# Sample Order to Show Cause by lld99380

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```									Name: (Last, First & Middle as they appear on roll sheet)
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Full Credit     Print these as
Half Credit     indicated with one on
No Response     each line starting at
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Late            of the card.
Statistics is the science of uncertainty. (Andrews)

Statistics is the study of variability. (Melton)

Statistical Thinking = "thought processes that recognize that variation
is present in all phenomena and that the study of variation leads to
new knowledge and better decisions." (Canavos & Miller, pg. 2)

Phenomenon: A single term that can be used to refer to either a 1.
Process or a 2. Population.
ariation
Phenomenon
1. Process "a set of conditions that repeatedly come together to
transform inputs into outcomes" (C&M, pg. 5)      Dynamic
2. Population "some particular group of persons or objects that share
a common characteristic" (C&M, pg 5)        Fixed or Static

Measurements can be taken on objects that make up a population or are
an outcome of a process. Knowing the values that these measurements
may have is valuable when making decisions that are related to the
population or process.

The first step is to identify the phenomenon of interest (target phenomenon).
However one is not always able to obtain data from that exact phenomenon.
Hence data are obtained from a phenomenon that is believed to closely represent
the phenomenon of interest.
at share

ly represent
Sampling Procedure: defines the process for selecting elements to be
measured and recorded as sample data.
Measurement Procedure: defines how measurements are to be taken.

Frame (Melton) is the window through which one will get the view of
the phenomenon of interest. (Frame = Source for sample data)
Frame (Melton) = Sampled Phenomenon, either process or population
(C&M)

Sample elements are selected from the frame or sampled
phenomenon as defined by the sampling procedure. The goal is to
obtain sample elements that adequately represent the phenomenon of
interest.
e taken.

pulation

menon of
Phenomenon characteristics are                   Sample information is selected from
called PARAMETERS.                               the FRAME (sampled phenomenon)
STATISTICS are calculated based on
Phenomenon                              sample information.

Frame               ==>    Sample Information            Phenomenon
Characteristics
It is ideal if the
Frame and the                                                                          are called
Phenomenon                                                                             PARAMETERS
Statistical Inference uses the statistics calculated from the
are identical        sample data to make inferences about the parameters that
but in many          describe characteristics of the phenomenon.                       Sample
cases this is                                                                          Characteristics
not possible.                 PARAMETERS          <==    STATISTICS
Each could have
are called
elements that are    We will use two types of statistical inference:                   STATISTICS
not in the other.
1. Estimation and 2. Hypothesis Testing
Statistical Inference uses sample information to make inferences about a phenomenon.
Estimation uses STATISTICS to estimate PARAMETERS
Hypothesis Testing uses sample information (STATISTICS) to test
hypotheses about the phenomenon (PARAMETERS)
Phenomenon
Characteristics
are called
PARAMETERS

Sample
Characteristics
are called
STATISTICS
Population of 10 numbers below               3
1    2   3    4   5     6  7    8   9 10           4
Population Average = 5.5 < PARAMETER          7
1
5
Sample of 2 items
8
selected from the Population
3
7    3                          6
Sample Average =     5 < STATISTIC         3
8
Phenomenon Characteristics are called PARAMETERS    6
9
Sample Characteristics are called STATISTICS        7
2
4
10
4
3
7
2
4
8
5
3
5
9
6
4
1
6
5
10
4
Operational Definition: provides a clear and precise statement of exactly
what is to be observed and how it is to be measured. (C&M)

Measurement Scales:
Qualitative or Categorical data (Nominal Scale Data)
Ordered or Ranked data (Ordinal Scale Data)

Quantitative or Numerical or Metric data
(Interval Scaled Data)
(Ratio Scaled Data)        (Steven's Data Types, C&M, pg 44)
f exactly
Sources of Variability
Special Cause                  vs.   Common Cause
Attributable Cause             vs.   Unattributable Cause
Assignable Cause               vs.   Unassignable Cause
Identifiable Cause             vs.   Unidentifiable Cause
Explainable Variability        vs.   Unexplainable Variability
Specifiable Reason             vs.   No Specifiable Reason
The variability of the values for a variable may be due exclusively to a
common or unassignable cause or causes. But it may also be due to both
unassignable and assignable causes and differentiating between the two is
not an easy task. For this reason statistics is a difficult subject for many
students.
Steps in a Process Study (Melton Module 3)
1. Identify a process to study
2. Form a team to perform the study
3. Define the boundaries of the process being studied
4. Document the current operation of the process (Flow Diagram #4)
5. Identify the customers and suppliers for the process.
6. Identify inputs to the process that cause the output. (Cause & Effect Diagram #5)
7. Develop a plan to collect data. (Check Sheets #6)
8. Analyze the data collected. (Pareto Charts #7 & Run Charts #8 )
9. Identify potential areas for improvement
10. Use the PDSA Cycle (Plan-Do-Study-Act)
ct Diagram #5)
Act       Plan

Study     Do

The PDSA Cycle
Flow Diagram Symbols (C&M, page 597 and Melton, Module 4)

Starting or ending point
One path exiting start and one or more path leading to an end.

Action to be performed
Can have multiple paths entering but only one path exiting.

Decision that affects actions that follow
Can have multiple paths entering must have at least two paths exiting.

Direction or path of the flow

A   Connecting points to allow flows to continue on another page
(Highlight circle, Click on Format, Autoshape & select no fill to allow letter to show in Excel)

A shadowed box indicates an action consisting of multiple steps
Can have multiple paths entering but only one path exiting.
B. Flow Diagram                   Start                                            Flow Diagram created by
Steve Schlapman,
unlock bike, turn it to the proper                              Fall 2003
direction, hop on, write down time,
start pedaling towards Park Ave.

Arrive at Park Ave.

No
traffic              stop and wait for
safe opportunity to

Yes

turn left onto Park Ave.
continue towards the Boulevard.

Approach Boulevard

Boulevard                                              Stop and wait for safe opportunity
traffic light red         Red         traffic      No     to cross while keeping track of
or green?                          clear?                    time spent waiting.
Yes

Green

Cross intersection
and continue towards

Approach

Harrison St.                                                  Stop and wait for safe
traffic light red
Red           traffic        No     opportunity to turn while
clear?
or green?                                                  keeping track of time spent
Yes
Green

Turn Right and
continue towards

A
A                                                  Steve Schlapman, Page 2

Approach

Grove Ave.                                                    Stop and wait for safe opportunity
traffic light red        Red            traffic       No         to cross while keeping track of
or green?                            clear?                         time spent waiting.
Yes

Green
Cross intersection and continue
towards Floyd Ave.

Approach Floyd Ave.

Floyd Ave.                        stop and wait for oncoming
intersection,           No        traffic to clear while keeping
traffic clear?                     track of time spent waiting.

Yes

turn left onto Floyd Ave. and
proceed to school

Find spot to park the bike, get off, set bike in
place, attach lock, check time, write down end
time and time spent at lights.

End
Cause and Effect, Fishbone or Ishikawa Diagrams (Melton Module 5 & C&M pg 597)

Machines              Measurement                   Methods

Place the name
of the effect here.
Student
EFFECT of

Teacher

Materials             Environment                   People

Diagram is used to list and categorize potential identifiable causes of variability in the data for a
specified effect. The six items listed for the main bones tend to fit most situations but are not fixed in
stone. Sub items are listed as branches off of each line. In the above example additional branches
can be added to the Teacher and Student branches for characteristics of each with an appropriate
label.
dule 5 & C&M pg 597)

Place the name
of the effect here.
EFFECT of

bility in the data for a
uations but are not fixed in
ach with an appropriate
Cause and Effect, Fishbone or Ishikawa Diagram for
Time Spent Online Daily                Created spring 2007 by Nazanin Mirshahi
Fish do not always have to                  Amount of time
swim to the right. This
spent online
creative diagram was created
spring 2007 by Nazanin                        each day
Mirshahi

Alone
Browse                      With friends
Search                                     Any friend online?
Chat
Email
Firefox
Internet Explorer                   People
Methods
Browser used

Home
School
Number of online times                    Night      Noisy
Accuracy of timer                         Day           Quiet
Environment
Measurement                        Time of Day

Number of interruptions
Have homework                        Desktop
Have mood                                Laptop
Have class
Have exam                                       Machines
Have free time

Influential activities
Steps for creating a run chart with Excel
17.00   1. Record the data in the order observed in a vertical column
17.00   2. Highlight the column of data
20.83   3. Left Click on the Chart Wizard
23.02   4. Select the Line Chart from the next menu
22.51   5. The default chart is OK so select Next>
24.09   6. The data are in columns so select Next>
24.09   7. Select Legend and remove the check by Show legend
27.53   8. Select Finish to obtain the run chart below for the data to the left
31.59    50.00
22.64    40.00
27.20    30.00
27.30    20.00
30.59    10.00
37.37     0.00
38.28            1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16
27.30
ta to the left
A stable process has constant parameters or characteristics.
A stable process has only constant random variation.
This variability is referred to as Common Cause Variability.
This is the inherent natural, customary or common variability for a stable process.
Common Cause Variability affects all observed data outcomes.

Special or Assignable Cause Variability does not have the same effect on all data.
Hence the underlying characteristics or parameters are not stable.
Changes in the parameters or characteristics show lack of stability.

A stable process does have variability in the observed data.
A large amount of variability does not indicate lack of stability.
a stable process.

e effect on all data.
A stable process has constant parameters or characteristics.
A stable process has only constant random variation (Common Cause Variability).

To determine if a lack of stability exists look for
a. changes in the location of the center of the variability
b. changes in the spread or magnitude of the variability
c. any identifiable patterns in the data
(cycles or saw-toothed patterns are the most frequent patterns)
d. data points whose values are very different from the rest. (Outliers)

A stable process does have variability in the observed data.
A large amount of variability does not indicate lack of stability.
Cause Variability).
For a process with stable parameters the variation in the data should be random.

If the data follow some pattern then this is probably not due to random variation but due to some
explainable cause.

Examples of patterns include:
Seven (Melton) or more points in a row above or below the centerline.
Seven (Melton) or more points moving in the same direction (increasing or decreasing).
Sawtooth pattern with a consistently regular up and down movement.
Any clear identifiable repeating pattern in the data.
be random.

ation but due to some

g or decreasing).
An OUTLIER or EXTREME POINT is a data value that is either
high or low relative to the other data value.

An invalid data point is a data value that is not indicative of the
phenomenon being studied. (Hence it should not be included in an
analysis for the phenomenon.) Invalid data values often appear in
the extremes of the distributions of data. DO NOT assume that all
extreme values are invalid data points.
Process of testing for the stability of a process
1. Create a Run Chart for the data collected from the process.

2. Is the center of the distribution constant across the chart?
An answer of NO implies NOT STABLE

3. Is the spread of the data constant across the chart?
An answer of NO implies NOT STABLE

4. Are there any patterns in the data?
An answer of YES implies NOT STABLE

5. Are there any outliers or extreme data points that are very different from the others?
An answer of YES implies NOT STABLE
The data point or points may be from another process.
fferent from the others?
Start

Is LOCATION stable?            NO

YES            Data are
Is VARIATION stable?           NO
NOT from a
single
YES             Stable
Any clear Patterns?           YES
Process

NO

Outlier Values?            YES

NO

Process is Stable             End

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