RMS vs standard deviation versus standard error

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RMS vs standard deviation versus standard error
Message posted by Chad English on June 7, 2000 at 12:00 AM (ET)

I'm confused on two issues.

1. All references I can find for "standard error" calculated it as ste = std/sqrt(n), where std is the standard deviation, and define it as an estimate for the standard deviation of the mean if the sampling was repeated many times.

Yet Excel has some function called the standard error (STEYX) that requires 2 sets of inputs (X,Y), uses a more complex calculation using both x and y (more like a correlation), and outputs something different than std/sqrt(n).

What is this Excel standard error?

2. I have several references that use "root-mean-square" (RMS) and "standard error" interchangeably. I also recall being told that RMS and standard deviation (not error) are equal when the mean is zero. However, I have taken the same data sets with zero means and calculated RMS, standard deviation, standard error, and even the Excel standard error (see above, using 1,2,... as the second sample set). None come out the same. Standard deviation and RMS are generally close, but in some cases are off by a factor of 2 or more.

Is RMS equivalent to any of them for a zero mean?

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: RMS vs standard deviation versus standard error
Message posted by Jack Tomsky on June 9, 2000 at 12:00 AM (ET)

The expression for the standard error which you referenced, ste = std/sqrt(n), is correct for the sample mean. Other statistics could have more complicated standard errors. For example, the sample standard deviation s from a normal distribution has a standard error which involves gamma functions.

Excel's STEYX function is applied in linear regression. With y as the dependent variable and x as the independent variable, STEEYX is the conditional standard deviation of y given x.

Jack

Re: RMS vs standard deviation versus standard error
Message posted by vijay (via 130.113.246.136) on August 22, 2001 at 1:05 PM (ET)

im calculating standard error for my data and im not sure whether to use root of N or root of N-1. can someone exlpain?

Re: RMS vs standard deviation versus standard error
Message posted by darius (via 200.23.217.10) on August 22, 2001 at 7:02 PM (ET)

The use of N (for the total population) = Root mean square deviation or N-1 (for a sample of the population) is so because = sample standard deviation.

The different dispersion statistics yield different values because each statistic characterizes the dispersion of the data in a slighly different way, there is little to recommend one of there dispersion statistics over the other.

In my opinion the use of within sample standard deviation (for Control Charting) is a better way to estimate the standard deviation, but each application has its own dispersion statistic.

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