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Re: [Phys-l] projectile motion lab


The standard deviation is related to
how close the center of the trials would be to the "true" value.


Here I think it should say "standard deviation _of the mean_ is related to
how close the center (which I understand as the mean) of the trials would be
to the "true" value." ? (seems like just a typo)

Yes, that is a typo!


If I were going to report the "time it takes for the marble to roll
between the two photogates", I would report <T> +/- s/Sqrt(N).
I hope that is correct.

Yes, I would agree with that, too. The more you repeat an experiment, the less variation there would be, so you can predict the "true" value better and better as N increases. Another way to look at it: if you were to repeat the full set of N measurements M times, then the stardard deviation of the M averages would be (approximately) s/Sqrt(N).


In propogating uncertainty through the calculation, should I use s
as Tim suggests, or should I use s/Sqrt(N) as I originally thought?

I suppose that depends on the goal. If you are trying to predict any given trial (which I think was the intent of the original post) then you want to use s (sample standard deviation) rather than SE (Standard Error = s/Sqrt(N)) to propogate the errors. The next trial will fall within +/- s 68% of the time and within +/- 2s 95% of the time (assuming a normal distribution which may or may not be a good approximation here). This would help you draw a ring that would contain most of the trials.

If you wanted to predict the "true" mean, then you would use the SE's. If you did several sets of N trials, the average for each set would be a little different, which would be related to a propergation of errors based on the SE's.

Or how about this as a summary:
The propogation of "s" would help you draw a target that would contain the individual trials most of the time. The propogation of "SE" would help you draw a (much smaller target) that would contain the average of the trials most of the time.



Tim F