# Error Defined

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• #47746

newbie
Participant

What is the difference between experimental error, standard error, and margin of error?  Thanks!

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#159576

Jim Shelor
Participant

Newbie,
Experimental error is variation in the results of an experiment under identical input conditions.  This is sometimes referred to as residual error.
Standard error is the square root of the variance of the sample distribution of a statistic.  If an experiment is run many times under the same input conditions, standard error = SQRT(experimental error).  Note also, standard deviation is the square root of the variance of the sample distribution of a statistic.
The margin of error is the probability that the answer obtained may be in error.  Example, a poll of political candidates normally has a margin of error or + or – 3%.
Regards,
Jim Shelor

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#159578

Chris Seider
Participant

newbie,
Why do you ask?  Is there some deeper reason because I’m sure you looked up the definitions with google, msn, or yahoo search already.
Jim S.’s definitions I might quibble a bit  with (e.g. look at the standard error formula) and the margin of error is actually related to the standard error and the degree of confidence (I’m assuming normality of course) but hopefully you have your question answered.
good luck….

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#159581

newbie
Participant

Standard error is the square root of the variance of the sample distribution of a statistic…..Note also, standard deviation is the square root of the variance of the sample distribution of a statistic.
So then standard error, error, and standard deviation are synonyms, as are experimental error, residual error, and variance?
Thanks Jim!

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#159582

newbie
Participant

Yes sir, looked them up, but there appears to be slightly different nuances that I dont understand in several of these error terms, which often appear to be essentially the same when i look at their calcuations.
Thanks for the input!

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#159583

Chris Seider
Participant

newbie…..
Nope.  Sorry.  Standard error is not the same as standard deviation and standard error is not the same as experimental error NOR is experimental error the same as standard deviation.
I’m hoping Jim reclarifies and helps….if he doesn’t I’ll check tomorrow.  I’m overseas and am quitting for the evening.

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#159584

newbie
Participant

Righto….again, thanks for the help…i’ll get back in the books.

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#159585

Chris Seider
Participant

newbie,
Glad to see you aren’t trying to be spoon fed.
Hint:  What is the name of s/sqrt(n)?

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#159586

Forms of error
Participant

Newbie, you are asking questions in regards to three distinct types of error. They relate to research design (Experiment), statistical tools (GLM, i.e. regression, ANOVA etc.) and error associated with the estimation of population parameters. I doubt that you will find the answer in one statistics book (If someone knows one, please let me know):
Research design (error):  The residual error is the remainder in an experiment after the main effect and the interaction effect have been “discounted”. Experimental error can have two meaninga: The more general meaning is related to the error associated with the fact that you run an experiment. The second meaning is technical. In the technical sense experimental error occurs in nested designs when you have error due to observation and error due to the experiment. It can also occur when subsampling in a single-factor study with completely randomized desing.
Statistical analysis tool (error): The residuals are the difference between the observed value and the “predicted” value in the estimation of a regression equation, or ANOVA or GLM. Residuals represent the error associated with the equation. Residuals belong to the estimated equation based on the sample, the error term is part of the statistical model underlying the analysis. Random error is differentiated from nonrandom error.
Estimation of population parameter (error): If the standard deviation of a statistic is estimated from data, the result is called the standard error of that statistic. For example, the standard error of the mean quantifies the precision with which the sample mean estimates the population mean. It is calculated as the standard deviation of the sample divided by square root of n and is the most frequently used standard error statistic. The standard deviation is calculated as the square root of the variance of a sample or a population. If the the variation is calculated based on the total population the denominator is n rather than n – 1.
The margin of error is often a short-form for the margin of error of the populaiton mean. It is the difference that the researcher allows between the sample result and the result that s(he) obtained if the entire population was sampled. It is affected by the level of confidence, the sameple size and the variation in the populaiton. Effectively the margin of error of the populaiton mean is calcuated by a multiplier of the level of confidence (t, z distribution) x the standard error.

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#159587

Big Deal
Participant

c. seider, don’t make such a big deal out of this question. give the answer and dont’ bore us with your silly little quizzes. nobody cares where you are anyway. big deal!

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#159608

Chris Seider
Participant

Hmmmph.
I guess you have just shown a propensity to disregard people in one post.  You just disregarded the quality of the original question and you just disregarded my approach……
Hope you aren’t this unhelfpul or disrespectful with your coworkers.

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#159612

Big Deal
Participant

Big DEAL!!!!

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#159616

Jim Shelor
Participant

Newbie,

There are some misleading statements in my first response.  Let me try this again.

Standard error is the square root of variance of the sample distribution of a statistic.  The sample distribution of a statistic is the distribution formed when many samples of the statistic are obtained from the sample distribution and plotted on a frequency plot.  The standard error is the standard deviation of the sample distribution for the statistic under consideration and can be estimated from the standard distribution of the population and the number of samples taken for the statistic under examination.  For example:

If many samples are taken of the population and the mean obtained from each sample is plotted on a frequency plot, the standard error of the mean is the standard deviation of the mean sample distribution.  This can be estimated by the equation sigma-mean = sigma-population/SQRT (n) where n is the number of samples taken to form the mean sample distribution.  Standard error of the mean is a very common, frequently used term.

There are other standard errors for other statistics.  A few examples of these standard errors and their estimation formulas are:

Standard error-median = 1.126 (standard deviation of population)/SQRT(n)

Standard error-standard deviation = 0.71 (standard deviation of population/SQRT(n).

As you can see, the standard deviation of the population is not the same as the standard error.

I hope this clears up standard error.

Best regards,

Jim Shelor

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#159617

Jim Shelor
Participant

In the second paragraph of the above post, standart distribution of the population should have been standard deviation of the population.
I hate it when I do that.

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#159625

newbie
Participant

Hey Jim,
Thanks for the follow-up…so let`s see….
If many samples are taken of the population and the mean obtained from each sample is plotted on a frequency plot, the standard error of the mean is the standard deviation of the mean sample distribution.  This can be estimated by the equation sigma-mean = sigma-population/SQRT (n) where n is the number of samples taken to form the mean sample distribution.  Standard error of the mean is a very common, frequently used term.

So standard error is simply the standard deviation of a set of means?  No different in purpose than std dev, it simply substitutes sample means for individual observations, yes?

So applied to a DOE format, the SE would then be the sq root of the (pooled ??) variance taken from all observations for a given response variable…yes?

I sure appreciate the help!

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#159626

newbie
Participant

Thanks so much….gotta digest this…hope you wont mind a follow up question or two.

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#159628

Jim Shelor
Participant

Newbie,
A correction.
If many samples are taken of the population and the mean obtained from each sample is plotted on a frequency plot, the standard error of the mean is the standard deviation of the mean sample distribution.  This can be estimated by the equation sigma-mean = sigma-population/SQRT (n) where n is the number of samples used to calculate each mean (this is equivalent to the number of samples in a subgroup).  Standard error of the mean is a very common, frequently used term.

Eventually, I am going to get this thing written down correctly.

Your summation statement on the standard error of the mean is essentially correct.

I am still working on the DOE format question.

Regards,

Jim Shelor

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#159629

Jim Ace
Participant

The following link provides several different perspectives about “error.”  I strongly recommend that you take a few minutes and click around in this reference, then review some of the key material.