More Statistical Formulas - HP RPN SCIENTIFIC WP 34S Owner's Manual

More Statistical Formulas

Note that complete results of measured samples must include both an information about
the expected value and about its uncertainty.
 For samples drawn out of a Gaussian (additive) process, the expected value is the
arithmetic mean and its uncertainty is given by its standard error (see x and SERR).
 For samples drawn out of a log-normal (multiplicative) process, the expected value is
the geometric mean and its uncertainty is given by its scattering factor (see x
 For samples drawn out of other processes other measures apply.
Be assured not everything is Gaussian in real world!
(and should be checked well in advance of calculating e.g. means) using suitable tests –
turn to applicable statistical reference literature.
The following functions as named in the left column are all found in STAT (except x and s,
which are added to this table for comparison only).
Name Remarks (see p.
(1) For a linear fit model, the correlation coefficient is
For an arbitrary fit model
determination; it indicates the fraction of the variation of the dependent data
CORR
mined by the variation of the independent data
2
x ; for
r
total variation of
A regression is significant if
inverse of the t-distribution.
(1) For a linear fit model, the population covariance is

COV

COV
xy
90
Generally, the statistical model shall be chosen that matches observations best. In many real life cases,
however, dramatic deviations from the model distribution are found – then you cannot expect the calculated
consequences matching the reality any better.
By the way: Since the pdf of the Gaussian distribution will never reach zero, this statistical model tells you
to expect individual items far, far away from the mean value when your sample becomes large enough.
This, however, does not match reality. So we must conclude nothing at all is really Gaussian in real world.
Nevertheless, the Gaussian distribution is a very successful model for describing a lot of real world
observations. Just never forget the limits of such models.
WP 34S Owner's Manual
74 for general information)
R ( x

, y is completely independent of
0
y is due to x .
  

n x y x y
i i i i
90

2
r 1
) , the value
x
x

n 2 

 
1
r t . 0


n 2
2
1 r

2
n . Compare s below.
XY
Edition 3.1
Process features can be detected
s

xy
. See s
r

s s
x y
 
 


2
R x y

i i
is the coefficient of
 


2
y y
i

2
. For r 1 , y is fully determined by

2
; and for e.g.
r

, with the right side being the
99

, ).
g m
and s below.
XY
y deter-
, 93% of the
. 0 93
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