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Expert: - 11/13/2008


Question
QUESTION: Hi Scott.

I am investigating variances between projected and actual costs in my workplace and plan to implement a solution to reduce the spread between the two.

At present, I have taken a baseline measurement of historical data.  Each figure is laid out as follows:

Estimate- $45,000
Actual cost- $65,000
Variance- +44%

This means I have a pre-intervention dataset which comprises of variances.

Following my “solution”, I plan to take another sample similar to the above and will then compare one with the other in an attempt to show how great I am.  Hmmm…

The trouble is, I don’t have the first idea how to compare 2 sets of data which comprise of variances.

If the sets were “normal” numbers, I would use either a Kruskal Wallis or t-test (depending on the nature of the data sets) to compare.

My real sticking point on this is that- as variance can be either positive or negative, the rance crosses zero.

Any ideas?  Any and all help appreciated.

Thanks,

Paul


ANSWER: I won't go into detail bu will mention that the variance is always known to be positive.  The variance is the σ˛ where σ is the standard deviation.  The ± on variance refers the to fact the variance (which is always positive) can be added or subtracted.

The F test compares variances.

---------- FOLLOW-UP ----------

QUESTION: Hi again Scott.

I've had another thought on this.

Won't this variance be inherently skewed?  The reason is that, you could come in at 300% over budget ($40k actual, when $10k was forecast).  However, it's not possible to come in at anymore than 99.9999999% under budget (that would mean spending 1c).

Does this make sense?  Am I just causing problems for everyone?

Cheers,

Paul


Answer
In real life, statistics are used everywhere but they aren't quite right.  For example, according to the normal distribution, whatever you are dealing with might be negative, even if it's a measurement.  The chances of this occuring are so small, however, it's usually just ignored.

In this problem, money might actually be lost, so $10 was spent and then $20 was lost, it would be said to have a -200% profit.

The chances of this happen may be so far out of question that they just aren't there, but that could be the same as being more than 4 or 5 standard deviations below on a normal curve.  The answers 0, even though it is actually 0.00003167 for 4 and 0.0000002867 for 5.

The curve that is being fit is only used as an approximation and usually there is a margin of error that usually is much larger than either of these numbers.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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