Applied Statistical Inference [Modo de Compa
-
Upload
noelia-eva-castillo-llica -
Category
Documents
-
view
226 -
download
0
Transcript of Applied Statistical Inference [Modo de Compa
-
8/11/2019 Applied Statistical Inference [Modo de Compa
1/89
Hypothesis Testing
Can you convert your data into meaningful information?
o you know how to conduct experiments?
- D r. O. -
-
8/11/2019 Applied Statistical Inference [Modo de Compa
2/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
3/89
Population Sample
Statistics
Inference
Parameters
Presumption: belief dictated by probability
-
8/11/2019 Applied Statistical Inference [Modo de Compa
4/89
IndependentRelatedIndependentRelated
Intervaland
Ratio
Ordinal
Nominal
Two Samples N-SamplesSingle
Sample
Hypothesis Testing Map
Eyes Color, Sex, Race
Level Pain, Preference,.. #of Children,..{Integers}
{Any Real #}
-
8/11/2019 Applied Statistical Inference [Modo de Compa
5/89
:
:
1
0
:
:
1
0
::
1
0
Two-Tailed
Test
One-Tailed
Test
One-Tailed
Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
6/89
LetX1,, Xnbe alarge(e.g.,n 30) sample from a
population with mean and standard deviation . To test a
null hypothesis of the form
H0: = 0
H0: 0
H0: 0
Compute thez-score:
If is unknown it may be approximated by .
nz
/
0
nSt
/
0
-
8/11/2019 Applied Statistical Inference [Modo de Compa
7/89
H0:D= 3%H1:D 3%
Single Sample CaseEXERCI SE #1
-
8/11/2019 Applied Statistical Inference [Modo de Compa
8/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
9/89
n
stn
2
0
1
H0: D= 3%
H1: D 3% =0.494
df = n-1
=10-1= 9
-
8/11/2019 Applied Statistical Inference [Modo de Compa
10/89
EXERCI SE #
-
8/11/2019 Applied Statistical Inference [Modo de Compa
11/89
EXERCISE #
-
8/11/2019 Applied Statistical Inference [Modo de Compa
12/89
df = 13
-
8/11/2019 Applied Statistical Inference [Modo de Compa
13/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
14/89
Many studies have shown that direct eye contact and even patterns that look like eyes are
avoided by many animals. Some insects, such as moths, have even evolved large eye-spot patterns on their wings to help ward off predators. This research example, modeled
after Scaife's (1976) study, examines how eye-spot patterns affect the behavior of moth-
eating birds.
A sample ofn = 16 insectivorous birds is selected. The animals are tested in a box that
has two separate chambers (see Figure). The birds are free to roam from one chamber to
another through a doorway in a partition. On the wall of one chamber, two large eye-spotpatterns have been painted. The other chamber has plain walls. The birds are tested one
at a time by placing them in the doorway in the center of the apparatus. Each animal is
left in the box for 60 minutes, and the amount of time spent in the plain chamber is
recorded. Suppose that the sample of n= 16 birds spent an average of = 35 minutes in
the plain side with SS = 1215. Can we conclude that eye-spot patterns have an effect on
behavior? Note that while it is possible to predict a value for, we have no information
about the population standard deviation.
EXE RCISE #4
-
8/11/2019 Applied Statistical Inference [Modo de Compa
15/89
H0:D= 30
H1:D 30
97.5% confidence
-
8/11/2019 Applied Statistical Inference [Modo de Compa
16/89
H0:D 30
H1:D> 30
95% confidence
-
8/11/2019 Applied Statistical Inference [Modo de Compa
17/89
More Applications
-
8/11/2019 Applied Statistical Inference [Modo de Compa
18/89
H0:D= 0
H1:D 0
Two Related Samples Case
nSt D
/
Cluster Before After
X2-X1
-
8/11/2019 Applied Statistical Inference [Modo de Compa
19/89
Site X2X1
nS
Dt D
/
-
8/11/2019 Applied Statistical Inference [Modo de Compa
20/89
Site X2X1
df=4
-2.13
0:H
0:H
1
0
-
8/11/2019 Applied Statistical Inference [Modo de Compa
21/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
22/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
23/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
24/89
Cluster Before
H0:D 0H1:D< 0
After
The environmental policy must be well known across all the company levels. To certify
ISO 14001 a company wide training effort has been made to make sure that every
cluster in the company need less overtime dedication to this matter.
Note that weested the
mean = 0
already
-
8/11/2019 Applied Statistical Inference [Modo de Compa
25/89
H0:D 0
H1:D< 0
-
8/11/2019 Applied Statistical Inference [Modo de Compa
26/89
In-Class Work
-
8/11/2019 Applied Statistical Inference [Modo de Compa
27/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
28/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
29/89
Compare the mean numbers of days
spent in hibernation by hedgehogs in
two areas of the country using
randomly selected samples of each.
Suppose 10 hedgehogs in each area are
captured, radio-tagged and released.Their movements are monitored
throughout the winter to determine the
number of days when they did not
leave their nests.
Two Independent SamplesTest ( comparable)
-
8/11/2019 Applied Statistical Inference [Modo de Compa
30/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
31/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
32/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
33/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
34/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
35/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
36/89
Two Independent Samples Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
37/89
Two Independent Samples Test ( comparable)
-
8/11/2019 Applied Statistical Inference [Modo de Compa
38/89
Two Independent Samples Test ( comparable)
df =
-
8/11/2019 Applied Statistical Inference [Modo de Compa
39/89
Exercise
-
8/11/2019 Applied Statistical Inference [Modo de Compa
40/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
41/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
42/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
43/89
More Applications
-
8/11/2019 Applied Statistical Inference [Modo de Compa
44/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
45/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
46/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
47/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
48/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
49/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
50/89
Goodness of fit test (Chi2 test)It is suggested that dispersal of seeds from the edge of a plantation of trees
follows an inverse square law (i.e. the number of seeds travelling m is
proportional to 1/x2). We want to test this theory using an isolated stand of
trees on an area of moorland. Seeds will be collected in four 0.25 m2 plots at
each of the five distances, on the downwind side of the plantation. The total
numbers of seeds counted at each distance were:
Using the equation (theoretical or empirical)0.04 0.0564
X 294
-
8/11/2019 Applied Statistical Inference [Modo de Compa
51/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
52/89
168.923
If P-value (=0.05) >P-score; Then, H0is true
If P-value (=0.05)
P=score; Then, we have
significant evidence that
the results are not
consistent w/H0 , so H1is true.
One tailDist.
Multiply by
2
=0.054
-
8/11/2019 Applied Statistical Inference [Modo de Compa
53/89
If P-value (=0.05) >P-score; Then, H0is true
If P-value (=0.05)
P=score; Then, we have
significant evidence that
the results are not
consistent w/H0 , so H1is true.
7.814
168.923
-
8/11/2019 Applied Statistical Inference [Modo de Compa
54/89
Highschool College Graduate
67 25 8
Education
A pool of 100 individual have been surveyed with respect to level of
education (see table below). The population is expected to show the
following trend: High school 60%, College degree 25%, and Master and PhD15%. Is the sample representative of the population?
EXE RCISE #1
-
8/11/2019 Applied Statistical Inference [Modo de Compa
55/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
56/89
Poor Average Rich
A 8.19 -1.35 -6.84
B -1.64 5.93 -4.29
C -6.55 -4.58 11.13
Reactant
cata
lyst
Poor Average RichA 25 12 7 44
B 6 12 2 20
C 3 3 19 25
34 27 28 89
catalyst
Reactant
Poor Average Rich
A 16.81 13.35 13.84 44
B 7.64 6.07 6.29 20C 9.55 7.58 7.87 25
34 27 28 89
Reactant
cata
lyst
Difference (O-E)
Observed
Expected
-
8/11/2019 Applied Statistical Inference [Modo de Compa
57/89
Poor Average Rich
A 3.99 0.14 3.38 7.51
B 0.35 5.80 2.93 9.08
C 4.49 2.77 15.76 23.03
8.84 8.71 22.07 39.62
Reactant
catalyst
Difference (O-E)2
E
If P-score> 0.05 Then,there is insufficient
evidence to conclude that
there is association
between two factors
If P-score 0.05 Then,
there is significantevidence of an
association between two
factors.
One tailDist.
Multiply by
2
=1.03E-07
62.3924
-
8/11/2019 Applied Statistical Inference [Modo de Compa
58/89
Poor Average Rich
A 3.99 0.14 3.38 7.51
B 0.35 5.80 2.93 9.08
C 4.49 2.77 15.76 23.03
8.84 8.71 22.07 39.62
Reactant
catalyst
Difference (O-E)2
E
If P-score> 0.05 Then,there is insufficient
evidence to conclude that
there is association
between two factors
If P-score 0.05 Then,
there is significantevidence of an
association between two
factors.
One tailDist.
Multiply by
2
=1.03E-07
62.3924
9.487
-
8/11/2019 Applied Statistical Inference [Modo de Compa
59/89
A scientist is concern that his new developed drug is affecting the proportion
of sheep having stillborn lambs in his flock of sheep. He has records from
before the drug was tested in the population so he is able to compare withcurrent data.
EXE RCISE #1
-
8/11/2019 Applied Statistical Inference [Modo de Compa
60/89
Compare the mean numbers of
days spent in hibernation by
hedgehogs in two areas of the
country, using randomly
selected samples of each.
Suppose 10 hedgehogs in each
area are captured, radio-tagged
and released. Their movements
are monitored throughout the
winter to determine the number
of days when they did not leave
their nests
Two Independent Samples Test ( check ifcomparable)
33.344
32.233
-
8/11/2019 Applied Statistical Inference [Modo de Compa
61/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
62/89
12 2
2
12 2
2
These are one-tailedprobabilities, so we need to
multiply them by 2.
Therefore P= 96%
4.0255
1.034
-
8/11/2019 Applied Statistical Inference [Modo de Compa
63/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
64/89
2
2
2
11
2
2
2
10
:H
:H
2
2
2
11
2
2
2
10
:H
:H
One-Tailed
Test
One-Tailed
Test
)1N,1N,( 21FFscore
)1N,1N,1( 21FFscore
The hypothesis that the two standard deviations are equal is rejected if
1.034
-
8/11/2019 Applied Statistical Inference [Modo de Compa
65/89
EXE RCI SE #1
-
8/11/2019 Applied Statistical Inference [Modo de Compa
66/89
3.912
1.34
-
8/11/2019 Applied Statistical Inference [Modo de Compa
67/89
ANOVA Test
A B C D
x x x x
x x x x
x x x x
x x x x
x x x x
ONE-FACTOR
FLUX
LEVELS
REPLICATES
SampleValues
1 2 3
A x,x,x,x x,x,x,x x,x,x
B x,x,x,x x,x,x,x x,x,x
C x,x,x,x x,x,x,x x,x,x
D x,x,x,x x,x,x,x x,x,x
LEVELS
REAGENT
LEVELS
CATALYST
One-Way ANOVA Two-Way ANOVA
1 2 3 c 1 2 3 c 1 2 3 c
1 x, x, x x, x, x x, x,x x, x,x x ,x, x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x x, x, x x, x, x2 x, x, x x, x, x x, x,x x, x,x x ,x, x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x x, x, x x, x, x
3 x, x, x x, x, x x, x,x x, x,x x ,x, x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x x, x, x x, x, x
a x, x, x x, x, x x, x,x x, x,x x ,x, x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x x, x, x x, x, x
FACTORB
FACTORC
LEVELS
1 2 b
LEVELS
FACTORC
LEVELS
FACTORA
LEVELS
FACTORC
LEVELS
Three-Way ANOVA
-
8/11/2019 Applied Statistical Inference [Modo de Compa
68/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
69/89
One-Way ANOVA Test
A B C D
x x x x
x x x x
x x x x
x x x x
x x x x
ONE-FACTOR
FLUX
LEVELS
REPLICATES
SampleValues
ONE FACTOR
-
8/11/2019 Applied Statistical Inference [Modo de Compa
70/89
One-Way ANOVA TestA B C Dx x x xx x x x
x x x x
x x x x
x x x x
ONE-FACTOR
FLUX
LEVELS
REPLICATES
SampleValues
ONE-FACTOR
FLUX
LEVELS
A B C
REPLICATES
SampleV
alues 16 38 19
13 21 14
36 36 17
29 39 15
18 26 12
22.4 32 15.4 23.267
ONE FACTOR
-
8/11/2019 Applied Statistical Inference [Modo de Compa
71/89
One-Way ANOVA TestA B C Dx x x xx x x x
x x x x
x x x x
x x x x
ONE-FACTOR
FLUX
LEVELS
REPLICATES
SampleValues
5.098
6.272
-
8/11/2019 Applied Statistical Inference [Modo de Compa
72/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
73/89
-
8/11/2019 Applied Statistical Inference [Modo de Compa
74/89
Two-Way ANOVA Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
75/89
Two-Way ANOVA Test
20y
i
iB
-
8/11/2019 Applied Statistical Inference [Modo de Compa
76/89
Two-Way ANOVA Test
20y
i
iB
-
8/11/2019 Applied Statistical Inference [Modo de Compa
77/89
Two-Way ANOVA Test
20y
i
iB)05.0%(5
-
8/11/2019 Applied Statistical Inference [Modo de Compa
78/89
Two-Way ANOVA Test
20y
i
iB)05.0%(5
-
8/11/2019 Applied Statistical Inference [Modo de Compa
79/89
Two-Way ANOVA Test
Two Way ANOVA Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
80/89
Two-Way ANOVA Test
Two Way ANOVA Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
81/89
Two-Way ANOVA Test
T W ANOVA T t
-
8/11/2019 Applied Statistical Inference [Modo de Compa
82/89
Two-Way ANOVA Test
Th W ANOVA T t
-
8/11/2019 Applied Statistical Inference [Modo de Compa
83/89
Three-Way ANOVA Test
1 2 3 c 1 2 3 c 1 2 3 c
1 x ,x ,x x ,x ,x x, x, x x, x, x x, x,x x, x,x x ,x ,x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x
2 x ,x ,x x ,x ,x x, x, x x, x, x x, x,x x, x,x x ,x ,x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x
3 x ,x ,x x ,x ,x x, x, x x, x, x x, x,x x, x,x x ,x ,x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x
a x ,x ,x x ,x ,x x, x, x x, x, x x, x,x x, x,x x ,x ,x x ,x, x x ,x, x x ,x, x x ,x ,x x ,x ,x
FACTORB
FACTORC
LEVELS
1 2 b
LEVELS
FACTORC
LEVELS
FACTORA
LEVELS
FACTORC
LEVELS
Simplified Case
Th W ANOVA T t
-
8/11/2019 Applied Statistical Inference [Modo de Compa
84/89
Three-Way ANOVA Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
85/89
Three-Way ANOVA Test
Th W ANOVA T t
-
8/11/2019 Applied Statistical Inference [Modo de Compa
86/89
Three-Way ANOVA Test
-
8/11/2019 Applied Statistical Inference [Modo de Compa
87/89
Th W ANOVA T t
-
8/11/2019 Applied Statistical Inference [Modo de Compa
88/89
Three-Way ANOVA Test
Computed F > F(5%)
Therefore, We reject Ho
for AB, AC, and BC. In
other words, these
interactions do have animpact in the dependent
variable.
-
8/11/2019 Applied Statistical Inference [Modo de Compa
89/89