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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
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Update: June 2012
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