View source for Statistics for Experimenters

= Definitions=

;Accuracy
: A measure of how close the experimental result is to the "true" value

; Precisison
: A meauser of close the result is determined without knowing the true vaule
: Precision is often used to predict the accuracy of a quantity to be measured (you don't know the answer before doing the experiment)


;Random Error
: The error in a result due to the finite precision of an experiment
: A measure of the statistical fluctuations which result after repeated experimentation

;Systematic Error
: Reproducable inaccuracies introduced by faulty equipment, calibration, or technique.

=Probability Distributions=

;Binomial distribtuion
:random, independent process with two possible outcomes
: best example is a coin toss, its either heads or tails
: mean (<math>\mu</math>) = number of tries <math>n</math>(coin flips) * probability of success<math>p</math> (head, 1/2)
:standard deviation(<math>\sigma</math>) = <math>np(1-p)</math>

; Poisson Distribution
: standard deviation (<math>\sigma</math>) = root of the mean (<math>\sqrt{\mu}</math>)
: use in counting experiments
: the distribtuion approximates the Binomial Distribution for the special case when the probability of the event occuring is small.
: In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.

The probability distribution is given as
:<math>P(k,\mu) = \frac{\mu^{k}e^{-\mu}}{k!}</math>

where

: <math>k</math> = number of occurances
: <math>\mu</math> = mean

;Gaussian/Normal Distribution
: Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) = <math>\Gamma</math>
:standard deviation (<math>\sigma</math>) = <math>\frac{\Gamma} {2 \sqrt{2 \ln 2}} = \frac{\Gamma} {2.354}</math>
:error = <math>0.675 \sigma</math>