As an elected Board of Education member I was concerned with the Spotlight on Education published in the Villager a few weeks ago and what Woodstock Truth published on the compound annual growth rate of spending for our different educational units.
 
For over ten years I have looked for a commonly agreed upon cost differential figure for PK-8, the town controlled schools, and our outsourced 9-12 system. The number needs to be black and white, no loose ends, like not including transportation or special needs. Just a hard number for what does a student in PK -8 cost, all inclusive, and the same for 9-12 regardless of where they go to school.
 
The Woodstock Academy has not weighed in on this but Mr. Richardson and Superintendent Baran seem to agree on the BOE published numbers at least in concept.
 
I read the post here on Truth and could not figure out how, using the same numbers, Mr. Richardson and Dr. Baran could come up with different answers. So not claiming to be a statistician I went to the internet to educate myself.

1. What is Compound Annual Growth Rate?
a. I went to several different sites – the most straight forward definition is shown below but all were very close.

2. What is the formula for figuring the Compound Annual Growth Rate?
a. Again I went to several sites, all variations of the same.

3.  Proof both answers published to see who was misleading the townspeople of Woodstock.
a. I ran Dr. Baran’s first, his answer was correct.
b. I ran Mr. Richardson’s, his answer was also totally correct.
c. How could they both be correct?
d. Back to the internet, I found many articles of Annual Growth and Annual Percent Rates. Interestingly they were not pointed at education but to the spinning and manipulation of numbers that have landed us in the deep recession we are now living in.

What is going on?

It seems to be a case of using numbers to prove a point that a person wants to prove and may truly believe. Dr. Baran’s statement: over the past five years, Woodstock’s total education budget has increased at a compound annual rate of growth of 5%, to $15,475,800 for this fiscal year 2008-09. This includes all regular education costs PK-8, all high school regular education costs, and all special education costs PK-12.

Ok, let’s check it out:

To understand the steps please see example below:
Find the time units- 2009-2005 = 4.
Start value: $12,551,462 (2004-2005)
End value: $15,475,800 (2008-2009)

So, divide $15,475,800 by $12,551,462 = 1.2329878383888665718782401603893
2009 -2005 = 4 or raise to ¼ power = .25

1.2329878383888665718782401603893 raised to the ¼ power or .25 = 1.0537551210704967150839179395851

1.0537551210704967150839179395851 – 1 = 0.053755121070496715083917939585116

Round to .054 and multiply by 100 to convert to a percentage = 5.4 percent or rounded down to 5%; Dr. Baran’s answer, and it is correct- Got that?

So how can Mr. Richardson also be correct?

The answer lies in how you look at it; total dollars or dollars per student. Much to the surprise of the BOE which was on a course to build more and bigger buildings, (remember the DRA study) the data was released that the PK-8 system enrollment was on a decrease. That was one of the points of information that came out of the $40,000.00 feasibility study. Don’t get me wrong, it was money well spent and the BOE would not be doing its job if forward thinking was not happening, ultimately it saved the townspeople money.

Back to our problem of how can both gentlemen be right; again, total dollars vs. dollars per student.

Using the same formula Mr. Richardson analyzed the dollars per student which yields much more detailed info. I went through the same steps to proof Mr. Richardson’s numbers.

You can follow Mr. Richardson’s figures here on the Truth site they are very straight forward and I was able to recreate them easily.

What is the take away on this? The 5% (rounded down from 5.4%) figure is correct for total education dollars spent. It is just a question of how and where those dollars were spent. Dr. Baran’s is looking at dollars spent at the High School level, not the per student cost. The population at the 9-12 level is growing still and the PK-8 level is shrinking.

We outsource our 9-12 students to several schools and pay tuition that varies widely from $0 to the spending limit of our special needs students. This means we pay for all of our 9-12 students on a per student rate or head count at all the schools. In this way we have provided a great education to our students who go on to perform very well at college and beyond. This is a team effort from all schools and teachers PK-4, 5-8, the Academy and all the other schools we send our 9-12 students to.

Remember, the 1st grader now will be a 12th grader before you know it, also remember we are talking about your kids and mine. This could be our biggest problem; unfortunately as a board, we seem to be more concerned about control and personal views than students.

I have been asking at CABE and at the State level how much more it costs for a 9-12 school vs. a PK-8 school, I have not gotten a definitive answer, but it has ranged from 10%-20%.

So, let’s look at where we are today using the published data:

PK-8 = $10,411 (08-09 budget).  10% = $1,041.10 added together = $11,452 which is where 9-12 should be if you believe 10% more is the correct cost differential. 

The current figure of $11,662 (‘08/09) is ~12% more than PK-8.  If 15% is what you think the differential should be, it equals $11,972 or $310 more than we now pay.

There is an old saying: “There are lies, damned lies, and statistics.” The statement refers to the persuasive power of numbers, the use of statistics to bolster weak arguments, and the tendency of people to disparage statistics that do not support their positions.

Please leave your comments.

Steven Rosendahl

As always I am speaking as a townsperson and parent and not a sitting member of the BOE.

Compound Annual Growth Rate
Compound Annual Growth Rate (CAGR) is a business and investing specific term for the geometric mean growth rate on an annualized basis. It represents the smoothed annualized gain earned over the investment time horizon. CAGR is not an accounting term, but remains widely used, particularly in growth industries or to compare the growth rates of two investments because CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. CAGR is often used to describe the growth over a period of time of some element of the business, for example revenue, units delivered, registered users, etc.

Formula



• V(t0) : start value, V(tn) : finish value, tn − t0 : number of years.
• Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion.