Jones, University of Phoenix, August 28, 2006
Symbols Provided by Tracie
(UOPhx QNT 531, Fall 2004)
By Steffanie (UoP 2005)
Statistics is defined as the science of
collecting, organizing, presenting, analyzing, and interpreting data to
assist in making more effective decisions.
Why are we studying statistics? Because we are all interested in
profits, hours worked, and wages. No matter what your subject is, all
are interested in what a typical value and how much variation there is
Here are a few examples of statistics:
• The mean time waiting for a phone operator
is 4 minutes
• The average starting salary of a college graduate is $22,000/yr
• The average number of deaths by Hurricane Katrina are 1,000
Why is Statistics required in so many
majors? It is because numerical information is everywhere; we need
the statistical techniques to make decisions that affect our daily
lives, such as insurance for your life, home and automobile. Another
reason is that medical researchers study the cure rates for diseases
using different drugs and different forms of treatment. Last but not
least, for environment protection. This agency is interested in the
water qualities. They take samples of different lakes and rivers to
establish the level of contamination and maintain the level of quality.
Another good reason to take a statistics course is that the knowledge of
statistical methods will help you understand how decisions are made and
give you a better understanding of how they affect you.
In chapter one, we learned that there are two types of statistics.
Descriptive statistics, are methods of
organizing, summarizing, and presenting data in an informative way. In chapter one, we also learned
about variables. A qualitative variable is nonnumeric and is usually
summarized in bar charts and graphs. With qualitative variables, we are
usually interested in the number or percent of the observations in each
of the categories. Quantitative variables are either a continuous variable
that can assume any value within a specified range or a discrete
variable that can assume only certain values, which have gaps.
Examples of qualitative variables:
• Religious affiliation
• Type of automobile
• State of birth
• Eye color
When the variable studied can be reported
numerically, the variable is called a Quantitative Variable.
Examples of Qualitative variables:
• The ages of company presidents
• The life of an automobile battery
• The balance in your checking account
• The number of children in a family
Quantitative variables are usually reported
In the Nominal Level, there is no particular
order to the categories. Observations of a variable can only be
classified and counted. These are also mutually exclusive and
Mutually Exclusive: A property of a set of
categories such that an individual or object is included in only one
YouTube Video - Craig A. Stevens Explains Nominal Data During a Stats Class
On the Ordinal Level,
YouTube Video - Craig A. Stevens Explains Ordinal Data During a Stats Class
The Interval level of measurement is the next
highest level. It includes all the characteristics of the ordinal level,
but in addition, the difference between values is a constant size.
The properties of the interval-level data are:
1. Data classifications are mutually exclusive and exhaustive.
2. Data classifications are ordered according to the amount of the
characteristic they possess.
3. Equal differences in the characteristic are represented by equal
differences in the measurements.
Examples of the Interval Scale of Measurement:
• Shoe Size
• IQ Scores
YouTube Video - Craig A. Stevens Explains Interval and Ratio Data During a Stats Class
Ratio Level is the “highest” level of
of a set
Blocking - A portion of the experimental material that should be more
homogeneous than the entire set of material (days, shifts, some other group). -
Used to increase the precision of an experiment. Rational subgroup selected so
that if assignable causes are present, the chance for differences between
subgroups will be maximized, while the chance for differences due to these
assignable causes within a subgroup will be minimized.
Box Plots -- Used to view the mean differences and distributions of
spread or variability of the data. - To determine if they appear equal.
Cause and Effect Diagram - How to Construct:
(1) Define the problem or effect to be analyzed;
(2) Form the team;
(3) Draw the effect box and center line;
(4) Specify the major potential cause categories and join them as boxes
connected to center line;
(5) Identify the possible causes and classify them into the categories in step 4
and create new categories, if necessary;
(6) Rank order the cause to identify those that seem most likely to impact the
(7) Take corrective action.
Central Limit Theorem- Regardless of the distribution of the
population the sum of n independently distributed random variables is
approximately normal. The approximation improves as n increases.
Measures of Central Tendency describe and locate the center of the data:
Mean (average of data set)
Sample mean (Xbar)
Population Mean (m)
Median (Sample median = x^~ = middle value)
Mode (measurement that occurs most often)
Common Cause Variability - Controlled Variation
Session-Webb (UoPhx 2008)
Quantitative or numerical information may be found almost everywhere.
However, not all quantitative information is regarded as statistical
data. Quantitative information suitable for statistical analysis must be
a set of numbers that are measurable and show significant relationships.
In other words, statistical data are numbers that can be subjected to
comparison, analysis, and interpretation. The area from which
statistical data are collected is generally referred to as the
population or universe. A population can be finite or infinite. A finite
population has a limited number of objects or cases, whereas an infinite
population has an unlimited number.
of collecting data from a small finite population is relatively simple.
If it is desired to obtain a complete set of data on the monthly incomes
of the college instructors in a university, we may simply ask each
instructor his/her monthly income. However, collecting such data from a
large population is sometimes impractical or nearly impossible.
to avoid the impractical or impossible task, a sample consisting of a
group of representative items is usually drawn from the population. The
sample is then used for statistical study and the findings from the
sample are used as the basis to describe, estimate, or project the
characteristics of the population.
YouTube Video - Craig A. Stevens Explains Continuous vs Discrete Data
Control Charts- Shows graphically, the results of many sequential
hypothesis tests. UCL = m + Ls, Center Line =m,
LCL = m - Ls, Benefits: Improve Productivity, Defect Prevention, Prevent
Unnecessary Process Adjustments, Diagnostic, Provide Process Capability
Information. Mathematically equivalent to a series of statistical hypothesis
test. Average Run Length (ARL) = 1/p = average number of points that must be
plotted before a point indicates an out-of-control condition. P= probability
that any point exceeds the CL. Average time to signal (ATS) = ARL (# Hour Sample
Taken) = Time elapses (on average) between shift and its detection. "X =
Average" and Variability "R = Range" Charts.
The Process is out of control if:
One point is out of 3-sigma control limits;
Two out of three consecutive points plot beyond the 2-sigma warning limits;
Four out of five consecutive points plot are a distance of 1-sigma or beyond
from the center line;
Eight consecutive points plot on one side of the center line;
Six points in a row steadily increasing or decreasing;
Fifteen points in a row in zone C (both above and below the center line);
Fourteen points in a row alternating up and down;
Eight points in a row both sides of the center line with none in zone C;
An unusual or nonrandom pattern in the data;
One or more points near a warning or control limit.
Collectively Exhaustive Events - Events are collectively exhaustive if
at least one of the events must occur when an experiment is conducted.
Controlled Variation (common cause variability) - many inherent sources
of variation that affect the process in a random manner. The distribution of
process output does not change overtime; thus, the pattern of variation is
consistent and stable. Result from a large number of chance causes. Distribution
of process output is stable over time. Removable only by process redesign.
Examples: Machine vibration, environmental fluctuations, and human variation in
Conway, William B., Ex-president of Nashua Corp. Founded Conway
Quality, Inc. in 1983. Quality Management. Eliminate waste of material and time.
Right way to management rather than simply how to improve. New system of
management whose primary task is continuous improvement which means changing all
the unwritten rules in a company. Advocate of statistical methods to achieve
quality gains. 85% of all problems can be solved by simple tools only about 15%
require more complicate statistical process control methods. -
6 Tools for Quality Improvement
(1) Human relation skills
(2) Statistical surveys
(3) Simple statistical techniques
(4) Statistical Process Control
(6) Industrial Engineering
Crosby, Philip B. - Book Quality is Free, Defines quality as
conformance to requirements and can only be measured by cost of non-conformance.
Prevention (means perfection) is the word summing quality. No place for
statistical levels of quality. Three ingredients - (1) determination, education,
and implementation. Management's responsibility (should be as concerned about
quality as profit).
Zero Defects as a management performance standard.
(1) make it clear that management is committed to quality.
(2) Form quality improvement teams with representatives form each department.
(3) Determine where current and potential quality problems lie.
(4) evaluate the cost of quality and explain its use as a management tool.
(5) Raise the quality awareness and personal concern of all employees.
(6) Take actions to correct problems identified through previous steps.
(7) Establish a committee for the zero defects program.
(8) Train supervisors to activity carry out their part of the quality
(9) Hold a zero defects day to let all employees realize that there has been
(10) Encourage individuals to establish improvement goals for themselves and
(11) Encourage employees to communicate to management the obstacles they face in
attaining their improvement goals.
(12) Recognize and appreciate those who participate.
(13) Establish quality councils to communicate on a regular basis.
(14) Do it all over again to emphasize improvement never ends.
Data, Types of - Variable (anything measurable) and attribute
(counting data, good or bad, conforming or nonconforming).
Distribution, Probability - Mathematical model that relates the value
of the variable with the probability of occurrence of the value in the
population. Continuous Distribution - Variable being measured is expressed on a
continuous scale. Discrete Distribution - Parameter being measured can only take
on certain value, such as integers 0,1,2,….
Degrees of Freedom - Are the number of independent elements that go
into a statistic.
Demings, Dr. W. Edwards - Believes responsibility for quality rests
with management, and the power of statistical methods. "People who expect
quick results are doomed to disappointment." Good quality is nor
necessarily high quality. It is predictable degree of uniformity and
dependability, at low cost and suited to the market. Statistical control doses
not imply absence of defective items. It is a state of random variation, in
which the limits or variation are predictable. Two type of variation: Chance and
Assignable. Not enough to meet specifications; one has to keep working to reduce
the variation. Advocate of worker participation in decision making. Management
action is required to improve quality (94% of all issues). Inspection is
designed to allow a certain number of defects to enter the systems. (Vendors
should be under statistical control. Advocates single sourcing.
(1) Create a constancy of purpose focused on the improvement of products and
(2) Adopt a new philosophy of rejecting poor quality.
(3) Do not rely on mass inspection to control quality.
(4) Do not award business to suppliers of the basis of price alone but also
(5) Focus on continuous improvement.
(6) Practice modern training methods and invest in training for all employees.
(7) Practice modern supervision methods.
(8) Drive out fear.
(9) Break down the barriers between functional areas of the business.
(10) Eliminate targets, slogans, and numerical goals for the workforce.
(11) Eliminate numerical quotas and work standards.
(12) Remove the barriers that discourage employees from doing their jobs.
(13) Institute an ongoing program of training and education for all employees.
(14) Create a structure in top management that will vigorously advocate the
first 13 points.
Erlang - Developed queuing for handling telephone switchboard
Error -- ÎI,j = Yi,j - Average Yj.
Event - An event is the collection of one or more outcomes of an
Exhaustive Data - Each individual, object, or measurement must appear
in one of the categories.
Experiment - A test in which purposeful changes are made to input - So
that we can observe and Identify Changes in Outputs of a Process. An
experiment is the observation of some activity or the act of taking some
Experimental Error Variance - MSE = E(s^2)
Feigenbaum, Dr. Armand V. - First introduced the concept of company
-wide quality control in his book Total Quality Control. More concerned with
organizational structure and a systems approach to improving quality than he is
with statistical methods, important, as quality improvement does not usually
spring forth as a "grass roots" activity; it required a lot of
management commitment to make it work. Once suggested that the technical
capability be concentrated in a specialized department, this differs form the
more modern view that knowledge and use of statistical tools need to be
Fixed Effects Model - E(MSTRT) = s^2 + (n(ĺtI^2))/(a-1) Where (I=1,2…a)
Graphical method -- from section 3-5.3 - SDV = s/(n)^1/2 @ (MSE/n)^1/2
- Draw Normal Curve with Grand average and lower and upper limits, then place
other data averages on curve.
Histogram - (1) Count number of observation in the sample (2)
Determine the range of values in the sample (3) Determine the class interval
size (4) Establish class midpoints and boundaries (5) Determine class boundaries
(6) Tally numbers of observations to fall in each class (7) Construct histogram
Class With = Range /(number of classes you want)
Class Relative Frequency = (Class Frequency) / (Total Number of
Hypothesis (from Larry Buess of Trevecca) -- A
hypothesis is a measurable statement about a condition you suspect
exists today that supports an objective. The hypothesis is a guess
about the strength of a current condition and is usually stated as a
proportion (a percent) or in some cases as a significant strength.
The hypothesis does not depend on any intervention or future events.
You know or suspect a problem or need exists today, but you have to
measure how big the problem or need is..
Objective: Within 3 months after implementing the new tube filler
procedure, there will be a 30% increase in production at the Oxydent toothpaste
factory in Nolensville, TN.
The “what” of this objective is “increase in production” . The new
tube filler procedure is the intervention. The hypothesis must support
“increase in production” and not reasons for the new tube filler procedure.
Possible hypotheses could arise from questions such as::
Why does production need to increase?
Hypothesis 1.1 Production at the Nolensville plant is 10% below the
average of other Oxydent factories in the USA.
Hypothesis 1.2 Production at the Nolensville plant is 15% below production
of all toothpaste factories in Tennessee.
Hypothesis 1.3 Production at the Nolensville plant has decreased by over
26% during the last 2 years.
How do employees feel about production?
Hypothesis 1.4 Over 75% of the employees feel that production could be
Hypothesis 1.5 Over 80% of the supervisors feel that production must
Another possible hypothesis:
Hypothesis 1.6 Over 30% of our Oxydent toothpaste distributors have orders
that can’t be filled.
Independent Events - Events are independent if the occurrence of one
event does not affect the occurrence of another.
Juran, Dr. Joseph M. -- One of the founding fathers of Statistical
Quality Control. Co-authored the Quality Control Handbook. Less focused than Dr.
Deming on statistical methods. Philosophy based on organization for change and
the implementation of improvement through "managerial breakthrough"
which is a structured problem-solving process. Management action is required to
improve quality (80% of all issues). Species of Quality: - Structural, Sensory
time orientated, commercial, and ethical. Two kinds of quality: fitness for use
and conformance to specifications. Three basic steps: structured annual
improvements combined with devotion and sense of urgency. All major problems are
interdepartmental. Quality is not free. Likes quality circles. Law of
diminishing returns where changes become too costly. Not in favor of single
sourcing. Training for purchasing managers should include rating vendors. No
such thing as improvement in general. Improvement is going to come about project
by project and no other way.
10-steps to Quality Improvement
(1) Build awareness of the need and opportunity for improvement.
(2) Set goals
(3) Organize to reach the goals,
(4) Provide training
(5) Carry out projects to solve Problems
(6) Report progress
(7) give recognition,
(8) Communicate results,
(9) Keep score,
(10) Maintain momentum by making annual improvement part of the regular systems
and processes of the company.
Levels of Measurement:
Nominal level of data is classified into categories
and cannot be arranged in any particular order.
Ordinal level involves data arranged in some
order. However, the differences between data values cannot be
determined or are meaningless. (Such as the which athlete is first second.)
Interval level is similar to the ordinal level
However, meaningful amounts of differences between data values can be
determined. There is no natural zero point. (example in book is temperature.)
Ratio level has an inherent zero starting point.
Differences and ratios are meaningful for this level of measurement.
Mean = sum of all observations divided by the
number of observations.
Discrete Mean and Average
Question: What would be the effect on the mean if all
observations are multiplied by the same constant?
Answer: The mean is also multiplied by the constant. Same
goes with division.
Mean, Mode, and Median
By Austine Ozubu (UoPhx 2008)
The mean of a list of numbers is the average of those numbers. Mean is calculated by adding all the numbers in the list and dividing by the number of numbers in the list.
Companies can use mean to calculate the average company salary as in the table below. The mean salary is higher than all but two salaries because of the salary of the manager of $60,000.
Table 1.0 – Employee Salaries
Machinist, level 1 $15,000
Machinist, level 1 $15,000
Machinist, level 1 $15,000
Machinist, level 2 $18,000
Machinist, level 2 $18,000
Machine supervisor $22,000
Sales Representative $20,000
Sales Representative $20,000
Mean or Average $21,273
Mode is the most frequent value. An advantage of mode is that it can be used for nonnumeric data. Mode can be used to describe the United States Senate by saying the mode sex of the senators is male and their race is Caucasian.
Median is the middle value of a list. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle entries, after sorting the numbers. A practical use of the median concept is to compute the mean weekly salary of a group of doctors.
In conclusion, there is no basis to judge the accuracy of a given statistical concepts or its distribution. The types of statistical information collected in the teams professional work setting and the types of data not collected that should be have been discussed in this paper. The description of the advantages of accurate interpretation of data improving decision making in work setting was discussed with an example provided on the result of positive outcomes from an analysis of data collection and statistical information.
Mutually exclusive - An individual, object, or measurement is included in
only one category. Events are mutually exclusive if the occurrence of any
one event means that none of the others can occur at the same time.
Nonparametric - Definition quoted from ...W. J.
Conover, Practical Nonparametric Statistics 2nd ed, 1980, John Wiley and Sons,
Inc, page 92.
" A statistical method is nonparametric if is satisfies at least
one of the following criteria:
The method may be used on data with a nominal scale of measurement.
The method may be used on data with an ordinal scale or measurement.
The method may be used on data with an interval or ratio scale of
measurement, where the distribution function on the random variable
producing he data is either unspecified or specified except for the infinite
number of unknown parameters."
Normal Probability Plots - Is a plot of data (either raw data or
residuals) against percent cumulative normal probability. - To check assumptions
of normality. If normal the data will follow a linear line with data parts near
the line, which is sometimes tested by covering these points with a pencil.
Quality Cost -- Reasons to consider 1. Increase in the complexity of
manufactured products associated with advances in technology. (2) Increasing
awareness of life cycle cost (maintenance, labor, spare parts, and cost of field
failures). (3) Need for quality professionals to effectively communicate the
cost of quality. Prevention Cost - Quality planning and engineering, New
products review, product & process design, Process control, Burn-in,
Training, Quality data acquisition and analysis. Appraisal Costs - Inspection
and test of incoming, material , product inspection and test, materials and
services consumed, maintaining accuracy of test equipment. Internal Failure Cost
- Scrap, Rework, Retest, Failure Analysis, Downtime, Yield Losses, Downgrading
(off-specing). External Failure Costs - complaint adjustment, Returned
product/material, Warranty charges, liability, Indirect costs.
Quality, Dimensions of - 1. Performance (will the product do the
intended job?); 2. Reliability (how often does the product fail?); (3)
Durability (how long does the product last?); (4) Serviceability (how easy is it
to repair the product?; (5) Aesthetics (what does the product look like?); (6)
Features (what does the product do?); (7) Perceived Quality (what is the
reputation of the company or its product?); (8) Conformance to Standards (is the
product made exactly as the designer intended?); (8+1) Use (is the product used
Quality Engineering the set of operational, managerial, and
engineering activities that a company uses to ensure that the quality
characteristics of a product are at the nominal or required levels.
Quality Improvement is the reduction of variability in processes and
Quality Program Evaluation - (1) Quality of materials, (2) accuracy
and precision of measurement systems, (3) Knowledge, ability, techniques and
support (time) to control the process over a long period of time (4) Capability
of a process measured over a short period of time (5) Modifying system for ht
process to ensure that the control techniques are operating properly (6) Company
policies concerning continuous Improvement
Queuing - Developed by Erlang for handling telephone switchboard
problems. Used arrival rates, service rates, number of servers type information
to find information related to server use, average waiting times, probability of
waiting times exceeding a certain limit, average length of queue, Average
waiting times in queue and in system.
Randomization - Both the allocations of the experimental material and the
order in which the individual runs or trials of the experiment are to be
performed are random - To Eliminate Biases.
Random Effects Experiments - Have the following in common: (a)
treatments are random sample from a larger population, (b) tI I=1,2,3,…a are
random variables, (c) Test of hypothesis is about the variability of tI
Random Effects Model -- E(MSTRT) = s^2 + (n * sT^2)
Random Error Component - See Experimental Error Variance
Rational Subgroup - Subgroups or samples selected so that the
assignable causes are present, the chance for differences between subgroups will
be maximized, while the chance for differences due to these assignable causes
within a subgroup will be minimized. (see blocking).
Regression Significance Test -- bo = ma; b1 = m1 -ma;; b2 = m2 - ma ;…….
Residuals - See step five above.
Replication - Duplication of the same test where all controls are the
same - Used to get an estimate of error and to estimate the central tendency
related to mean and variability to observe differences in the data to determine
if they are really statistically different. If the sample mean is used this
permits the experimenter to obtain a more precise estimate of effects.
Shewhart, Walter -- Father of SPC - While every process displays
variation, some processes display controlled variation (common cause
variability), while others display uncontrolled variation. Defined Special-Case
Variability and Common Cause Variability.
by Terri-Jane Hammerle (UoPhx 2008)
is the process of choosing a few from a larger group or population. If
data can be obtained on every member of a population, sampling is not
needed. If data cannot be obtained, sampling is needed from the
population from which to analyze the data. The television industry uses
sampling to measure what television programs people are watching.
According Nielsen Media Research (2003), “We continually measure
television viewing with a number of different samples all across the U.S”.
step is to develop representative samples. This must be done with a
scientifically drawn random selection process. No volunteers can be
accepted or the statistical accuracy of the sample would be in jeopardy.
Nationally, there are 5,000 television households in which electronic
meters (called People Meters) are attached to every TV set, VCR, cable
converter box, satellite dish, or other video equipment in the home. The
meters continually record all set tuning. In addition, we ask each
member of the household to let us know when they are watching by
pressing a pre-assigned button on the People Meter, which is also
present. By matching this button activity to the demographic information
(age/gender) we collect at the time the meters are installed, we can
match the set tuning – what is being watched – with who is watching. All
these data are transmitted to Nielsen Media Research's computers where
they are processed and released to our customers each day.
standard deviation method is one of the most commonly used statistical
tools. It gives a precise measure of the amount of variation in any
group of numbers. One practical use of standard deviation is to measure
risk of investing in mutual funds or other investment products. It can
also be used for a number of different purposes in investment
decision-making. As a measure of volatility, standard deviation measures
the tendency of data to be spread out.
looking at the historic returns of a mutual fund, standard deviation can
be used to measure the variation of expected return that has taken place
in the past giving a sense of range of performance that can be expected
given different probabilities of return for the future. According
Harrell (1997),"When used to measure the volatility of the performance
of a security or a portfolio of securities, standard deviation is
generally calculated for monthly returns over a specific time
period--frequently 36 months. And, because most people think about
returns on an annual, not monthly, basis, the resulting number is then
modified to produce an annualized standard deviation."
Lower case sigma means = standard deviation
Capital sigma means = the sum of
x bar means = the mean
Standard deviation is a term used to measure the range of data around
the mean value.
When the data is bunched tightly together and the bell-shaped curve is
steep, then the standard deviation is small. When the data is spread
apart and the bell is more flat, this means that you have a larger
standard of deviation.
Statistics - What is Statistics? – A Study of how to best (a)
Collect Data, (b) Describe and Summarize Data, and (c) Draw Practical
Conclusions Based on Data. A way to: test theories and practices in some cases
related to doing work determine the characteristics of a population by using a
sample Using data to make inferences under uncertainty Big Picture - Science of
amassing data, taking a portion of it, and seeing what that portion tells us
about the whole Little Picture - actual statistics themselves statistics with
little “s” is any number that represents something else.
Statistical Process Control -- Program Elements - (1) Management
Leadership, (2) A team approach. (3) Education of Employees at all levels. (4)
Emphasis on Continuous Improvement. (5) A mechanism for recognizing success and
communication this throughout the organization. Goal to remove all special-cause
variation, so that process is predictable. Characteristic parameters like the
mean, standard deviation, and probability distribution are constant. Can
determine -Process Capability, if redesign is economically feasible, affect on
the final product. Benefits - Increase Customer Satisfaction, Decrease scrap,
rework, inspection, operation cost, Maximize productivity, Establish a
predictable and consistent level of quality.
Special-Case Variability -- see Uncontrolled Variability
Special Rule of Addition - If two events A and B are mutually
exclusive, the special rule of addition states that the probability of A or B
occurring equals the sum of their respective probabilities: P(A or B) = P(A) +
Subjective Approach - Based on opinions could have different
Total Variability - SST
Transformations - Used to analyze data that is non-normal in its
standard form (but becomes normal in the transformed form) or data that has
Treatment Effects - See 4.3 above
Type I Error -- a = r (reject Ho|Ho is true)
Type II Error -- b = r (fail to reject Ho|Ho is false) ---Power = 1-b
= r (reject Ho|Ho is false)
Types of Data:
Qualitative or Attribute variable is nonnumeric.
Quantitative variable information is numeric.
Discrete variables can only assume certain values (such as counting
the number of cars).
Continuous variables can assume any value within a specified range
(such as height of a person).
From an example in book.
Uncontrolled Variability - Special-Case Variability - typically
results from the influence of one or two identifiable sources. Sources also
known as assignable cause variability tend to be unpredictable and may come and
go. Distribution of process output is unstable and unpredictable. Removable by
systematic identification and elimination on the shop floor. Examples: Operator
error, inferior raw stock, over adjustment, and poor setup.
Category (Less Exact)
Nominal Variable (Name)
Ordinal Variable (relative condition)
Discrete Variable (countable units, integers)
Continuous Variable (infinite but measurable possible
Variability Between Treatments - E(s^2) = (MSTRT - MSE)/n
Variability, Types of - Controlled Variation (Common Cause Variability) and
Uncontrolled Variation (Special-Cause Variability)