Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Statistical Analysis
Name: Jamie
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
I read your email to a young gentleman regarding Statistical Significance.

Lets say we have a 12 month rolling return rate of 3.88% in July and the 12 month rolling return rate jumps to 3.97% in Aug. Would the sample size contain all products produced in the last 12 month?

If the 12 month Sample size on avg(x)=39,581,411
The July Sample size(y)=3,043,863
The Aug Sample size(z)= 3,913,006
The Initial Rolling Return Rate(D)=3.88%
The Second Rolling return Rate(F)=3.97%

Can you please give me an equation to calculate the Stat Significance?



Replies:
Hello and thanks for your email.

I am forwarding your question and my response to the Newton web site for posting. Please feel free to post your questions there as you may end up getting several answers which are better than one alone.

A 12-month moving average adds the immediate past 12 months data and divides the sum by 12. This way, monthly or seasonal changes are smoothed over, and a trend over this time span becomes discernible.

In so far as moving averages are concerned, the sample size is irrelevant. You may have 2 month, 3 months, ... or longer moving average numbers. You can have other moving averages, for example, weighted moving averages. As an example, you can give more weight to the most recent data.

Any kind of averaging, however, tends to smoothen rather than accentuate variations (necessary to establish statistically significant changes). In your example, you may want to plot a histogram of number of parts and look at the standard deviation of the best fitting curve. Then, those months that production is in excess of the mean by more than say 1 or 2 standard deviations, you may attach some statistical significance to it and seek the reason for the "sharp" variation from the mean. Statistically significant is a subjective measure and relates to all sort of case-specific factors.

I hope I have answered your question.

Dr. K.


Probably the best explanation will come from one of your people after they understand the idea. It's a simple idea, really, though the mechanics of arriving at reliable answers from raw data are not simple.

The idea behind statistical significance is that the information you want is obscured by other information you don't care about. In the textbook case, you measure something, and the result you get is influenced by random events that have nothing to do with your measurement. Until you know something about the random events and how they affect your measurement results, you don't know what those results mean.

When you've made enough measurements that you have a representative sample of all the nasty things random events can do to your measurement, then you can begin to distinguish the effects of random events from effect you're trying to measure. If the effect you're measuring (let me call this the "signal") is huge compared to the effects of random events (the "noise"), then you can get away with only a rough idea of how the random events perturb the measurement. But if the signal is small compared to the noise, you must understand the noise very well. When you do understand the noise well enough to distinguish it from the signal, you have statistically significant results.

Tim Mooney



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory