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Ground rules, Suggestions, Syllabus Find a good study/homework partner work together regularly
You will REQUIRE a 2-variable statistics graphing calculator, preferably the TI-83 or TI-84(if you have a TI 89, it will do, but I am not as familiar with its usage). We will also useMINITAB a lot.
Bring book and calculator to every class.
Read materials ahead of time, and try (at least try) section EXERCISES prior to beingcovered in class. (I suggest trying pretty much every other odd number.)
Homework assigned for GRADING will include work posted in BlackBoard and selectionsfrom the text. These will be representative of applications and QUIZZES/EXAMS.
Bring your homework, problems, questions to class. After I cover the material, examples, and
some homework problems, DO THEM AGAIN. Due dates for collection of gradedhomework are given in the schedule in the syllabus. There is either a Quiz or Homeworkassignment due each week.
I am neither a cop nor an entertainer. I am your guide to this material, and you will get out ofit what you put into it.
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Syllabus
Quick review
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1-1 The Engineering Method and
Statistical Thinking
Engineers solve problems of interest to society by theefficient application ofscientific principles
The engineering or scientific method is the approach to
formulating and solving these problems.
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What is Statistics?
(Insides of the box on previous chart)
Statistics is the making ofinferences anddecisions in the face ofuncertainty.
Terms and Concepts
1/22/2012 5Dr. Sidik
Individuals
Are measured by Populations
Samples
Variables-Numeric/quantitative
-Categorical/qualitative
form
From which we take
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1-2 Collecting Engineering Data
Three basic methods for collecting data: A retrospective or observational study
A designed experiment
Simple Comparative Experiments
Factorial experiments
Case Studies (papers and data in BlackBoard):
Michelson Speed of Light (Michelson)
Retrospective analysis of some observational data
Heart Rate Variation (Gelber, Shields)
An observational study
Bladder Stimulation (Dalmose)
A Simple Comparative Experiment
Electro-spun micro-fiber vascular grafts (Nottelet)
A Factorial Experiment examining/modeling multiple variables
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Michelson/Speed of Light
Exercise 2-68, pg 55, and associated document
and web sites
Detailed observational studies
Illustrating several roles of theory, measurement
methodology, and experimental methodology with
respect to random error
http://njsas.org/projects/speed_of_light/
http://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/measure_c.html
BlackBoard: Case Studies & Readings folder. Michelsons 1879 Determination
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History
Date Author Method Result (km/s) Error
1676 Olaus Roemer Jupiter'ssatellites
214,000
1726 James BradleyStellar
Aberration301,000
1849 Armand Fizeau Toothed Wheel 315,000
1862 Leon FoucaultRotating
Mirror298,000 +-500
1879Albert
Michelson
Rotating
Mirror 299,910 +-50
1907 Rosa, DorsayElectromagneti
c constants299,788 +-30
1926Albert
Michelson
Rotating
Mirror299,796 +-4
1947Essen, Gorden-
Smith
Cavity
Resonator299,792 +-3
1958 K. D. FroomeRadioInterferometer
299,792.5 +-0.1
1973 Evanson et al Lasers 299,792.4574 +-0.001
1983 Adopted Value 299,792.458
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Background
Michelson: Rotating Mirrors approach
The data consist of 100 measurements, made over 28
days. Each measurement was an average of several
replicates. The 100 measurements were made in 5 runs of 20
measurements each. Presumably something was done to
the measurement process which distinguishes these
runs.
For now, we focus on descriptions of each set of 20.
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Questions/Discussion
Type of data collection?
Population of interest?
Representativeness of sample?
Adherence to Engineering Method?
Variables and models possible?
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Data Chapter 2, EX2-68
Loaded in Minitab
Graph Individual Value PlotMultiple Ys,
simple, OK
Select the Graph Variables and OK
Tr1 Tr2 Tr3 Tr4 Tr5
850 960 880 890 890
900 960 880 810 780
930 880 720 800 760
950 850 620 760 790
980 900 970 750 820
1000 830 880 910 870
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Histograms & Boxplots Minitab, TI,Technology tips
Numerical descriptions SOCS Shape
Outliers
Center Spread
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Heart Rate Variation
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What & Why
Some autonomous system neuropathic conditions can be identified
readily and non-invasively from examination of an electrocardiogram(ECG)
Time between successive heartbeats, the R-R interval, is easily read
from an ECG. Its variation is called the Heart Rate Variation (HRV)
To determine abnormal, one must first determine normal.
D. Gelber et al. describe a study of 611 normal subjects observed
across 63 hospitals, and also captured age, gender, bmi, and blood
pressure for many.
More info on this subject is also described by R. Shields of the
Cleveland Clinic.
The two articles and the Gelber dataset are in BlackBoard.
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Study datarr_var heart rate variation to deep breathing
valsal_1 valsalva measurement 1
valsal_2 valsalva measurement 2age age of subject
gender gender of subject
systol systolic blood pressure
diastol diastolic blood pressure
bmi body mass index
mbp mean blood pressure
val1sq square of valsalva 1
val2sq square of valsalva 2val1val2 product of valsalva 1 & valsalva 2
val_cat valsalva in categories
age_cat age in categories
rr_cat rr-variation in categories
Value Codes:
gender 1 = men, 2 = women
RR_VAR VALSAL_1 VALSAL_2 AGE GENDER SYSTOL DIASTOL BMI MBP VAL1SQ VAL2SQ
VAL1VA
L2
VAL_CA
T
AGE_CA
T RR_CAT
39.40 2.08 2.08 102.00 67.00 84.50 4.33 4.33 4.33 9.00 35.00
14.00 1.78 1.71 112.00 81.00 96.50 3.17 2.92 3.04 6.00 10.00
71.00 22.00 25.00 75.00
140.50 19.00 15.00 100.00
39.40 38.00 35.00 35.00
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Data in Minitab
Graph Individual Value Plot One Y, simple
Select data, OK
Graph Scatterplot simple, OK
Select RR_VAR for Y, AGE for X, OK
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Questions/Discussion
Type of data collection?
Population of interest?
Representativeness of sample?
Adherence to Engineering Method?
Variables and models possible?
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Bladder Control by Electrical Stimulation
Aims: To investigate the feasibility of conditional short duration electrical stimulation
of the penile/clitoral nerve as treatment for detrusor hyper-reflexia, the present studywas initiated. Methods: Ten patients with spinal cord injury, 4 women and 6 men, with
lesions at different levels above the sacral micturition center had a standard cystometry
performed. During a subsequent cystometry, conditional short duration electrical
stimulation of the penile/clitoral nerve was performed as treatment for one or more
detrusor hyper-reflexia contractions. Results: In all patients, at least one contraction
(mean, 7.8, range, 1-16 contractions) was inhibited by the stimulations. The mean
cystometric capacity was increased significantly by conditional electrical stimulation,from 210 mL in the control cystometries to 349 mL in the stimulation cystometries
(P=0.016). The maximal detrusor pressure during the first contraction in the control
cystometries was mean 51 cm H2O, whereas the maximal pressure of the first
contraction in the stimulation cystometries was reduced to mean 33 cm H2O
(P=0.045). Conclusions: The authors conclude that repeated conditional short duration
electrical stimulation significantly increased cystometric capacity in patients with
spinal cord injury. The increase was caused mainly by an inhibition of detrusor
contractions. The need for a reliable technique for chronic bladder activity monitoring
is emphasized, as it is a prerequisite for clinical application of this treatment modality.
Conditional Stimulation of the Dorsal Penile/Clitoral Nerve May Increase Cystometric Capacity in Patients With Spinal
Cord Injury, Dalmos et.al., Neurology and Urodynamics, 2003
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1/22/2012 19
Recent Advances: completed studies (KJG)
Efferent Afferent Animal model proof of conceptStimulation of urethral afferent nerves generatesbladder contractions and voiding.
Translational tool developed
Urethral afferents can be electrically stimulatedminimally invasively in humans.
Human studiesStimulation generates bladder contractions in SCI
humans. (new)First data generating bladder contractions via intra-urethral electrical stimulation in humans.
Genital nerve stimulation inhibits bladdercontractions in SCI humans. (accepted)
(Gustafson, 2003)
(Gustafson, 2004)
(Dalmose, 2003)
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1/22/2012 20
Simple Comparative Experiment In people with Spinal Cord Injury or with certain
neurological conditions, Functional ElectricalStimulation of appropriate nerves may enable subjects toregain some control over bladder activity.
Capacity data (ml) from Dalmos et al (table at left) isused to recap the essentials of simple statisticalcomparison.
Conditional Stimulation of the Dorsal Penile/Clitoral Nerve May Increase Cystometric Capacity in Patients With Spinal Cord Injury,
Dalmos et.al., Neurology and Urodynamics, 2003
A urethral afferent mediated excitatory bladder reflex exists in humans, Gustafson et.al., Neuroscience Letters, 2004
Sub Ctrl Stim S-C
1 290 500 210
2 188 424 236
3 208 268 60
4 77 279 202
5 86 159 73
6 376 500 124
7 400 320 -80
8 57 500 443
9 353 500 147
10 68 42 -26
Mean (S-C) = 138.9
S.D. (S-C) = 147.9
T = 2.97, P = .016
5001000-100
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Questions/Discussion
Type of data collection?
Population of interest?
Representativeness of sample?
Adherence to Engineering Method?
Variables and models possible?
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1-2 Collecting Engineering Data
1-2.3 Designed Experiments
Simple Comparative Experiments
Factorial experiments Replicates
Interaction
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1-2 Collecting Engineering Data
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1-2 Collecting Engineering Data
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1-2 Collecting Engineering Data
1-2.4 Random Samples
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1-2 Collecting Engineering Data
1-2.4 Random Samples
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Populations and Samples
Physical vs. Conceptual
Individuals physically exist and all available
Hypothetical set of all possible individuals that could
exist, possibly in the future
Enumerative vs. Analytic
Sample used to enumerate (describe physical
population of existing individuals)
Sample used to analytically describe some futurepopulation (which may or may not yet exist)
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Using Random Numbers for Sampling How to get a Simple Random Sample (from a small population)
Construct a list (sampling frame) of every population member Number each member from 1 to N (population size)
Use the TI 83/84 function: Math PRB 5:randInt
randInt( lower,upper[,numtrials])
Simulates the act of blindly drawing a slip of paper from a box with numbered slips of
paper between lowerand upperand replacing the selected slip into the box.
To simulate multiple draws, WITH replacement, provide optional argumentnumtrials.
To simulate multiple draws, withOUT replacement, simply discard any repeats as
they occur. You would want to set numtrials to something somewhat larger than
the sample size you actually need.
To save the numbers to a List,
STATEDIT 1:Edit, ENTER
Cursor up to the List name desired, then
Math PRB 5:randInt with desired parameters and Enter
You will want to generate random numbers for project 1.
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1-3 Mechanistic and Empirical Models
A mechanistic model is built from our underlying
knowledge of the basic physical mechanism that relates
several variables.
Example: Ohms Law
Current = voltage/resistance
I=E/R
I=E/R +
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1-3 Mechanistic and Empirical Models
An empirical model is built from our engineering and
scientific knowledge of the phenomenon, but is not
directly developed from our theoretical or first-principles understanding of the underlying mechanism.
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1-3 Mechanistic and Empirical Models
Example of an Empirical Model
Suppose we are interested in the number averagemolecular weight (Mn) of a polymer. Now we know that Mnis related to the viscosity of the material (V), and it alsodepends on the amount of catalyst (C) and the temperature
(T) in the polymerization reactor when the material ismanufactured. The relationship between Mnand thesevariables is
Mn=
f(V
,C
,T
)say, where the formof the function fis unknown.
where the s are unknown parameters.
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Descriptions
SOCS
Shape Outliers
Center
Spread
Use Minitab or TI calculators
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Minitab: Text Example 2-4: Compressive Strength
BlackBoard, text datasets, chapter 2 Minitab
StatBasic StatisticsGraphical Summary
Variables: EX-24, OK
TI: Exercise 2-38: sewage discharge
Put data in L1
StatCalc1-Var Stats 2nd
1 2nd Stat plot, plot 1, turn on, select histogram or
boxplot
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2-1 Data Summary and Display
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2-1 Data Summary and Display
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2-1 Data Summary and Display
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2-1 Data Summary and Display
Population Mean
For a finite population withNmeasurements, the mean is
The sample mean is a reasonable estimate of the
population mean.
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2-1 Data Summary and Display
Sample Variance and Sample Standard Deviation
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2-1 Data Summary and Display
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2-1 Data Summary and Display
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2-1 Data Summary and Display
The sample variance is
The sample standard deviation is
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2-1 Data Summary and Display
Computational formula for s2
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2-1 Data Summary and Display
Population Variance
When the population is finite and consists of N values,
we may define the population variance as
The sample variance is a reasonable estimate of the
population variance.
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2-2 Stem-and-Leaf Diagram
Steps for Constructing a Stem-and-Leaf Diagram
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2-2 Stem-and-Leaf Diagram
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2-2 Stem-and-Leaf Diagram
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2-2 Stem-and-Leaf Diagram
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2-2 Stem-and-Leaf Diagram
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2-2 Stem-and-Leaf Diagram
2 2 S f i
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2-2 Stem-and-Leaf Diagram
2 3 Hi
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2-3 Histograms
A histogramis a more compact summary of data than a
stem-and-leaf diagram. To construct a histogram for
continuous data, we must divide the range of the data into
intervals, which are usually called class intervals, cells, or
bins. If possible, the bins should be of equal width toenhance the visual information in the histogram.
2 3 Hi
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2-3 Histograms
2 3 Hi t
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2-3 Histograms
2 3 Hi t
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2-3 Histograms
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2-3 Histograms
2 3 Hi t
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2-3 Histograms
An important variation of the histogram is the Pareto
chart. This chart is widely used in quality and process
improvement studies where the data usually represent
different types of defects, failure modes, or other categoriesof interest to the analyst. The categories are ordered so that
the category with the largest number of frequencies is on
the left, followed by the category with the second largest
number of frequencies, and so forth.
2 3 Hi t
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2-3 Histograms
2 4 B Pl t
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2-4 Box Plots
The box plotis a graphical display thatsimultaneously describes several important features of
a data set, such as center, spread, departure from
symmetry, and identification of observations that lie
unusually far from the bulk of the data.
Whisker
Outlier
Extreme outlier
2 4 B Pl t
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2-4 Box Plots
2 4 B Pl t
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2-4 Box Plots
2 4 B Pl ts
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2-4 Box Plots