Post on 18-Jan-2018
description
Teaching Statistical Concepts with Simulated Data
Andrej Blejec
National Institute of Biology andUniversity of LjubljanaLjubljana, Slovenia
andrej.blejec@nib.si
Kinds of data
• real life data• invented data• simulated data
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Real life data
• interesting for students• need subject matter knowledge to interpret
statistical results• oversimplified problems• complex problems• unclear relevance of statistical results
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Invented data
• a collection of data, no story• useful mostly for calculation drill• no possible interpretation of results• uninteresting for students
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Simulated data
• sampled from known distribution• composed according to prespecified model
e.g. Y = a + b * X + , with known distribution of X and
• known statistical propertiese.g. mean, variance, regression coefficient
• analysis results can be compared to true values
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Goals of teaching statistics
• interest for statistics• understanding of statistical methods• skills in use of statistics• experiences in analyzing data• other ( insert your own :) ___________
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
real life data
invented data
simulated data
interest understanding skills experiences
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Sun
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Absorption spectrum
Sun
Hydrogen
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Sun
Hydrogen
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Least squares estimate of the mean
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
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d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
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23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
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d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
x
0 1 2 3 4 5 6
02
46
810
12
m*
Varia
nce
0 1 2 3 4 5 6
01
23
4
True mean value μ
LS estimate
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Mea
n sq
uare
d de
viat
ions
Maximum likelihood estimation of the mean
x
0 1 2 3 4 5 6
x
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
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0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
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m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
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0.2
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0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
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m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
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m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
-80
-60
-40
-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
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m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
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0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
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m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
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-20
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
m)
0 1 2 3 4 5 6
0.0
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m*
Log
likel
ihoo
d
0 1 2 3 4 5 6
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0
True mean value μ
ML estimate
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Maximum likelihood estimate of standard deviation
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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0.4
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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0.4
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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-20
Log
likel
ihoo
dp
( x |
sd )
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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sd
Log
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ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
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-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
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sd
Log
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ihoo
d
0 1 2 3 4 5 6
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Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
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0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
p(x|
sd)
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
sd
Log
likel
ihoo
d
0 1 2 3 4 5 6
-100
-60
-20
Log
likel
ihoo
dp
( x |
sd )
ML estimate
True standard deviation σ
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Hypothesis testing:
significance
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Hypothesis testing:
significance
or rather a surprise ?
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
020
4060
8010
012
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
H0: mu= 50
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
020
4060
8010
012
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
H0: mu= 50
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
020
4060
8010
012
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
H0: mu= 50
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
020
4060
8010
012
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12
H0: mu= 50
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
020
4060
8010
012
0
SAMPLE
H0: mu= 50
020
4060
8010
012
0
SAMPLE
H1: mu= 80
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
020
4060
8010
012
0
SAMPLE
H0: mu= 50
020
4060
8010
012
0
SAMPLE
H1: mu= 80
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Confidence intervals
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Weldon, K.L. Statistics: A Conceptual Approach.. Prentice-Hall. New York. 1986
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Bad sampling implies bias
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Bias due to “leave max out”
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Confidence intervals for variance
Biased and unbiased estimators
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 5 10 15 20 25
020
4060
8010
0rnorm | var | n= 5 | biased
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
02
46
810
12
var var
0 1 2 3 4 5
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 5 10 15 20 25
020
4060
8010
0rnorm | var | n= 5 |
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
02
46
810
var var
0 1 2 3 4 5
020
4060
8010
0
unbiased
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 2 4 6
020
4060
8010
0rnorm | var | n= 10 |
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
05
1015
var var
0 1 2 3 4 5
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 1 2 3 4
020
4060
8010
0rnorm | var | n= 25 |
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
05
1015
var var
0 1 2 3 4 5
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0.0 0.5 1.0 1.5 2.0
020
4060
8010
0rnorm | var | n= 50 |
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
05
1015
2025
var var
0 1 2 3 4 5
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0.0 0.5 1.0 1.5 2.0
020
4060
8010
0rnorm | var | n= 100 |
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
010
2030
var var
0 1 2 3 4 5
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0.0 0.5 1.0 1.5
020
4060
8010
0rnorm | var | n= 200 |
var
0 1 2 3 4 5
020
4060
8010
0
0 1 2 3 4 5
010
2030
40
var var
0 1 2 3 4 5
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Confidence intervals for variance:
what if assumptions are not met?
Case of asymetric parent population
var
0 100 200 300 400
020
4060
8010
0rlnorm | var | n= 5 |
var
0 5 10 15 20
020
4060
8010
0
0 5 10 15 20
010
2030
40
var var
0 5 10 15 20
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 50 100 150
020
4060
8010
0rlnorm | var | n= 10 |
var
0 5 10 15 20
020
4060
8010
0
0 5 10 15 20
05
1015
2025
30
var var
0 5 10 15 20
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 50 100 150 200
020
4060
8010
0rlnorm | var | n= 25 |
var
0 5 10 15 20
020
4060
8010
0
0 5 10 15 20
05
1015
2025
30
var var
0 5 10 15 20
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 10 20 30 40 50
020
4060
8010
0rlnorm | var | n= 50 |
var
0 5 10 15 20
020
4060
8010
0
0 5 10 15 20
05
1015
2025
var var
0 5 10 15 20
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 5 10 15 20
020
4060
8010
0rlnorm | var | n= 100 |
var
0 5 10 15 20
020
4060
8010
0
0 5 10 15 20
05
1015
20
var var
0 5 10 15 20
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
var
0 5 10 15 20 25 30
020
4060
8010
0rlnorm | var | n= 200 |
var
0 5 10 15 20
020
4060
8010
0
0 5 10 15 20
05
1015
2025
30
var var
0 5 10 15 20
020
4060
8010
0
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Confidence band in linear regression
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3
y = 0 + 1 *N(0, 1 )+N(0, 1 ) n= 50 Conf. level = 0.95 r^2 = 0.5
y = 0 + 1 *N(0, 1 )+N(0, 1 ) n= 50 Conf. level = 0.95 r^2 = 0.5
y = -0.142 + 0.974 * Xr^2= 0.538
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3
y = 0 + 1 *N(0, 1 )+N(0, 1 ) n= 50 Conf. level = 0.95 r^2 = 0.5
y = 0 + 1 *N(0, 1 )+N(0, 1 ) n= 50 Conf. level = 0.95 r^2 = 0.5
y = -0.142 + 0.974 * Xr^2= 0.538
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3
y = 0 + 1 *N(0, 1 )+N(0, 1 ) n= 50 Conf. level = 0.95 r^2 = 0.5
y = 0 + 1 *N(0, 1 )+N(0, 1 ) n= 50 Conf. level = 0.95 r^2 = 0.5
0.153 + 1.07 * Xr^2= 0.413
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 1 )
n= 40 Conf. level = 0.95 r^2 = 0.5
-0.0934 + 0.923 * X
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 1 )
n= 40 Conf. level = 0.95 r^2 = 0.5
-0.0934 + 0.923 * X-0.0934 + 0.923 * X-0.11 + 1.04 * X-0.11 + 1.04 * X-0.00754 + 1.01 * X-0.00754 + 1.01 * X0.0667 + 1.23 * X
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 1 )
n= 40 Conf. level = 0.95 r^2 = 0.5
-0.0934 + 0.923 * X-0.0934 + 0.923 * X-0.11 + 1.04 * X-0.11 + 1.04 * X-0.00754 + 1.01 * X-0.00754 + 1.01 * X0.0667 + 1.23 * X0.0667 + 1.23 * X-0.0458 + 1.18 * X-0.0458 + 1.18 * X0.0297 + 1.08 * X0.0297 + 1.08 * X-0.205 + 0.785 * X-0.205 + 0.785 * X0.0115 + 0.833 * X0.0115 + 0.833 * X0.0933 + 1.2 * X0.0933 + 1.2 * X0.00637 + 0.968 * X0.00637 + 0.968 * X
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 1 )
n= 40 Conf. level = 0.95 r^2 = 0.5
-0.2 + 0.841 * X-0.2 + 0.841 * X-0.257 + 1.18 * X-0.257 + 1.18 * X0.116 + 0.751 * X0.116 + 0.751 * X0.00216 + 0.907 * X
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 1 )
n= 40 Conf. level = 0.95 r^2 = 0.5
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 4 )
n= 40 Conf. level = 0.95 r^2 = 0.2
-0.4 + 0.683 * X
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 4 )
n= 40 Conf. level = 0.95 r^2 = 0.2
-0.4 + 0.683 * X-0.4 + 0.683 * X-0.514 + 1.36 * X-0.514 + 1.36 * X0.232 + 0.501 * X0.232 + 0.501 * X0.00432 + 0.815 * X0.00432 + 0.815 * X-0.695 + 1.04 * X-0.695 + 1.04 * X-0.0815 + 0.528 * X-0.0815 + 0.528 * X-0.234 + 1.07 * X-0.234 + 1.07 * X-0.723 + 0.653 * X-0.723 + 0.653 * X0.161 + 1.56 * X0.161 + 1.56 * X-0.359 + 0.595 * X-0.359 + 0.595 * X
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
x
y
-3 -2 -1 0 1 2 3
-3-2
-10
12
3y = 0 + 1 *N(0, 1 )+N(0, 4 )
n= 40 Conf. level = 0.95 r^2 = 0.2
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
Final remarks
• Graphically supported simulations can to some extent ‑ ‑replace the proofs, usually not understandable to non-mathematics majors. Maybe they are the answer to some questions:
• "If an audience is not convinced by proof, why do proof? (Moore, 1996)
• “Do [students] need to know the theory or do they need to understand the concept?” (J Brown and I David, ICOTS8, 2010)
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011
• Simulated data have to be combined with real life data and projects
• Simulated data can serve as pure and simple data on which we can train our perception for statistical results and learn what patterns and properties in data can be revealed by applied method
• After such preparation students will be able to interpret the real life and subject matter data in all their complexity
Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011