Physics 257
Lecture 4:
χ
2
Prof. Matt Dobbs
Physics Department, McGill U.
Prof. M. Dobbs,
Physics 257
Oct 5, 2006
2
Outline
±
Questions ?
±
Comments from Assignment and Lab reports.
z
Be careful not to round off numbers in intermediate calculations!
±
Review of
χ
2
and DoF
±
The Language of Probability – rolling dice.
±
Linearizing Fits
z
Power law fits
z
Exponential fits
±
Lab Break next week.
z
Class at NORMAL TIME will be more fun than usual.
z
Assignment 4 will be due TWO weeks from now (available from
WebCT by the weekend)
Prof. M. Dobbs,
Physics 257
Oct 5, 2006
4
Prof. M. Dobbs,
Physics 257
Oct 5, 2006
5
χ
2
±
The
χ
2
is used to evaluate the level of compatibility
between observed data and a theoretical hypothesis
for the PDF of that data.
z
E.g. given the errors of my measurements, does my data
agree with a straight line hypothesis?
±
Inferential statistics
: the use of statistics to make
inferences concerning some unknown aspect
(usually a parameter) of a population.
z
E.g. Does this best fit line accurately describe the data?
z
What is the
statistical significance
of this
measurement?
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View Full DocumentProf. M. Dobbs,
Physics 257
Oct 5, 2006
6
χ
2
()
2
1
2
2
2
1
2
2
2
1
2
2
1
reduced
)
;
(
1
reduced
)
;
(
∑
∑
∑
=
=
=
⎥
⎦
⎤
⎢
⎣
⎡
Δ
+
−
−
=
=
⎥
⎦
⎤
⎢
⎣
⎡
Δ
−
−
=
=
⎥
⎦
⎤
⎢
⎣
⎡
Δ
−
=
N
i
i
i
i
N
i
i
i
i
i
N
i
i
i
i
i
y
b
ax
y
N
DOF
y
a
x
f
y
M
N
DOF
y
a
x
f
y
χ
±
Quantifies the degree to which a theoretical function
(like a straight line ax+b) agrees with the data.
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 Fall '07
 Dobbs
 Physics, Regression Analysis, Radioactive Decay, Nonlinear regression, Prof. Matt Dobbs, Prof. M. Dobbs

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