Lectures Ch 1&2

8/3/2019 Lectures Ch 1&2

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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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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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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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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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1-2.3 Designed Experiments

Simple Comparative Experiments

Factorial experiments Replicates

Interaction


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1-2.4 Random Samples


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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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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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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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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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Sample Variance and Sample Standard Deviation


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The sample variance is

The sample standard deviation is


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Computational formula for s2


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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 S f i


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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

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2-3 Histograms

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2-3 Histograms

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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

Lectures Ch 1&2

Documents

Transcript of Lectures Ch 1&2