggregate cost than individual comparisons (as in comparisons between, say, teachers and private-sector workers). Again, consider my hypothetical series: the sum of the numbers is 988. The sum if they were all the average would be... 988. The sum if they were all the median would be 736. To the point, you'd use the median if you intended to minimize the sense of the group's total salary expense.
For the record, my objection isn't to the Projo's using the median, but to its doing so in a manner that presents it as a correction when it is actually an alternative. Your assertion notwithstanding, it isn't a "doubtless" matter.
As to the nit/knit thing, among the various items on my multitasking list is looking at shirts, so yes, I did initially put up "knit-picking," but I changed it pretty soon thereafter.
Posted by: Justin Katz at January 23, 2008 10:17 PMInstead of arguing about statistical distributions, I dug up the projo article from July of 2007.
http://www.projo.com/news/content/STATE_EMPLOYEE_SALARIES_07-29-07_3G67LS2.241f5a1.html
Here's the breakdown
Total Employees: 16,106
Under 30K 1423 (8.8%)
Between 30K and 60K 9,908 (61.5%)
Between 60-100 4155 (25.8%)
Above $100K: 620 (3.9%)
Range: $1-$286,840 (2 people including the Gov's wife take $1/year. The URI basketball coach is the highest paid state employee).
Median Salary: $46.6
Mean Salary: $51.5
70% made less than the $60K that the Governor says is the average salary, but how did Carcieri got $61K as the mean? I can't believe the average state salary jumped $10K since July.
Posted by: chalkdust at January 24, 2008 12:20 AMI realize I didn't respond to Justin's point. If you're interested in the aggregate cost, you'll report the aggregate cost. Averages don't help with this.
If you're interested in the question of whether state workers are paid too much, you'll report what workers make. The question is whether the mean or the median best represents that.
Carcieri used the mean because it makes it sound like the "average" worker makes a ton of money. However, if you realize that 70% of workers make less than Carcieri's number, you'll know that it's not a fair representation of the "average" state worker.
Posted by: chalkdust at January 24, 2008 12:42 AMJustin,
Absolutely excellent explanation of average vs. median. Kind of reminds me of "their, they're, there" -- but they all sound alike, so what's it matter, right?. I guess the Projo writers never made it through 8th grade math.
Chalkdust,
Thank you for pointing out this gem:
"The URI basketball coach is the highest paid state employee."
I don't doubt it for a second. We certainly have our priorities straight.
Posted by: Will at January 24, 2008 1:15 AMJustin,
The State house employees for Pravda are not journalists or reporters but propagandists closely aligned with the unions and Democratic party. If you have a few minutes sometime take a look at Gregg's 'reporting' on the Smart Staffing contracts from last year. Pure propaganda! Think you'll find her spin on the 22% overhead particularly disingenuous and dirty. Gregg in particular has a long history of misinforming the reader by intentionally omitting relevant information from her articles. Sadly you can't trust a single thing written in Pravda these days. They don't even try to mask their agendas anymore. Just can't help but wonder if in their quiet moments the lack of journalistic integrity and standards they employ ever bothers them. Oh wait Pravda is a union shop isn't it? Means they have no integrity and no standards for quality work product.
Posted by: Tim at January 24, 2008 6:26 AMNevermind! lol
Chalkdust.
Your cite doesn't include overtime. I don't have the time right now to seek (or collect) comparable data for that, but in an "industry" in which workers often have shortened workweeks (e.g., 35 hours), overtime could be significant.
As to the current debate, it could be that Carcieri's analysis cut out folks who made nominal amounts ($1) and a college student who worked a half hour and made under $4. Your/the Projo's numbers include part-time, seasonal, basically all employees. A very good argument could be made that many of them can be excluded. (Although, if a significant number make around $50,000 for a 20-hour week, that would certainly be interesting.)
So, add in overtime, remove some of the peculiarities, and what do you have? I don't know... I'm out of blogging time this morning. But the point is that the Projo oversimplified things — essentially making a spun claim from the governor's opponents' side.
It's understandable that the governor wouldn't go into extended statistical detail in a verbal speech. It's poor reportage that the Journal would do the same.
Posted by: Justin Katz at January 24, 2008 6:28 AMAverage vs median.
If you take the average compensation earned and multiply it by the number of workers, you will arrive at the actual total cost of the work force. If you take the median compensation and multiply by the number of state workers, you will fall short by quite a bit.
The ProJo wished to put forward a falsely lower number by "correcting" the Governor.
Posted by: Monique at January 24, 2008 7:44 AMWelp, looks like they changed tack this morning, but still find the Guvs numbers too high:
In Tuesday’s speech, Carcieri said the average state employee works a 35-hour workweek and earns $61,000 per year. A separate Journal analysis found that the average state employee earned $51,400 last year.
Of course, as has been stated, the methodology of each party needs to be revealed or its just political he said/she said.
Posted by: Marc at January 24, 2008 8:32 AMWill: At some schools, they argue that boosters contribute far more to the school than the school spends, so a winning team is worth it. I can't speak for URI.
Justin: I don't think the 2 $1/year workers make any difference, but you're right about overtime and part time workers being included. However, if you exclude those, you'll then have to include all part-time and overtime from any private sector wages you compare it to.
The Governor has a political agenda he's trying to achieve and he's going to present the numbers in the way most favorable to that agenda. I don't have a problem with him doing that, and I don't have a problem with the ProJo pointing out that the median is different. I agree that the Projo might have added a line to explain mean v. median to edify readers. Now the Governor's office can explain how they got an mean that is $10K higher than the projo, and why the mean is better than the median. Maybe we can get them to do a follow-up story.
Monique: What you say about the relationship between mean and median and total is correct, but it is not relevant to determining which is the best representation of the data, or which is a "false" representation". Skewness in income distributions is exactly why income is often, if not typically, reported in in terms of median. This is pretty standard stuff, and not really controversial.
There is nothing "false" about the Projo's reporting of the median income. In fact, it's a more telling figure than the Governor's use of average. Knowing both numbers is even better than knowing one or the other.
Posted by: Chalkdust at January 24, 2008 8:48 AMMarc-
Posted by: Mike at January 24, 2008 8:57 AMI have a feeling the Projo "average" doesn't include either overtime or longevity. The governor's $95,000 figure is correct. If you take ALL compensation (overtime, pension, health care, longevity,, etc.), divide that by the number of FTE you will get to the $95,000 average.
Hell, we have prison guards in this state making $120,000 in pay alone, without benefits.
As to overtime, I believe (but can't say for certain) that many state employees (if not most) get overtime on a daily basis, i.e., if they work over seven hours in a particular day the overtime rate kicks in (unlike the real world in which overtime rates kick in once one works over 30 hours in a week).
Also, with the average workers in RI only making something in the $30's, without a pension and far less (if any) health care and other benefits - for a workweek that is about 15% longer than a state employee - then the discussions regarding mean vs. average pay for state employees becomes somewhat academic for it is inarguable that public sector compensation is grossly out of line with private sector compensation (which, being determined by the free market, tells us what positions are actually worth).
Posted by: Tom W at January 24, 2008 10:22 AM