HFIT-565

Assessment & Evaluation of Health Fitness Parameters

Fall Semester 2009

Dr. Marc Schaeffer

mschaef@american.edu
 
 

Lecture Notes Class #1

Thursday August 27, 2009

Go to Course Syllabus

Course Outline & Syllabus - if you are reading this in hard copy, this page is located at:

http://www1.american.edu/academic.depts/cas/health/dhf/HFIT565/notes1a.html

and the course URL is at:

http://www1.american.edu/academic.depts/cas/health/dhf/HFIT565/syllabus.html

• Objectives and Course Outline & Syllabus
• Preparing for Class
• Posting of Student Scores
• Assignment Submission (links to examples)
• The assignment checklist page (link)
• Decimals (real numbers) and Integers
• Q&A about the course, content and format
• Some Definitions & explanations
• Answering Questions using the SCIENTIFIC METHOD
  • An in-class case study
  • An in-class empirical study
• Measurement scales
• Displaying scientific results
• Data Arrays
• Calculating the arithmetic mean using Excel
• Assignment see below for due date options

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Lecture 2

Preparing for Class - How to use the text book & prepare for each class meeting

• read the lecture notes and text assignment prior to class

• if the lecture notes have "under construction" icons like this at the page top

it means that this lecture is still being completed and that you should check back later until these icons have been removed, indicating that the lecture is in final form.

• even if a lecture is not "under construction," it is a good idea to view the lecture notes a few times during the week to see if there are any important announcements (displayed at the head of the page) that have been posted since your last visit to the lecture

• print a copy of the lecture & place the copy in a notebook to take to class

Most weeks there will be at least one problem to solve with a source other than the text. Comprehensive solutions will be posted by hyperlink to the assignment, but these solutions will NOT be available until after each assignment's deadline.

This course is extremely time intensive. Unless you are extremely mathematically talented, you should prepare yourself to spend at least three - five hours (and perhaps a good deal more time) studying for each one hour of lecture. I hope that it is no surprise that most students do pass this course.

Assignment Submission (be sure you have seen the Assignment Submission page) - brief summary of submission rules:

• assignments should be sent by email with an Excel attachment
• you must use the proper nomenclature for your attachment file name
• due dates are always by the exact hour (and minute) of the start of class
• earliest submission each week receives an automatic 10% bonus credit on that assignment score
• all assignment receipts will be confirmed
• no late assignments are accepted
• you may drop your two lowest assignment scores from the computation of your assignment average
• try not to tempt fate by waiting until the last moments before the deadline to submit your assignment
• please follow ALL instructions and your scores will exhibit higher values; ignoring instructions will result in extremely unpleasant consequences
• please take some time to become very well acquainted with the details for assignment submission

The assignment checklist page

• this list of things to do and to avoid is extremely important
• many of these rules are simply common sense
• other rules here pertain to THE ADHERENCE to mathematical conventions
• some of the rules may seem rather arbitrary, but each rule is intended to help you demonstrate what you know and to help me to find and to assess what you know
• please carefully review the checklist and ask questions about anything that is unclear

Decimals (real numbers) and Integers

• each year, students have considerable trouble with the proper administration of decimal places
• the content of a decimal value and/or rounding can impact the correct answer
• calculators and spreadsheets will often automatically supply greater or fewer decimals than are appropriate for any given answer
• thus, you must learn the rules for determining significant digits and proper rounding
• measurements always produce approximations of which some portion is error free and the remainder is error (be sure that you know what this means!)
• we derive most measurements with some sort of device or instrument of given precision (reliability)
• the accuracy of a measurement is the ratio of the maximum error in measurement to the measure itself
• using a normal scale for measuring weight, how do we normally express a person's weight?
  • let's take a woman who is 62 inches tall and fairly fit with an actual weight of 112.624 pounds
  • what weight will this woman probably read from her bathroom scale?
• with rare exceptions, most instruments in this course will supply precision to the nearest unit
• precision of measurement dictates the maximum number of decimal places for the summary statistics we will use
• in some instances, we may use a more arbitrary rule for test statistics in this course

Posting of Student Scores (please click here to see an example)

if you want scores posted, I need to use a code number that you supply and this code should be a number that is confidential

if you do not want your scores posted, please notify me so that I know that you have reached a decision and again, this decision not to have grades posted is perfectly acceptable if that is your preference

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Definitions

What is MATHEMATICS? ...at the least, mathematics is the language of the sciences...

What is STATISTICS? and Why should we study STATISTICS? ... statistics is a dialect of mathematics

a set of techniques for describing data & making decisions with incomplete information

statistics aids us in turning DATA into INFORMATION

• data can be considered raw elements requiring organization to acquire meaning; in their raw form, data represent chaos
• when properly applied to data, statistics can help us in describing, explaining, and predicting various phenomena

What is the difference between DESCRIPTIVE and INFERENTIAL statistics?

Descriptive - summarize the characteristics of groups allowing us to compare and contrast individuals to the group

Inferential - generalization from samples to a larger population; determining the probability that particular sample observations are the result of chance variation

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Some interesting and some mundane questions that can be handled with statistics.

I have flipped a coin for coffee with my best friend and lost 5 times in a row. Could something be wrong with the coin we have been using?

My favorite BRAND NAME yogurt seems to consistently have more fruit on the bottom than the generic brand which costs less. Is it possible that the generic brand is more variable?

Even people who are not sick often have a body temperature that is higher or lower than normal. If we were to pick a dozen people at random who claim to feel quite well, I believe that the majority of them will have a temperature other than 98.6 degrees F. Why is this?

I have examined worksite health promotion (WSHP) data gathered from over 5,000 participants and I have come to the conclusion that people who participate in WSHP the most, seem to exhibit the least job absenteeism. Could this be true?

In comparing the heights of women with men, which group is taller on the average? How do we know this?

In comparing two ethnic groups with one another for prevalence of smoking, do Vietnamese or Hispanics smoke more? How can we determine an accurate answer?

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We need to apply STATISTICS so that we can reduce the complexity of the human organism, including the organism's physiology, affect, behavior, and cognition...but what does this mean..."reduce the complexity"...?

We need to use STATISTICS to manage natural VARIABILITY into fundamental objective consistencies so that we can better predict and explain phenomena. But what does this mean?

How can we manage to cope with natural variability? Can we do it by an in depth examination of a single subject, case, individual, or observation? No - variability stems from several values, some or many of which are different.

What is VARIABILITY? and How can we deal with VARIABILITY?

...the textbook suggests that data vary because we do not see and measure everything; further, what we do see and measure, is performed imperfectly -- fundamentally, STATISTICS deals with aiding our understanding of our real, imperfect world

Let us take an example comparing the relative heights of men and women. It is generally accepted that on the average, men are taller than women. How do we know that? Can we replicate this accepted truth in this class? What method should be used?

A single case or even a few cases is not enough to give CONFIDENCE in making a scientific determination. Instead we must use appropriate SAMPLES.

How do we select an appropriate SAMPLE to reach a SCIENTIFICALLY valid conclusion? (this will be covered later)

What is SCIENCE anyway...? at least in part, science deals with a...

...search for consistencies in variation of natural phenomena with the goal of establishing replication

Procedures & Results must be communicated with much objectivity.

Subjective communication of scientific findings may be worse than no communication at all. In contrast objective communication of findings is both an Art and a Science. (This course is geared to help your understanding of the world and how to communicate your understanding.)

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MEASUREMENT is a refined method of objective communication

Incidentally, height is variable, but what does this mean?

So when we set out to measure a VARIABLE we need to be careful, if not obsessive about how we are going to define the VARIABLE and how it will be measured. Methodologists refer to this step of measurement definition as the OPERATIONALIZATION of a variable (i.e., what is being measured, who is being measured by whom, when is the mesurement made, where does this measurement happen, why is this measurement being chosen relative to other possibilities, how is the measurement made [the device or instrument, units of measure, special averaging of multiple trials, or a single determination]).
 
 

Think about...

Is there any use in quantifying the average illness in a selected hospital?

How about the average marital status of the AU community?

Does the average height of the member of this class make more sense than the previous two?

Is there a greater variability in height among men than among women?

Four Measurement Scales

NOMINAL (or CATEGORICAL)

categories are different, but there is a lack of sense of value for each unique category of member

ORDINAL (RANK)

property of order, but a lack of specific amount of difference among the values

INTERVAL

properties of order and amount; arithmetic properties apply, but there is not an objectively defined zero point

RATIO

properties of order, amount, arithmetic functions apply, & there is an objectively defined zero point

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Consider the data from check-in/check-out computers in a health promotion facility. In some operations, participants use a computerized system to log their visit time. Participant either enter a unique code or pass a magnetized card through a reader when entering and exiting the facility.

If the check-in/check-out system records a date time stamp, participant time in the facility can be known to the nearest minute (or even second). At the end of a month, calendar quarter, year, etc., it would possible to quantify participation time in several ways.

• ratio - hours (or minutes) per unit observation interval (month, quarter, etc.)
• interval - compare participants above the 75th with those above the 25th percentile
• ordinal - we could rank the participants from most to least participation
• nominal - visited the facility or not

IMPORTANT: The textbook simplifies these four measurment scales into two basic classifications

• categorical or qualitative
• quantitative

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Important Solution Paradigm

Think - what do we know & what do we hope to learn based on the given information & question; intro stats 3 primary rules to problem orientation - draw a picture, draw a picture, draw a picture!

Show - calculating the results

Tell - what did you learn? explain the results or conclusion
 

Displaying your results with Graphs

• ordered pairs (X, Y)
• the X-axis and the Y-axis

Graphing Frequencies

• this is a relatively simple example of graphing 28 different height measurements
• the data elements are:
  • 68, 70, 64, 74, 71, 68, 66, 69, 70, 70, 67, 74, 67, 69, 71, 67, 69, 72, 68, 71, 69, 70, 67, 68, 70, 69, 68, 70
  • note the lack of organization and lack of summary of the data as given
  • what if anything can you tell just by reading these scores as given?
• STEP 1 of organization: SORT the raw data
  • SORTED list of 28 height values: 64, 66, 67, 67, 67, 67, 68, 68, 68, 68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 71, 71, 71, 72, 74, 74
  • if we can CREATE a FREQUENCY TABLE of these values it will be more meaningful
• the table makes it easier to see how FREQUENTLY each score appears
• note how the table has two columns and that there is a corresponding value for each HEIGHT entry in the FREQUENCY column; the values on each specific row of this table constitute an ORDERED PAIR.
• a graph of this set of ordered pairs will help us to obtain more information
  • ordered pairs (X, Y)
  • the X-axis and the Y-axis
• a table of the given data are shown below below
• why have there been four new height values 63, 65, 73, and 75 been inserted in the table below?
• why do each of these four added values have a frequency of zero?

 

Frequency Distribution of 28 Heights
Height	Frequency
63	0
64	1
65	0
66	1
67	4
68	5
69	5
70	6
71	3
72	1
73	0
74	2
75	0

 

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• Now, below we can create a Frequency Polygon (of ordered pairs)
  • note that the x-axis (abscissa) exhibits HEIGHT in inches
  • note that the y-axis (ordinate) exhibits FREQUENCY (or counts)
  • this sounds like a trick question, but can you identify the X & Y variables in the graph below?
  • to reduce ambiguity, I like to state the title of a graph in terms of the "Y variable as function of the X variable"
  • in your math studies, you may have been exposed to the expression "y = ƒ(x)" which is read: y is a function of x; please note the similarity to the graph title a few lines above, "Y variable as function of the X variable"
  • lets say that we have a function defined as y = 2x + 1
  • if x = 1, y = 2(1) + 1 or y = 3 and we say that the value of y depends on the value of x
  • it is not a coincidence that we often refer to Y as the dependent variable (DV) and X as the independent variable (IV)
  • this is all so simple, but I bet you two wooden nickels that someone will still be tempted to identify the dependent variable in the graph below as HEIGHT, but this is NOT CORRECT; the IV = HEIGHT and the DV = ? why?

• The values on the x-axis increase by one unit - this is called the INTERVAL size
  • INTERVAL sizes can vary depending on several factors
  • our rule of thumb will be to use about 12 INTERVALS
  • how do we define the LIMITS of an INTERVAL?
• Please note the emerging similarity between this frequency polygon and the normal curve
• How would this graph appear if we transformed it into a HISTOGRAM?

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Data Arrays and Research Data Spreadsheet Construction

Although the work described below can be completed with a process which is totally manual with paper and pencil, manual methods have long since become obsolete. This outline assumes the use of a computer spreadsheet application. As with the use of all computer applications, please remember to save your work frequently. It is nothing short of amazing how closely bound Murphy's Law is to the use of a computer. Also below, you will note that the term "Quality Checking" (reviewing your work, even if it is as simple as data entry) appears frequently. There is a reason for this. One can make an error doing just about anything. Simple, common place tasks are perhaps more susceptible to error than some complex tasks. I promise that it will be more pleasant to follow these words of caution now from the start of this course, rather than having to admit downstream that it is time to develop the discipline to audit even your most simple operations.

• Application choice - we use MS Excel because it is probably in widest use
• Top row of sheet becomes the location for the VARIABLE names
  • only one variable to a column
  • variables should be uniquely named
  • variable names should be no more than 8 characters beginning with alpha
  • the 8 character limit allows easy import into most statistical software (e.g., SAS, SPSS); contrary to what the textbook states, many statisticians still use 8-character variable names, but it is true that this is a carry over from original software restrictions
  • the 8 characters should be chosen to help identify the variable using an abbreviated spelling (for example a variable marital status could be represented by the variable name MSTATUS)
  • the following snapshot reveals some sample variable names in the first row and code numbers in the first column

• After the first row (reserved for variable names), the subsequent rows will represent the subjects (sometimes called cases, observations, participants, or patients)
  • note in the first row the variable names are CASE, VAR1, VAR2, etc.
  • only a single row for each case
  • each case should be identified with a CASE number to maintain subjects' confidentiality - no subject names should appear in this spreadsheet; this is extremely important and is governed by LAWS that regulate experiments with human subjects
  • above you see the codes 001, 002, 003, etc. have been assigned as case identifiers
  • consider this generic example relative to the textbook's discsussion of WHO, WHAT, WHEN WHERE, WHY and HOW
    • WHO = cases; usually identified in given information of a problem
    • WHAT = variables (usually a mix of independent and dependent variables); usually identified in given information of a problem
    • WHEN = the chronological backdrop for data collection - only infrequently apparent in the data set; usually identified in given information of a problem
    • WHERE = scope of sampling collection - only infrequently apparent in the data set; usually identified in given information of a problem
    • WHY = rarely apparent in the data set; usually identified in given information of a problem
    • HOW = rarely apparent in the data set; usually identified in given information of a problem
    • see page 3 of text for a concise description that is fairly memorable

     

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Consider the following array for 5 subjects who have each provided six variables

• A data dictionary/codebook is imperative
  • list spreadsheet variables in order of the names at the top of each column
  • define each of these variables
  • identify the set of variable codes or the code range
  • identify the missing value codes

   

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• Quality Checking of data dictionary/codebook
  • check to make sure that all variables have been identified
  • check that the variable codes are comprehensive
  • check to make sure the missing values are properly identified
• Enter variables and data according to the dictionary/codebook
  • try to learn how to use the numeric keypad
  • if you are new to data entry, you will be tempted to enter the contents for more than one variable into a single cell; this will not work
  • pay attention that each row ends in the appropriate column; this is easy to check!
  • check that each case does end in the column of the last variable
  • print a copy of the spreadsheet
• Quality Check your data entry
  • compare the contents of the spreadsheet you just printed with data source
  • for beginners, all entries should be checked
  • mark errors in your spreadsheet with corrections
  • update your spreadsheet with corrections; depending on the project, it may be necessary to document corrections that you make to your spreadsheet
  • be sure to keep a copy of spreadsheet in each iteration of updating

We can use these data from a class from a few years ago to demonstrate the mean calculation in Excel

The following computations are performed on the data set pictured above named sample1.XLS.

• Your assignment this week involves making some similar calculations
• Please do not get confused and use the data set named sample1.XLS (for your assignment) as this data set will look very similar to the data set you are assigned to operate upon.
• If you want to demonstrate to yourself that you can derive the same results as below (extremely highly recommended), you may download a copy of sample1.XLS

• click anywhere on the spreadsheet [sample1.xls] above. When you mouse onto the sheet, the cells will turn yellow and the cell contents will turn red, just click and sample1.xls will load on your computer. 
  

• try to pay as close attention to the detail as possible
• I find that most students who have difficulties executing these steps are a bit too casual
• there are only four steps, but you must execute these steps perfectly to avoid error
• First, move the cursor and click in cell "E18" just below the cell containing the last age of "21"
• Second, in the worksheet below, we see results of clicking the cursor on "Paste Function" tool button;
  locate this button on the Standard toolbar just beyond the middle of the toolbar and click the button

• note that an "=" sign automatically appears in cell E18
• also, you see a pop-up named "Paste Function" and this pop-up has two scroll boxes
  • Third, in the scroll box "Function category" select "All" and...
  • ...in the scroll box "Function name" select "AVERAGE"
  • now click "OK" to see the next panel

• before clicking "OK" in this "AVERAGE" function pop-up, note a few details
  • the formula bar reveals the complete syntax of this function: "AVERAGE(E2:E17)"
  • the box to the right of "Number1" reflects the cell range over which the average is being computed ("E2:E17")
  • a preview of the answer is presented in the lower left of the pop-up: "Formula result =25.1"
  • Fourth, go ahead and click "OK"

• the selected cell E18 contains the average of the contents of cells E2:E17 - the syntax displays in the formula bar as long as E18 remains selected
• thus, the mean age for the 16 cases in sample1.XLS is 25.1 years
• depending on the defaults in your version of Excel, you may see fewer or more decimal places - we will express this mean to a single decimal place

You may feel that this is an awfully huge amount of extra work to compute a simple average and that you could do this operation much faster with pencil and paper. For what it's worth, almost 150 years ago, the legendary railway trackman John Henry felt that he could drive spikes with his hammer faster than a man using the new steam drill technology. You may be inclined to tell me that some trackmen still drive spikes with a hammer today and you would be correct. If one only has one or two spikes to drive, a hammer could be the best tool for the job. However, if one has several hundred or several thousand spikes to drive, an automated method will probably make for a more efficient outcome. You will have between several hundred and several thousand computations to make in this course. Therefore, I believe that an automated method is better suited for our purposes.

I know this Excel method may seem extremely awkward at first, but I also believe that you will quickly adapt. Moreover, I expect that you will find many uses for Excel that will transcend the content of this course. Please give Excel a chance. Trust me, it is going to take a while for Excel to go out of style, and knowing it could make a difference when it comes time for you to get your next job.

Read the Course Syllabus and Outline, including all of the linked documents

For your convenience each of the hyperlinks on the syllabus & outline is listed & linked below:

• student computing laboratories (with respect to computer access on campus)
• AU's e-academics (with respect to the different forms of computer training)
• my.american.edu extremely helpful AU computer website
• Grades (with respect to course grading)
• specific instructions about submitting your assignments
• Academic Integrity Code
• assignment checklist
• see examples of problem solutions by clicking here (EXTREMELY IMPORTANT) - if you do not study this example carefully, you will probably have your first assignment returned ungraded
• see example of a weekly grade report posting by clicking here

Text Reading &Text Problems

One of the first parts of the assignment below is to notify me whether or NOT you want to have your grades posted. For some reasons totally unknown to me, each semester a small subset of students cannot complete this simple task. To foster some incentive, each individual who complies with this part of the assignment will obtain an automatic 10% bonus added to their first assignment score. However, neglect of this task will result in a 10% penalty. As stated above, you may choose to have grades posted or not, but you must indicate to me that you have made a choice. I have learned repeatedly that students who ignore this request do not necessarily want to refrain from having their grades posted.

I recommend getting started on this entire assignment as soon as possible, and remember the first submission to reach me each week will be awarded bonus points.

Even if you think that you are an Excel PRO, I highly recommend creating a cartoon of your entire assignment (the cartoon is to help you AND not to be submitted) before beginning Excel. It is probably a good idea to begin by reading a problem and making some brief notes with pencil and paper. Where appropriate, make a sketch of your solution with pencil and paper using the notes you took from the given information. Make notes on your sketch of how you think you will use Excel to solve the problem. After you have a reasonable looking solution by hand, one that agrees with the answer in the back of the text, then translate your manual solution to Excel. You may think that creating the cartoon is a waste of time. With some rare exceptions, and I am begging you to trust me on this, layout of a well-designed cartoon is actually a short-cut to completing our weekly assignments. Unfortunately, I find that less than a third of the class follows this advice.

here is a rare exception to the one submission per assignment rule - you may send a separate e-mail about your grade posting if you have not contacted me yet, please e-mail your decision whether or not to have your scores posted each week by confidential code number - please include your code number if you want your grades posted. The first grade posting will probably appear between Lecture #2 and Lecture #3.

• Read De Veaux & Velleman Chapters 1, 2, 3, 4, & 5
• Chapter 1, problem zero (0) what do you suppose the authors had in mind in the upper left green box on page 3 in their statement..."Don't be a datum." Why?
• Chapter 2, Problems 11, 19, 20. Please remember to use Excel, but there are no calculations in these three problems.
• Chapter 3, problem zero (0) what do you suppose the authors had in mind for a photo at the bottom of page 31? why do you suppose the picture that appears was chosen?
  • Problems 15, 36, 38 Please remember to use Excel.

Additional Problems (Please see the spreadsheet & detailed instructions at this link) - the 2009 data are now yet available

A. Download the blank Excel array and enter the data into an Excel worksheet.

• 1) make sure that your data set looks EXACTLY (with the exception of the column for 'age' see detail below) the same as this one
• 2) you must verify your data entry before proceeding - you might consider checking your entry again, if not two more times! (failure to duplicate the data exactly will probably result in errors for some or all of the part B problems below) see next point for reminder about 'age'
• please be sure that you note that the column O headed 'age' is blank in the data display, but you will need to make sure that the cells in this column contain the appropriate value (expressed as a formula) for each case - this is necessary for problem B2

B. Calculate the following from the data you supplied in class on Thursday 27 August. Make sure that you display the means for the variables listed below to a single decimal place.

• 1) mean HT all students
• 2) mean age for all students (this variable's values are not yet in the data set and must be calculated by you using Excel; if you did not leave a blank column for Column O (for the variable age), insert or add a new column to your array and make sure that the computational formula is entered into each cell of this new column)
• 3) mean number of PA (physical activity) sessions for all students

C. Supply the type of measurement scale for each of the following.

• 1) SMOKE
• 2) SBELT
• 3) DIA
• 4) TCHOL
• 5) GENDER
• 6) HT
• 7) age

Solutions to text and additional problems (click here when it displays in blue underline)

Go to Lecture 2----->

<------ Go back to Syllabus
 
 

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this page last modified by M Schaeffer

on September 03, 2009