Statistics for Managers AHS 360

1
Statistics for ManagersAHS 360

• UNIT 4
• A Picture Really Is Worth a Thousand Words
• Illustrating Descriptive Statistics
• Chap. 4, NJS

2
OBJECTIVES Unit 4

• Why pictures are worth a thousand words
• How to create
• Histogram
• Polygon
• Using the Data Analysis Toolpak to create
  histograms
• Distinguish between a quantitative and a
  qualitative distribution.
• Using the SKEW and KURT functions
• Using Excel to create and modify charts
• Different types of charts and their uses

3
Presentation of Data

• Descriptive statistics methods used to present
  information in a more useful format
• Used to review streams of data
• Clinical
• Financial
• Operating activity
• Summarizes information
• What is the level of detail?

4
Frequency Distributions Patients and Length of
Stay







PATIENT ID DAYS
473528 19
58930 14
214129 1
987973 2
175474 13
692529 5
710470 8
947133 8
176857 3
43008 20
946967 15
275066 4
740316 18
296280 10
758281 20
884235 2
701551 5
824470 8
PATIENT ID DAYS
823117 5
987647 10
314435 7
546065 4
330233 1
267526 15
192958 5
673579 13
334366 14
676380 4
417604 12
150297 14
474010 20
901837 20
271951 16
823066 5
725294 18
778009 4
PATIENT ID DAYS
412058 8
612149 17
529269 17
490189 7
3235 4
302927 4
933821 5
545422 17
341657 15
330600 17
156147 12
388707 2
372666 19
465126 1
441428 4
793344 3
Imagine another 900 or more of these
rows/columns!!! What does it mean?
5
Illustrating Data

• When describing a set of scores, you will want to
  use two things
• One score for describing the group of data
• Measure of Central Tendency
• Measure of how diverse or different the scores
  are from one another
• Measure of Variability
• However, a visual representation of these two
  measures is much more effective when examining
  distributions

6
SAMPLE DATA SET
Nicotine Levels in smokers
Each box represents an individual and their
nicotine level.
7
Frequency Distribution
So, 11 individuals had a nicotine level between 0
and 99, 12 had a level between 100 199, etc.
8
CLASS FREQUENCY

• The term class frequency refers to the number of
  observations or items assigned to a given
  category
• Example The number of individuals in a specific
  group

CLASS INTERVAL

• The class interval indicates the range of values
  contained in a given category of a frequency
  distribution
• Example 1 5, 6 10, 11 15, etc.

9
Class Interval (or Width)

• The difference between two consecutive lower
  class limits or two consecutive class boundaries

Class Width
10
CLASS LIMITS

• The upper class limit identifies the maximum
  value that appears in a given category while the
  lower class limit corresponds to the minimum
  value appearing in a given group

11
Upper/Lower Class Limits

• Upper The largest number belonging to each class
• Lower The smallest number belonging to each class

Lower Class Limits
Upper Class Limits
12
Class Mark (Midpoints)

• The mid-point is the mid-point between the upper
  and lower class interval of a given category

Class Midpoints
For example (199.99 100 ) / 2 100 (base
value) 150
13
Frequency Table ExampleOutpatients Use of
Ancillary Services
CLASS INTERVAL
CLASS FREQUENCY
CLASS MIDPOINT 3
Units Per Patient Number of Patients
1 to 5 450
6 to 10 210
11 to 15 19
16 to 20 150
Total 1,000
UPPER LIMIT
LOWER LIMIT
14
Frequency Distributions

• What does a frequency distribution tell us?
• Rearranges information into a more useable and
  understandable form
• Groups the data
• Proportion of items in each category
• What it does not tell us?
• Minimum or maximum services per patient
• Details for individuals and groups
• What was the service level or length of stay for
  patient 101?
• We dont know with a frequency distribution

15
COLLECTIVELY EXHAUSTIVE

• The term collectively exhaustive simply tells us
  that the distribution will accommodate all
  observations, ranging from the smallest to the
  largest value in the set of data
• Example Individuals grouped by race
• Two Categories Chosen African-American and White
• Problem 10 Hispanic individuals are in our
  sample
• Your categories were not collectively exhaustive

16
MUTUALLY EXCLUSIVE

• The term mutually exclusive simply tells us that
  an observation is assigned to one and only one
  category
• Example Hospitals grouped by type
• Types Rural, urban, academic, for-profit,
  not-for-profit, and government
• What about Cooper Green (government and urban)
  and Shelby Baptist (rural and not-for-profit)?
  Where do they fit?
• Problem Your categories were not mutually
  exclusive.

17
Frequency Distributions

• How do you determine the groups / categories?
• How many are in the overall sample?
• Generally (may vary by data and/or textbook)
• No fewer than 3
• No more than 10 groups
• More than 10 groups can get VERY messy note
  this especially in regards to your assignments
  and the exams (the book says 10 20)
• Groups must be
• Collectively exhaustive
• Mutually exclusive
• Include all classes, even if the frequency is
  zero
• Try to use the same width for all classes
• Select convenient numbers for your class limits
• The sum of all class frequencies must equal the
  number of original data values

18
QUANTITATIVE FREQUENCY DISTRIBUTION

• A quantitative frequency distribution is defined
  as one in which the categories used to group the
  subjects (e.g., patients) are expressed
  numerically.

Units Per Patient Number of Patients
1 to 5 450
6 to 10 210
11 to 15 19
16 to 20 150
Total 1,000
19
Relative Frequency DistributionsQuantitative
Distribution Example

• Lets say we have the number of ancillary
  services for a set of patients during their
  hospitalization
• Number of services received (Medication, blood
  transfusion, shot, X-ray, catheter placement,
  etc.)
• 1,000 patients in sample
• We have data for 1,000 patients and their
  hospitalization

20
Quantitative Frequency Distribution Example
Number of Ancillary Services Per Patient Number of Patients Relative Frequency
1 to 5 450 0.45 (45)
6 to 10 210 0.21 (21)
11 to 15 190 0.19 (19)
16 to 20 150 0.15 (15)
Total 1,000 1.00 (100)
21
Relative Frequency Distributions

• Steps
• Select the categories that will characterize the
  distribution.
• Sort the data into the selected categories.
• Count the items in each group.
• Compute the relative frequencies for each group.
• Equation fi/T
• fi the number of observations per category
• T total number of observations
• Example 1 450 / 1,000 0.45

22
QUALITATIVE FREQUENCY DISTRIBUTION

• The groups that comprise a qualitative frequency
  distribution are defined in categorical terms
• These are non-numerical categories

Category Frequency Relative Frequency
Digestive Disorders 250 0.25
Eye Disorders 150 0.15
Respiratory Disorders 200 0.20
Nervous System Disorders 400 0.40
Total 1,000 1.00
23
Relative Frequency DistributionQualitative
Distribution

• 1,000 patients
• Patients grouped by diagnosis type
• Can you describe the results from the frequency
  distribution?

Category Frequency Relative Frequency
Digestive Disorders 250 0.25
Eye Disorders 150 0.15
Respiratory Disorders 200 0.20
Nervous System Disorders 400 0.40
Total 1,000 1.00
24
Constructing A Relative Frequency Distribution

• Decide on the number of classes.
• Determine the class width by dividing the range
  by the number of classes (range highest score
  - lowest score) and round up.
• Select for the first lower limit either the
  lowest score or a convenient value slightly less
  than the lowest score.
• Add the class width to the starting point to get
  the second lower class limit, add the width to
  the second lower limit to get the third, and so
  on.
• List the lower class limits in a vertical column
  and enter the upper class limits.
• Represent each score by a tally mark in the
  appropriate class.
• Total tally marks to find the total frequency for
  each class.

range
class width ? round up of
number of classes
25
Tabulating Numerical Data Frequency
Distributions

• Sort Raw Data in Ascending Order12, 13, 17, 21,
  24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43,
  44, 46, 53, 58
• Find Range 58 - 12 46
• Select Number of Classes 5 (usually between 3
  and 10)
• Compute Class Interval (width) 10 (46/5 then
  round up)
• Determine Class Limits 10-19.99, 20-29.99,
  30-39.99, etc.
• Compute Class Midpoints 15, 25, 35, 45, etc.
• Count Observations Assign to Classes

26
Frequency Distributions, Relative Frequency
Distributions and Percentage Distributions
Data in an ordered array 12, 13, 17, 21, 24, 24,
26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46,
53, 58
Relative Frequency
Percentage
Class Frequency
10 19.99 3 .15
15 20 29.99 6
.30 30 30 39.00
5 .25 25
40 49.99 4
.20 20 50 59.99 2
.10 10
Total 20 1
100
27
Cumulative Frequency Distribution
Data in an ordered array 12, 13, 17, 21, 24, 24,
26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46,
53, 58
Lower Cumulative Cumulative Limit
Frequency Frequency 0
to 10 0
0 0 to 20 3
15 0 to 30 9
45 0 to 40 14
70 0 to 50
18 90 0 to 60
20 100
28
CUMULATIVE DISTRIBUTION EXAMPLEInpatients,
Grouped by Age, Presenting with Diseases of the
Respiratory System
Age Number of Patients Years or Less Cumulative Frequency Relative Frequency
20-29 150 20-29 150 0.06
30-39 235 20-39 385 0.16
40-49 270 20-49 655 0.28
50-59 340 20-59 995 0.42
60-69 400 20-69 1,395 0.59
70-79 450 20-79 1,845 0.78
80-89 510 20-89 2,355 1.00
Total 2,355
29
CUMULATIVE DISTRIBUTIONS

• Example Diagnostic Category Respiratory
  Illnesses
• Variables
• Age Range How many categories?
• Number of patients?
• N (number in sample) 2,355
• Equation CFi/T
• CFi the cumulative frequency associated the
  category i
• T total number of observations
• Example (79 years old or less) 1,845 / 2,355
  0.78

30
Frequency Distribution Types

• Frequency Distribution only give you the
  numbers in each group
• Relative Frequency Distribution gives you the
  proportion in each group
• Cumulative Frequency Distributions give you the
  total in a given group plus previous groups (can
  be reversed low to high or vice-versa)

31
FREQUENCY DISTRIBUTIONS Excel Example 4.1

• Open Excel Example 4.1
• Review Raw Numbers tab
• We have 20 patients
• ID number for each patient is in cells A6 to A25
• The number of secondary diagnoses for each
  patient in located in cells B6 to B25

32
FREQUENCY DISTRIBUTIONSUSING EXCEL EXCEL
EXAMPLE 4.1

• We want to categorize the data so that is makes
  more sense
• Assumption
• All patients had at least one secondary diagnosis
• Sort observations into categories
• No patient had more than 15 secondary conditions
• Categories should be collectively exhaustive 1
  to 15
• Count the number of items assigned to each

33
Excel Example 4.1Categories Using Bins

• We are now going to create the categories
• Review instructions on the bottom of the Working
  Sheet tab
• Review upper and lower limits
• Bins Receptacles into which the observations are
  sorted cells C6 to C9
• Maximum value for each category (upper limit for
  each category)

34
Excel Example 4.1

• Summarize Results - What does this information
  tell us?
• Be able to explain your results so that your
  grandmother could understand it!
• We have 20 patients and the number of secondary
  diagnoses for each one.
• Weve divided the sample into four groups based
  on their secondary diagnoses (1 to 4, etc.)
• There are 7 patients who has a 1 to 4 diagnoses,
  which represent 35 of the overall sample.
• There are 4 patients (20) in the group that has
  9 to 12 diagnoses.
• 90 of the sample had 12 or fewer secondary
  diagnoses.

35
Excels Histogram Function

• Very limited
• Not enough information
• Not detailed enough
• So, use the steps/directions in the previous and
  following slides to create your bar/column charts
  and frequency distribution tables

36
ABSOLUTE CELL REFERENCES (just an aside,
hopefully to make your Excel work a little
easier)

• When you copy formulas from one cell to another,
  Excel also copies any cell references in those
  formulas. But Excel adjusts the cell references
  in the copy of the formula so that the reference
  has the same relative relationship to the new
  formula. See the example shown here.
• Usually these relative references are exactly
  what you want. But suppose you want to copy a
  formula but maintain the reference to the exact
  same cells it originally referred to? You can do
  this using absolute cell references. To create an
  absolute cell reference, simply place a dollar
  sign before the row and/or the column. For
  example, an absolute cell reference to B3 is
  B3. (You can create partially absolute
  references by placing a dollar sign before only
  the row or only the column. Then, when you copy
  the formula, the part with the dollar sign stays
  constant, but the part without the dollar sign is
  adjusted like a relative reference.)

37
HISTOGRAM

• A histogram is a graphical tool that compares the
  sizes of the response groups. Heights of bars
  show counts for categories.
• Usually depicted as a bar chart or column chart
• Graphical way to represent a frequency
  distribution or a distribution of relative
  frequencies
• Series of rectangles with the area of each given
  by the product of its base and height
• Height class or relative frequencies
• Base class interval (on horizontal scale)
• If class intervals are equal, the area of a given
  rectangle indicates the relative importance of
  the class in the set of categories that defines
  the distribution
• See Excel Examples 4.2 and 4.3

38
Histograms
39
Histograms
40
Graphing Numerical Data The Histogram
Data in an ordered array 12, 13, 17, 21, 24, 24,
26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46,
53, 58
Class Limits
Class Midpoints
41
Frequency Polygon

• A continuous line that represents the frequencies
  of scores within a class interval

42
Fat and Skinny of Frequency Distributions

• Distributions can be different in four ways
• Average value
• Variability
• Skewness
• Kurtosis

43
Same Mean, Median, Mode - Different Shapes Though
44
Average Value
How distributions can differ in their average
score
45
Measures of Central Tendency

• Normal Curve Mean, mode, and median are same
  score

Mean. Mode Median
46
COMPARISON OF MEAN, MEDIAN MODE

• If the data are unimodal and symmetrical, the
  three measures of central tendency (mean, median,
  and mode) will be of similar value

47
Variability
How distributions can differ in variability
48
SYMMETRY ASSEMETRY

• A distribution is symmetrical if it is possible
  to construct a perpendicular line that divides it
  into two identical halves.
• A distribution is asymmetrical if a tail appear
  at either end.

49
SHAPE OF A DISTRIBUTIONSKEWNESS SYMMETRY

• Describe How Data are Distributed
• Measures of Shape
• Symmetric or skewed

Positively (Right) Skewed
Negatively (Left) Skewed
Symmetric
Mean lt Median lt Mode
Mean Median Mode

Mode lt Median lt Mean
50
Mode
Median
Mode
Median
Mean
Mean

• Skewed Curve
• Mode peak of distribution
• Median in middle
• Mean closest to tail of distribution

51
SKEWNESSInterpreting histograms

• Shape

Mean lt Median lt Mode
Mean gt Median gt Mode
52
COMPARISON OF MEAN, MEDIAN, MODE

• When data are skewed, the mean and median will
  not be equal. The mean will be pulled towards
  the skew
• For example, for a positive skew, the mean will
  be greater than the median
• For a negative skew, the mean will be less than
  the median

53
Skewness

• Positive and negative skewness

Degree of skewness in different distributions
54
Kurtosis

• Platykurtic (A) - flat curve
• Leptokurtic (C) peaked curve

55
USING EXCEL TO PREPARE GRAPHIC PRESENTATIONS

• Excel is very useful for creating charts
• However, often you will need to clean up your
  charts, play with the settings, or even add a
  text box to your chart to make it appropriate for
  the data and understandable for the reader
• A chart should be able to stand alone and not
  need an explanation
• For our purposes, we are going to use Excel to
  create the following types of charts
• Column Charts (a type of Histogram)
• Bar Charts (a type of Histogram)
• Pie Charts
• Line Charts

56
Column Charts - Excel Example 4.2

• Select
• Insert

3. Select Column
4. Select 2-D Clustered Column
2. Highlight Data (Hold Left Mouse Key While You
Drag Over the Appropriate Cells)
57
Column Charts - Excel Example 4.2
2. Select Select Data
3. Select Edit
1. Move Mouse Over Chart and Hit Left Mouse
Button
58
Column Charts - Excel Example 4.2
2. Select Chart Tools
3. Select down arrow on Chart Layouts

• Select appropriate chart layout with legend,
  title, and axis options (in this case, Layout 9)
• NOTE You can also use the layout function to
  choose these items.

1. Move Mouse Over Chart and Hit Left Mouse
Button
59
Column Charts Excel Example 4.2
1. Edit Axis Titles and Chart Title as
Appropriate.
NOTE I deleted the Series 1 as it did not add
any value to the chart.
FINALLY Make your charts very readable they
should be able to stand alone without any need
for explanation.
60
Column Charts - Excel Example 4.2

• Describe your chart
• What are the categories?
• How many are in each group?
• What is the implication for the manager or the
  reader?
• Are the groupings appropriate?
• Does the chart adequately summarize your data?

61
Column Charts - Excel Example 4.3

• Open Excel Example 4.3
• Note that we now have the cumulative frequency
  distribution as well
• The exercise here involves selecting the groups
  by the cumulative frequency distribution and
  creating a column chart

62
Bar Charts - Excel Example 4.3

• Select cells C5C10 while holding your left mouse
  button
• Release mouse key and hit and hold the control
  button
• With the control button down, also hold the left
  mouse button and select cells A4A10
• Release all buttons and the appropriate cells
  should be highlighted

63
Bar Charts - Excel Example 4.3

• Select Insert ? Bar ? 2-D Clustered Column
• Select (highlight) the chart ? select Chart
  Tools (at the very top) ? select 2-D Clustered
  Bar

64
Bar Charts - Excel Example 4.3
1. Note how the axis titles on the left is not
correct.
2. With the chart selected, hit select data,
then edit axis labels.
65
Bar Charts - Excel Example 4.3
1. Select the appropriate axis labels (A7A10)
and hit okay.
2. Now your axis labels for your groups are
correct.
66
Bar Charts (Histograms)Excel Example 4.3

• Go to your chart layouts and select the
  appropriate chart type
• In this case, I selected Layout 9
• Add your chart title and axis titles, labeled
  appropriately
• Delete series labels on the right they dont
  add anything for this chart.
• Add data labels to each bar (select bars and then
  right click, then Add Data Labels
• Wholla! You have a great looking bar chart
  histogram!

67
LINE CHARTS
68
LINE CHARTS - Excel Example 4.4

• Condenses information about two or more variables
  and portray the interrelation among the variables
  of interest
• Show changes in the value of the variables over a
  period (of time, often)
• Often useful when you are comparing TWO variables
• See Excel Example 4.4

69
LINE CHARTS - Excel Example 4.4
2. Select Insert
3. Select Line
4. Select 2-D Line (not stacked)
1. Select (Highlight) the Data (B3C14)
70
LINE CHARTS - Excel Example 4.4

• Select the chart and go to an appropriate line
  chart layout (in this case, I chose Layout 8,
  which had a chart title and axis titles)
• Change the axis and chart titles to appropriately
  match the data
• Add data labels if youd like
• Resize the chart as appropriate

71
Pie Charts

• The Pie Chart is a graphical tool that helps us
  see what part of the whole each group forms
• Typically you dont want any more than 10
  slices (3 5 is more typical)

72
PIE CHARTS - Excel Example 4.5

• The area of the chart represents the total of the
  phenomenon of interest
• Each slice represents the relative importance of
  each category or class
• See Excel Example 2.5

73
PIE CHARTS - Excel Example 4.5

• Select the appropriate data (A4B10)
• Select Insert
• Select Pie Chart 2-D Pie
• Select chart layout as appropriate
• Labels the chart appropriately (title)
• Choose percent data labels if appropriate

74
Excel Example 4.6 Pulling it all together

• Now, lets try another example using all of the
  previous tools plus two additional tools
• Review Example 4.6
• Review Raw Data tab
• What do we have?
• How many subjects do we have?
• What are the variables of interest?
• Can you describe the data set as is?
• So, we must use Excel to help us summarize,
  describe, and graphically represent our data

75
Excel Example 4.6

• Open the data set in Excel (Example 4.6)
• We have 5,099 cases (subjects/patients)
• We have the weight (in pounds) and gender (1
  male, 2 female) for each subject

76
Excel Example 4.6

• Using Sort
• Using the Descriptive Statistics tool to help
  you categorize your data

77
Excel Example 4.6 Sorting

• Sometimes it may be helpful at first to sort your
  data to see how your data looks when it is in
  order
• In this case, lets sort our data by weight so we
  can see values from low to high

78
Excel Example 4.6 Sorting
3. Select the variable you wish to sort by in
this case, weight and then select okay
1. Highlight your variables (just select columns
A, B, and C)
2. Select Data
79
Excel Example 4.6 Sorting

• We can see that our subjects range in weight from
  76 to 350 pounds
• But uh-oh, we have a problem 16 of our subjects
  do not have a weight
• We have several options, but the easy one (but
  not necessarily sound statistics though) is to
  just delete those cases
• Why may this not be appropriate? When you delete
  some cases, you are deleting part of your sample
  and this could influence your overall results
• If you do this, just make sure you note it in
  your write-up
• So, lets take the easy route and delete those
  cases

80
Excel Example 4.6 Descriptive Statistics

• Descriptive Statistics tool
• Make sure you have added your Data Analysis
  toolpak

81
Excel Example 4.6 Descriptive Statistics
1. Select Data
2. Select Data Analysis
3. Select Descriptive Statistics
82
Excel Example 4.6 Descriptive Statistics
3. Select the Output Range this can be
anywhere, but generally a blank space on your
sheet note that you need to hit the white box
first or Excel will try to bump you to the input
range I used an output range of E20
1. Select Input Range B2B5100 the weights
of all the subjects
2. Check the Summary statistics box
83
Excel Example 4.6 Descriptive Statistics
1. Note the Descriptive Statistic table that
pops up
2. We can now see the Mean, or the average
weight of the subject more on this later the
average weight of the subjects is 157 pounds
3. We can also see the minimum and maximum 76
and 350
84
Excel Example 4.6 Frequency Distribution

• Using the Descriptive Statistics table will
  make it easier to determine the appropriate
  groups for our data
• With a minimum of 76 and a maximum of 350, lets
  make our groups like this
• 50 99, 100 149, 150 199, 200 249, 250
  299, and 300 350
• Note that the last category is one higher than
  the others (350)
• That gives us six groups, which is reasonable,
  and it is collectively exhaustive (includes
  everyone) and mutually exclusive (no two subjects
  are going to fall into more than one category)

85
Excel Example 4.6 Frequency Distribution

• So, in the Excel Example 4.6, lets create our
  bins and out labels for each column groups,
  relative frequencies, and cumulative frequencies
• Now, lets use Excel to create our frequency
  table
• Select Data ? Data Analysis ? Histogram

86
Excel Example 4.6 Frequency Distribution
1. Select the input range B2B5100

1. Select the Bin range E4E9

3. Select the output range (anywhere on a blank
spot on the page) I chose
4. Check the cumulative percentage box
5. Click OK
87
Excel Example 4.6 Frequency Distribution

• Now, paste your Histogram output into the
  appropriate places in the table
• Calculate your relative frequencies for each
  group (see the instructions in Excel Example 4.1)
• Create a column chart by frequency, a bar chart
  by relative frequency, and a pie chart (any way
  you want)
• a line chart for this data would not be
  appropriate
• Label charts appropriately
• Vertical axis, horizontal axis, title, get rid of
  column label, add data labels, etc.
• Now, describe your results in words your
  grandmother would understand

88
Ten Ways to a Great Figure

• Minimize the junk
• Plan before you start creating
• Say what you meanmean what you say
• Label everything
• Communicate one idea
• Keep things balanced
• Maintain the scale in the graph
• Remembersimple is best
• Limit the number of words
• The chart alone should convey what you want to say

89
Principles of Graphical Excellence

• Well-Designed Presentation of Data that Provides
• Substance
• Statistics
• Design
• Communicates Complex Ideas with Clarity,
  Precision and Efficiency
• Gives the Largest Number of Ideas in the Most
  Efficient Manner
• Almost Always Involves Several Dimensions
• Telling the Truth about the Data

90
Errors in Presenting Data

• Using Chart Junk
• No Relative Basis in Comparing Data between
  Groups
• Compressing the Vertical Axis
• No Zero Point on the Vertical Axis

91
Chart Junk
?
Good Presentation
Bad Presentation
Minimum Wage
Minimum Wage

1960 1.00
4
1970 1.60
2
1980 3.10
0
1960
1970
1980
1990
1990 3.80
In the depiction on the left, you cant really
tell the detailed significance between the
groups. The sizes can be deceptive.
92
No Relative Basis
?
Bad Presentation
Good Presentation
As received by students.
As received by students.
Freq.

30
300
200
??
???
10
0
?
FR
SO
JR
SR
FR
SO
JR
SR
FR Freshmen, SO Sophomore, JR Junior, SR
Senior
In this case, there are many more freshmen than
juniors or seniors so the larger number of As
for freshmen deceptive. When put into relative
frequencies, the percentages are the same.
93
Compressing Vertical Axis
?
Bad Presentation
Good Presentation
Quarterly Sales
Quarterly Sales


50
200
25
100
0
0
Q1
Q2
Q4
Q1
Q2
Q3
Q4
Q3
When the vertical axis is compressed, it is more
difficult to see the differences between the
groups.
94
No Zero Point on Vertical Axis
?
Good Presentation
Bad Presentation
Monthly Sales
Monthly Sales


45
45
42
42
39
39
36
36
0
J
F
M
A
M
J
J
F
M
A
M
J
Graphing the first six months of sales.
95
ARTICLE REVIEW

• DesRoches Electronic Health Record
• DesRoches, C., Campbell, E., Vogeli, C., Zheng, J.
  , Rao, S., Shields, A., Donelan, K., Rosenbaum, S.
  , Bristol, S.,  Jha, A.  (2010). Electronic
  Health Records' Limited Successes Suggest More
  Targeted Uses. Health Affairs, 29(4), 639-46. 

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UNIT SUMMARY

• Frequencies
• Distributions
• Basic terms
• Using Excel
• Creating graphs

NOTE This slide contains information that is
not in the chapter.
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Homework Unit 4 Assignment

• Question 1 combine what youve learned from
  Excel Examples 4.1 and 4. 6 (see the Excel files
  in the Unit 4 Material)
• BIN values are 3, 7, and 11 (the upper limits
  these will be placed down the left column this
  looks a bit different in the back of the book in
  the answer section)
• Use the Excel formulas and instructions from the
  slides and the Excel examples
• DO NOT simply insert numbers or use a calculator
  use the formulas weve learned in class
• For Question 2, label each axis thoroughly and
  label each piece of the pie in detail. Someone
  should be able to look at each chart and be able
  to immediately tell you the full story about it.
• Questions 3 4 written answers only

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Practice, Practice, Practice

• Dont go crazy yet!
• Review and practice all of the exercises weve
  gone over in class.
• Call or e-mail me with any questions.

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NEXT WEEK

• Unit 5 Computing Correlation Coefficients
  Hypotheticals
• Review Unit 4, Chap. 4
• Deliverables Due Before the Next Class
• Unit 4 Quiz
• Reidpath, D. D., Allotey, P. (2003). Infant
  mortality rate as an indicator of population
  health. Journal of Epidemiology and Community
  Health, 57(5), 344-346.
• Unit 4 Assignment

NOTE This slide contains information that is
not in the chapter.