i. The document provides instructions for Assignment V which involves collecting and analyzing data. Students are asked to measure a population and sample of their choosing, calculate relevant statistics, and compare theoretical probabilities to actual results from experiments. They are also asked to discuss principles of reliability and conduct their own failure experiment. ii. Key aspects students must include are defining the population and sample measured, describing the measurement tool and method, calculating measures of central tendency and dispersion, and comparing expected to actual results from experiments like coin tosses. iii. Students should discuss how to make things more reliable generally and calculate reliability metrics like Lambda and Theta from their own failure experiment.

1. TMGT 361
Assignment V Instructions
Lecture/Essay
Statistics 001
Though you might have forgot most of it, you have already had
course work on most of the math and statistics required in this
course. There was a prerequisite math quiz to review some of
this math. Statistics is merely math (mostly algebra) aimed at
(a) summarizing data (descriptive statistics) or (b) judging how
well sample data fits a population of data (inferential statistics).
Statistics as a term refers to doing a or b, the results of a or b,
or the profession or field of study of the math to do a or b.
What makes statistics difficult or scary is not the math
(software does that in a second) but the qualitative knowledge
you need to do the statistics correctly (especially when software
will do the number crunching) and interpret the results.
Terminology
It is helpful to understand the interrelationship of the following.
Population. A population is made up of things (or units or
pieces, subjects, or test blanks, dogs, test tubes, persons,
molecules, or other things). The population is the big set of
things we are really interested in. Most hypotheses have to do
with a population. Knowledge is most useful and generalizable
when it pertains to a population. Usually, we do not have access
to a population (because of time, money, availability, or other
reasons).
Sample. A sample is a subset of the population. We can look at
(test, measure, observe, experiment with) a sample much easier
than we can the population. We can make decisions about the
population based on the results of the sample (inferential
statistics).
Sampling unit. The sampling unit is often called the unit of
observation. The population and sample must have the same
types of units or things because the sample is a subset of the

2. things/units in the population. It is easy to understand a unit
when it is common, discreet, individual thing, e.g., a person or
a car. However, the unit can be a foot of rope, or a mile of rope,
one marble, a gram of marble dust, a bag of marbles. The unit is
often called the unit of observation due to the traditional
reminder that for it to be measurable it must be observable. If I
was measuring empathy or love or other emotion or desire, the
same is true. I have to define those qualities (those variables,
those characteristics) but I also need to know what they are
qualities of. Aristotle's explanation is still used and valid. There
are objects (things) like an apple. The object has qualities (like
color or sugar content or weight or number of worms).
Characteristic or quality. A unit/object has any number
of characteristics or qualities. The important characteristics are
often redundantly called quality characteristics (meaning that
those are the important characteristics). Characteristics are also
called variables (when they can vary; they are not constant),
factors, inputs, descriptors, signals, attributes, and many others
depending on the situation or profession.
Variable value. Variables have values (or levels, amounts,
settings, labels, quantities, and many other synonymous terms,
depending on the situation or profession). For example, the
variable could be color; the value could be red. We make a lot
of distinctions (accompanied by different or modified
terminology) about variables depending on whether they are an
input or an output, if they are the cause or the effect, how much
influence they have, if we care about them or not, and other
distinctions. Variables that we can’t control and might mess up
our experiments can be called noise, environmental, extraneous,
or confounding. There are too many variations of variables to
discuss all of them here. The thing to remember is that things
(units of observation) have variables and those variables have
values, regardless of the specific terminology used. Quality as a
discipline gets its name from its focus on keeping the values of
the important variables at the levels the should be.
Measurement.Measurement can be a noun or a verb; it might

3. mean the thermometer (the instrument or tool), the process
(instructions, protocol, method) of using a thermometer to find
someone’s temperature, the act of finding that temperature
(performing the process), or the data resulting from finding the
temperature, i.e., the temperature. In metrology (the science of
measurement), measurement usually means the result, e.g., the
temperature, but always be careful (written or oral
communication) to be clear about the meaning of all terms.
Measurement requires and instrument or tool, which might be a
classroom quiz, a questionnaire, a micrometer, a bath scale,
your eyes, ... We generically call this instrument a test. Be
aware that we also use the word test as a verb synonymous with
measure used as a verb (English, gotta love it!). We often call
the instrument by its name or its process name, e.g., the SAT,
quiz 1, tryouts, ruler, bath scale, gauge, inspection, etc. The
best measurement situations use standardized instruments and
procedures (to use the instrument, produce a result-the
measurement, and analyze the results). The analysis of
measurement results is called an evaluation or a validation (and
other things). The point is that evaluation places a value
judgement on the measurement, e.g., my temperature is too
high, the cake tastes good, the part is too small, etc.
Data scale levels. The following table summarizes the scale
levels. I have chosen to call the lowest level—1.
Level
Name
Characteristics
Appropriate measures of central tendency
Appropriate measures of dispersion
Examples
1
Nominal, categorical
Data are labels (though the label may be a number)
Mode (largest category)
Frequency (number or percent/proportion) of each category
Color, gender, part numbers

4. 2
Ordinal, rank
The labels are in a meaningful order
Median
Range (difference between high and low values)
Education degrees, your favorite foods
3
Interval
The distance between each of the things labeled is uniform.
Mean
Variance, Standard deviation (the square root of the variance)
Temperature in C or F. A scaled, standardized psychometric
instrument, e.g., IQ, test or SAT exam
4
Ratio
Interval with an absolute zero
Mean
Variance, Standard deviation (the square root of the variance)
Length, weight, temperature in Kelvin
Note that each level has all the characteristics of all lower
levels and that all the appropriate measures for each lower level
are interpretable.
One of the biggest problems in using data is using the wrong
type of data and/or measure of central tendency or variation.
Various mathematical procedures require data that are
categorical, rank, or interval/ratio. For a certain technique or
situation, some data have to be continuous or dichotomous. Data
might need a minimum discrimination or range. There is nothing
you can do to make categorical or rank data into interval/ratio
data, therefore, the mean or standard deviations of those data
types will never be interpretable (although you can calculate a
number). To find the average part number, to rank employee
numbers, to find the standard deviation of region of the country
(labeled region 1, region 2, etc.), or the range of game show
guests (labeled contestant no. 1, no. 2, etc.) is meaningless.
Remember that software doesn’t know what a number

5. represents; you have to be smarter than the software.
We often have to break things down (cross tabulate) into
subcategories to compare counts, percentages, and other
information. There is never a need to show all descriptive
statistics of any variable or subcategories or combinations of
variables. The general rule always applies: Show what is
necessary to accurately describe what needs to be described.
The nature of the variables is important, e.g., categorical,
interval, etc. The purpose of the data is important, e.g., to
describe (to teach, to inform, to convince, etc.) to show a
relationship (or not), to test a hypothesis, etc. The audience and
what they want to know and/or can understand is important,
e.g., can they understand statistical conclusions, are you
presenting to clients or your boss, do you need to get the idea
across in 30 seconds or do you have an hour. The type of
summary statistic is important, e.g., do you need a count, a
percentage, a row total, an average, etc. Remember that just
because something can be calculated (assuming the math is done
correctly) doesn’t mean that it is interpretable. Even if
something is calculated correctly and it is a meaningful statistic
(e.g., the mean of salary, instead of the mean of eye color),
doesn’t mean that it will be useful. You have to know when the
frequency, the relative frequency, the cumulative frequency, the
proportion, the ratio, the average, etc. is important. Likewise,
you need to know what combinations and subcategories are
important. If I tell you that the average person lives to be 75
years, this tells you nothing about females compared to males,
smokers compared to non-smokers, etc.
Distributions. Strictly speaking, a distribution only pertains to
interval or ratio data. However, the term is often used to
describe the pattern or results of summarizing nominal or
ordinal data, e.g., in a frequency table or bar chart. You are
going to learn much more about distributions later in the course.
For this assignment, simply go by eye and make a judgement if
your data looks like it has a certain distribution, e.g., normal,
exponential, etc.

6. There are many other related terms, e.g., accuracy and
precision, that you will learn about in future assignments.
Reliability
Reliability is the broad (and mathematically intensive) area of
quality that is concerned with things (products, machines,
processes, etc.) working as they should (cost, quality, safety,
etc.) for as long as they should with minimal maintenance or
repair and if preventative or corrective maintenance is needed is
it quick and easy. Reliability includes (or is greatly related to
the following).
· Designing things to be more reliable.
· Testing things to see how reliable they are.
· Predicting the reliability or uptime of things (and conversely
the downtime for maintenance, repair, changeovers, coffee
breaks, etc.).
· Figuring out the best way to use things, maintain things, and
service things to increase the reliability.
· To do all the above with the most quality, safety, economy
(best use of money and resources), and other important
concerns.
We do know general rules of thumb for making something more
reliable, e.g., make it simple, build in parallel redundancies or
backups (as compared to series elements, where if one part quits
the entire thing quits). The simplest type of reliability test is to
calculate the mean time until a unit fails. As an example, you
turn on 10 light bulbs; you record how long each one works
until it burns out. Then you state that average. Of course it
usually is much more complicated. The average is often an
exponential mean (not the mathematical average) because the
failures usually are not normally distributed but some sort of
exponential distribution. What if you don’t have time to test
every light bulb to failure? Are you going to time-terminate the
test (e.g., quit testing after 100 hours)? There is math to do this
and estimate the failure rate even if no bulb burnt out in the 100
hours. During the testing, are you going to replace failures?
Initial Post

7. See the general assignment instructions for information about
the quality and quantity expectations and evaluation criteria.
V. Data collection and analysis.
a. Decide on something you are going to measure. In your initial
post write up, include the following. Keep an industrial focus if
possible but you can measure anything. The measurement
instrument can be anything, e.g., your eyes, a bath scale, a
micrometer, etc.
i. Define the population measured.
ii. Define the unit of observation (e.g., case, subject).
iii. Define the sample measured and state the sample size (must
be at least n=10).
iv. Describe the variable measured. Include scale level, i.e.,
nominal, ordinal, interval, or rank.
v. Describe the measurement tool and measurement method.
vi. Define the variable values measured and/or that could have
been measured, e.g., there might have been green apples but
none in your sample were.
vii. Calculate appropriate measures of central tendency and
dispersion.
viii. Create an appropriate chart to display the data. Does the
data look like it fits a particular distribution; should it, i.e.,
does the data fit the definition of a particular distribution?
b. Similar to example 5.8 in the Primer, calculate the mean and
3 sigma limits for 10 coin tosses. Toss an actual coin 10 times
and compare the theoretical and actual results*. Are the
theoretical and actual results different? If so, why? How do you
interpret the control limits, e.g., what do they tell us?
c. Create your own probability example of compound events*
(similar to examples 5.20 – 5.23 in the Primer).
d. Discuss the general principles of how to make something
more reliable.
e. Do your own failure experiment.* Calculate Lambda and
Theta.
Obviously, for a you have to measure something yourself and

8. cannot get data from a source such as the internet, book, or
company data.
For b, follow the example but use the values you need to for 10
coin tosses. You have to actually toss the coin to compare the
theoretical population results with your actual sample results.
For c, come up with your own example. The goal is to make you
practice with something more real than the text book. Do not
get an example from any source except your life or your
imagination.
For e, you could test anything to failure. I would pick
something that fails in short order under testing, e.g., flexing
something until it breaks (the bends can be the unit instead of
time, but time would work too if you keep your flex rate
constant). You could consider a basketball shot the event and a
miss as a failure. You could bother your roommate until he or
she gets mad (the failure) and see how long that takes (maybe
that isn’t a good idea)! The point is to really do this, with
something simple if need be (and not use an internet or book
example and merely change some words around).
Page 4 of 5
HLTH 556 Worldview Reflection Rubric
Criteria
Levels of Achievement
Content 70%
Advanced 92-100% (A)
Proficient 84-91% (B)
Developing 1-83% (< C)
Not present
Personal Perception
18- 16.5 points
Provides several perceptions of how their worldview influences
their viewpoint on the current healthcare debate.
16.49- 15.0 points
Provides some perceptions of how their worldview influences

9. their viewpoint on the current healthcare debate
14-1 points
Perceptions are discussed, but there is very little connection of
how their worldview influences their viewpoint on the current
healthcare debate
0 points
Does not provide how their worldview influences their
viewpoint on the current healthcare debate
Reflection
18- 16.5 points
Shows great clarity on their current worldview and how that
affects their value of healthcare for the needy
16.49- 15.0 points
Shows clarity on their current worldview, and how that affects
their value of healthcare for the needy
14-1 points
Shows limited clarity on their current worldview and how that
affects their value of healthcare for the needy
0 points
Shows no clarity on their current worldview and how that
affects their value of healthcare for the need
Biblical support/ value support
17-15.5 points
Defends with clarity their worldview with several biblical
passages or defined value statements that support healthcare for
the needy.
15-14 points
Defends their worldview with several biblical passages or
defined value statements that support healthcare for the needy
13-1 points
Defends their worldview with few biblical passages or defined
value statements that support healthcare for the needy.
0 points
Missing biblical support
Structure 30%
Advanced 92-100% (A)

10. Proficient 84-91% (B)
Developing 1-83% (< C)
Not present
Mechanics, Format, & Length
22 - 20 points
Well-written with correct grammar, spelling and formatting.
Length requirement is met.
19 – 17 points
Well-written with a few grammar, spelling, and/or formatting
errors. Length requirement is met.
17 -1 points
Generally readable, but with several errors in spelling,
grammar, and formatting. Length requirement met.
0 points
The paper does not meet length requirement, and/or
demonstrates extremely poor grammar, spelling, and/or
formatting.
Instructors comments:
/75