ivt 2016 june - strategies to graph, analyze, and present · pdf filestrategies to graph,...

Strategies to Graph, Analyze, and Present DataHOW TO PICK THE BEST CHART / GRAPH FORTHE JOB

RAUL SOTO, MSC, CQEIVT STATS CONFERENCE - JUNE 2016

PHILADELPHIA, PA

The contents of this presentation represent the opinion of the speaker; and not necessarily that of his present or past employers.

(C) 2016 / RAUL SOTO 2

About the Author• 20 + years of experience in the medical devices, pharmaceutical, biotechnology, and consumer electronics industries

• MS Biotechnology, emphasis in Biomedical Engineering• BS Mechanical Engineering• ASQ Certified Quality Engineer (CQE)

• I have led validation / qualification efforts in multiple scenarios:

• High-speed, high-volume automated manufacturing and packaging equipment; machine vision systems• Laboratory information systems and instruments• Enterprise resource planning applications (i.e. SAP)• IT network infrastructure, Cognos & Business Objects reports• Manufacturing Execution Systems (MES)• Mobile apps• Product improvements, material changes, vendor changes

• Contact information:• Raul Soto [email protected]

(c) 2016 / Raul Soto 3

What is “Data Visualization”?• Presentation of data in pictorial or graphical format• Advantages:

• Comprehend information quickly• Identify relationships and patterns• Discover trends• Communicate effectively

• Human brain typically does better job at understanding large amounts of data when presented in visual form vs when represented by just numbers


Data Visualization

• A chart is a visual representation of distances between data points• A pattern is how we connect these data points• A chart type is a set of transformations we apply to this basic layout, used to improve:

• How we see the chart• Insight we gain from it

• The human brain’s perceptive and cognitive processes play a big part on how people interpret a chart.


Why Graphs?

• Graphs use spatial arrangements to convey• Numerical information• Trends• Relationships

• Often easier to interpret than repetitive numbers or complex tables


Graphs vs Tables

• Oral presentation: • emphasis on graphs

• Written: Validation report, research reports, published papers:• Use both graphs and tables• Can use graphs on main text, data tables on Appendix


Advantages vs Disadvantages

• Advantages• High information density• Rapid assimilation of overall result• One graph can have multiple levels of detail• Can show complex relationships among multiple variables

• Disadvantages• May misrepresent data, accidentally or intentionally• May suggest interpolation between data points, even when it’s not applicable• Exact numeric values may be hard to read


Human Perception

• Can you tell the difference in length between the white parts of both bars?

• What about the black parts?


Human Perception

• They differ by exactly the same amount (1 unit)• It’s easier for the brain to tell the difference between the white bars because the

percentage difference was bigger

15

16

2

1

(c) 2016 / Raul Soto 10

Human Perception: Accuracy• Position on a common scale/ axis• Position on an identical, non-aligned

scale• Length• Angle• Slope• Area• Volume• Density• Color saturation• Color hue

Easierto judge accurately

Harderto judge accurately

(c) 2016 / Raul Soto 11

(c) 2016 / Raul Soto 12

Human Perception: Why is this Important?

Because features / limitations in human perception may lead to accidental or intentional misrepresentation of data in graphs

(c) 2016 / Raul Soto 13

Misrepresentation

How much larger is the Product C bar than the Product A bar?

(c) 2016 / Raul Soto 14

Misrepresentation• y-axis not starting in zero• makes a small % increase look much larger

0

1

2

3

4

5

6

Product A Product B Product C

% defective

% defective

4

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6

Product A Product B Product C

% defective

% defective

(c) 2016 / Raul Soto 15

Misrepresentation

• Vertical axis suggests an equalinterval between sampling dates, which is not true

• Intervals are 6 and 23 years

0

1

2

3

4

5

6

7

1977 20161993

(c) 2016 / Raul Soto 16

Misrepresentation

• More examples:

• Misleading graphs. http://gator.gatewayk12.org/~smcgrail/myweb/powerpoint/misleading_graphs/here_are_some_examples_of_mislea.htm

• Misleading graphs: Real Life Exampleshttp://www.statisticshowto.com/misleading-graphs/

(c) 2016 / Raul Soto 17

Best Practices• Make your data stand out

• Draw the audience’s attention to the important / relevant aspects of your graph

• Focus on, and improve, the visual aspect of your message

• Graph should make your point without distracting the audience

• Reduce clutter, distraction of non-essential elements in graph

• Use color sparingly: use it for emphasis, not for eye candy• Color should help make your point

(c) 2016 / Raul Soto 18

What to Avoid

• Anything that distracts from the data, or from the point you want to make• Clutter• Avoid false-3D representations

• 3D pie charts, 3D bar charts

• Minimize fill patterns and background fills• Keep them subtle, don’t distract from the data

• Keep grid lines to a minimum, make them subtle and light• Use of color for decorative purposes

(c) 2016 / Raul Soto 19

Pie Charts: Proportions• Visually highlight the relative proportion of one slice

(or a few slices) to the whole• Use colors and shades to group together related slices• Pre-sort data so slices show in decreasing order of size• In the example, you can analyze individual slices, and

also the blue group vs the orange group• Keep it simple:

• Avoid 3D tilt effects, distorts proportions• Keep the number of slices to a minimum (≤5) ,

group them if necessary• Don’t overuse or abuse the “slice explode out”

feature

(c) 2016 / Raul Soto 20

Pie Charts: ProportionsDisadvantages: • Information is represented in angles, which are

low in the perception accuracy scale• 3D tilt effect distorts the angles• Slice explode out effect doesn’t really improve

the information conveyed• Relative sizes of the samples are not easy to

judge visually• i.e. Blue slice is 30x bigger than brown slide

• Audience can’t really get much information

553

1591

Concentration of 1080 in sample

Over 2 ppb

0.1 to 2 ppb

under 0.1 ppb

(c) 2016 / Raul Soto 21

Pie Charts: Proportions

5

53

1591

0 400 800 1200 1600Number of samples

Concentration of 1080 in sample

< 0.1 ppb

0.1 - 2 ppb

> 2 ppb

• The same information can be conveyed better with a bar graph.• Relative sizes of the samples are easier to judge with this graph type.

(c) 2016 / Raul Soto 22

Stacked Bar/Area Charts: Changes in Proportions

4.32.5

3.54.5

2.44.4 1.8

2.8

2 2

3

5

01

1

2

0

2

4

6

8

10

12

14

16

Line 1 Line 2 Line 3 Line 4

# de

fect

s

Lines

Class 3 defects Class 2 Defects

Class 1 Defects Critical Defects

Used to display trend of proportions as well as the actual amounts

4.32.5

3.54.5

2.44.4 1.8

2.8

2 2

3

5

01

1

2

0

2

4

6

8

10

12

14

16

Line 1 Line 2 Line 3 Line 4

# de

fect

s

Lines

Class 3 defects Class 2 Defects Class 1 Defects Critical Defects(c) 2016 / Raul Soto 23

100% Stacked Bar/Area Charts: Change in Proportions

4.35

3.5

2.5

3.5

2.43.1

1.8 4.4 1.8

2

1.13

2

3

0

21 1 1

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Jan Feb Mar Apr Jun

Class 3 defects Class 2 Defects Class 1 Defects Critical Defects

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Jan Feb Mar Apr Jun

Class 3 defects Class 2 Defects Class 1 Defects Critical Defects

Use this when you only care about the trend of proportions, not the actual values

(c) 2016 / Raul Soto 24

Real Life Example: 100% Stacked Area Chart

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 52 103

154

205

256

307

358

409

460

511

562

613

664

715

766

817

868

919

970

1021

1072

1123

1174

1225

1276

1327

1378

1429

1480

1531

1582

1633

1684

1735

1786

1837

1888

1939

1990

2041

2092

2143

2194

2245

2296

2347

2398

2449

Red Fluorescence (RED-HLog)

Yellow Fluorescence (YLW-HLog)

Green Fluorescence (GRN-HLog)

Flow cytometry data.

Antibodies to α5 integrin were tagged with fluorescent tags, to study the levels of expression of α5 in rhabdomyosarcoma cancer cells.

Plot shows that α5 fluoresces mostly in the yellow region of the spectrum.

(c) 2016 / Raul Soto 25

Bar / Column Charts: Comparisons• Easiest way to compare data across categories

• Clearly see differences.

• Displays a quantitative variable vs a categoricalvariable.

• If labels on x-axis are too long, use horizontalbars instead of vertical columns

• For multiple data sets, you can use stacked bars or multiple bars

• Multiple bars make it easier to compare values

50

35

66

88

55

30

8092

60

32

94104

0

20

40

60

80

100

120

# Re

ques

ts

Department

Software Change Requests per year

2013

2014

2015

(c) 2016 / Raul Soto 26

Stacked Bars vs Multiple Bars

0

20

40

60

80

100

120

Labs Ops Labs R&D Engineering IT

# Re

ques

ts

Department


2013

2014

2015

0

50

100

150

200

250

300

Labs Ops Labs R&D Engineering IT

# Re

ques

ts

Department


2015

2014

2013

?

Multiple bars make it easier to compare values 27

Bar / Column Charts: Comparisons• Watch out for clutter, readability if too many data

sets are plotted in a single chart.

• If your horizontal (x) axis is quantitative, use a line chart or an x-y graph instead

• If all y-axis values are positive, start the y-axis at zero

• If the y-axis has positive and negative values, use zero as the midpoint

50

35

66

88

55

30

8092

60

32

94104

0

20

40

60

80

100

120

# Re

ques

ts

Department


2013

2014

2015

(c) 2016 / Raul Soto 28

Bar / Column Charts: Comparisons

2

1

1

10

2

3

5

5

12

3

2

25

0 5 10 15 20 25 30

CR Initiate

Business Pre-Approval to TST

QA Pre-Approval to TST

Execution in TST

Business Post-Approval TST Results

QA Post-Approval TST Results

Business Pre-Approval to PROD

QA Pre-Approval to PROD

Execution in PROD

Business Post-Approval PROD Results

QA Post-Approval PROD Results

CR Closure

Current Software Change Requests by Phase

• If labels on x-axis are too long, use horizontal bars instead of vertical columns

(c) 2016 / Raul Soto 29

Error Bars in Line Charts (MS Excel)

30

Error Bars in Line Charts (MS Excel)

• Use error bars to display the uncertainty / variability of your data

• You can use either the Standard Error of the Mean (SEM) or a 95% Confidence Interval (CI)

• SEM is smaller when sample sizes are small

• 95% CIs are more widely used in the sciences

• You must state in the caption AND text which type of error bars you are illustrating

(c) 2016 / Raul Soto 31

• Once you create a line or barchart:

• Left click on a line or a bar• On the upper menu click on

Layout / Error Bars/ More Error Bar Options/ Custom / Specify Value

• to use the Standard Error of the Mean, shade the SE Mean cells

• to use the Confidence Interval, shade the CI cells

(c) 2016 / Raul Soto 32

(c) 2016 / Raul Soto 33

Hypothesis test / p-values in Bar Charts• Use asterisks to display hypothesis

test comparisons between columns• In general

* => p< 0.05** => p< 0.01*** => p< 0.001**** => p<0.0001

• p-value should be reported in the figure description

• Notice how color is used to distinguish the controls from the experimental data

(c) 2016 / Raul Soto 34

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Production Campaign for Product A

SKU 1 SKU 2 SKU 3 SKU 4

Line Charts: Trends• Mainly used to plot a

quantitative variable (y axis) vs time (x axis)

• Visualize a sequence of values, display trends over a period of time

• This line chart makes it easy to see the trends for each SKU

• Stacked bar graph can display aggregate trends for all SKUs

(c) 2016 / Raul Soto 35

Scatter Plots: Relationships

• A scatter plot is a plot of the values of Y versus the corresponding values of X:

• Vertical axis: variable Y--usually the response variable

• Horizontal axis: variable X--usually a variable we suspect may be related to the response

(c) 2016 / Raul Soto 36

Scatter Plots: Relationships

• Allows us to see graphically if there is a relationship between X and Y

• Use regression to determine correlation between X and Y, and to fit lines or curves to data

• Plot the regression line vs the data point to determine visually if the regression is really a good fit, even if your R2

adj ≈ 1

• Remember : correlation DOES NOT necessarily mean causation

(c) 2016 / Raul Soto 37

No relationship Strong Linear RelationshipPositive correlation

Strong Linear RelationshipNegative correlation

Quadratic Relationship

(c) 2016 / Raul Soto 38

(c) 2016 / Raul Soto

100806040200

133

132

131

130

129

128

Day

Y-D

ata

Line 1Line 2Line 3Line 4Line 5

Variable

Scatterplot of Line 1, Line 2, Line 3, Line 4, Line 5 vs DayScatter Plots

• Multiple data sets can be plotted simultaneously for comparison.

39

Scatter plot example: Flow Cytometry

(c) 2016 / Raul Soto 40

Scatter plot example: Flow Cytometry

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800 900 1000

FSC-

Hlin

SSC-Hlin

Day 0: Collagen 5mg/ml

Green Fluorescence (GRN-HLog)

Yellow Fluorescence (YLW-HLog)

Red Fluorescence (RED-HLog)

FSC-HL : forward scattering/ cell density SSC-HL : side scattering/ fluorescence

(c) 2016 / Raul Soto 41

Scatterplot Matrix

• Displays pairwise relationships between multiple variables

(c) 2016 / Raul Soto 42

Contour and 3D Surface Plots: Multivariable

• Used to represent how one dependent variable (z-axis) changes / behaves as a function of twoindependent variables (x and y axes)

• Very useful for DoE, process optimization• Similar to a topographical map, where x = longitude,

y = latitude, and z = elevation• In a contour plot, colors or elevation lines can be

used to display the values of z. • In a 3D surface plot, the values of z can be displayed

directly

(c) 2016 / Raul Soto 43

Contour and 3D Surface Plots: Multivariable

(c) 2016 / Raul Soto 44

Radar (Spider) Charts: Multivariable

• Used to compare the aggregate values of multiple data series

• Display 3 or more quantitative variables on axes starting from the same point

• Plots values of each category along a separate axis that starts in the center of the chart, and ends at the outer ring

• Helps see clusters in the data• Not intuitive, requires explanation

(c) 2016 / Raul Soto 45

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Production Campaign for Plant A

SKU 1 SKU 2

SKU 3 SKU 4

SKU 1 SKU 2 SKU 3 SKU 4Jan 0 2500 500 0Feb 0 5500 750 1500Mar 0 9000 1500 2500Apr 0 6500 2000 4000May 0 3500 5500 3500Jun 0 0 7500 1500Jul 0 0 8500 800Aug 1500 0 7000 550Sep 5000 0 3500 2500Oct 8500 0 2500 6000Nov 3500 0 500 5500Dec 500 0 100 3000

Radar (Spider) Charts

46

• Radar chart highlights the “clusters” (i.e. for SKU 2)

• Does not display the aggregate (total) production well

SKU 1 SKU 2 SKU 3 SKU 4Jan 0 2500 500 0Feb 0 5500 750 1500Mar 0 9000 1500 2500Apr 0 6500 2000 4000May 0 3500 5500 3500Jun 0 0 7500 1500Jul 0 0 8500 800Aug 1500 0 7000 550Sep 5000 0 3500 2500Oct 8500 0 2500 6000Nov 3500 0 500 5500Dec 500 0 100 3000 0 0 0 0 0 0 0

1500

5000

8500

3500

500

2500

5500

9000

6500

3500

0 0

0

0

0

0

0

500

750

1500

2000

5500

75008500

7000

3500

2500

500

100

0

1500

2500

4000 3500

1500

800 550

2500

6000

5500

3000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Production Campaign for Plant A

SKU 1 SKU 2 SKU 3 SKU 4

• Stacked bars allow us to see the aggregatedproduction and relative proportions

• Harder to see the clusters

47

Bubble Charts: Multivariable

• Type of scatter plot, that represents three (3) dimensions of data

• X and Y axis are value axes, no categorical axes• 3rd dimension (Z) represented by the size of the

bubble• Some software packages allow display of a 4th

dimension in the color of the bubbles• Human perception does not judge proportional

increases / decreases in circle area or color hues accurately

(c) 2016 / Raul Soto 48

$0

$10,000

$20,000

$30,000

$40,000

$50,000

$60,000

$70,000

0 5 10 15 20 25 30

Sale

s

# Products

Market Share vs Sales and # Products

Bubble size represents % market share

# products Sales% Market Share

5 $5,500 314 $12,200 1220 $60,000 3318 $24,400 1022 $32,000 42

(c) 2016 / Raul Soto 49

http://www.esteco.com/cmis/browser?id=workspace://SpacesStore/c8d9e58e-a183-435a-a6ef-c81c6ec586bf

4D Bubble chart used as part of materials design and evaluation for Lamborghini automobiles

(c) 2016 / Raul Soto 50

Histograms: Distribution• The purpose of a histogram is to graphically summarize the distribution of a univariate

data set.

• The histogram graphically shows the following: • center (i.e., the location) of the data; • spread (i.e., the scale) of the data; • skewness of the data; • presence of outliers; and • presence of multiple modes in the data.

• These features provide strong indications of the proper distributional model for the data.

• The probability plot or a goodness-of-fit test can be used to verify the distributional model.

(c) 2016 / Raul Soto 51

C1

Freq

uenc

y

5352515049484746

9

8

7

6

5

4

3

2

1

0

Mean 49.63StDev 1.497N 30

Histogram

Lot

Freq

uenc

y

363330272421

18

16

14

12

10

8

6

4

2

0

Mean 28.49StDev 3.733N 60

Histogram - Bimodal Mixture of 2 Normals

(c) 2016 / Raul Soto 52

Multiple Histograms: Distribution Comparisons

• Compare multiple data sets

• Visualize before/after changes (see example) in distribution

(c) 2016 / Raul Soto 53

Multiple Histograms: Distribution Comparisons

10

2

4

6

8

01

21

41

61

81

5.4 0.6 5.7 0.9 5.01 0.21 5.31 0.5

7.392 0.9618 3010.29 0.9634 3013.30 0.8041 3010.07 1.226 30

6.635 0.8716 3012.71 0.8753 30

9.237 0.9759 309.947 2.492 210

Mean StDev N

D

ycneuqerF

ata

LelbairaV

llarevO7 toL6 toL5 toL4 toL3 toL2 toL1 to

P lamroN

emiT revO gnitfihS naeM ssecor

• More than 3 data sets: too much clutter, use box plotsinstead

(c) 2016 / Raul Soto 54

Box Plots

• Box Plots give good indication of:• central tendency• spread of data• outliers

• Unlike histograms, box plots do notgive a direct visual display of the data distribution


Lot DLot CLot BLot A

35.0

32.5

30.0

27.5

25.0

Dat

a55

Box Plots : Elements• Asterisk : Outlier - an unusually large or small

observation. Values beyond the whiskers are outliers.

• Top of the box : third quartile (Q3) - 75% of the data values are less than or equal to this value

• Upper whisker : the highest data value within the upper limit.

• Upper limit = Q3 + 1.5 (Q3 - Q1)

• Line in the middle of the box : Median, the middle of the data. Half the observations are less than or equal to it.

• Bottom of the box is the first quartile (Q1) - 25% of the data values are less than or equal to this value

• Lower whisker : the lowest value within the lower limit.

• Lower limit = Q1- 1.5 (Q3 - Q1)

(c) 2016 / Raul Soto 56

Multiple Box Plots


Dat

a

C3C2C1

57.5

55.0

52.5

50.0

47.5

45.0

Boxplot of C1, C2, C3

57

Multiple Box Plots• We can compare multiple lots and visually determine if the process mean or variation are

consistent

• Compare X validation lots to determine consistency• Compare samples from different lines, raw materials, operators• Compare before-after a process change• Compare samples from a process taken at different points in time

• We’d like the means to line up, and the spread to be consistent across the board.

• If the multiple lots were manufactured under the same conditions then we’ve discovered that the means and the process capability are shifting, and therefore inconsistent

• In order to actually determine if there has been a statistically significant shift on the mean or the variation, we need to perform a hypothesis test.

(c) 2016 / Raul Soto 58

Heat Maps: Comparisons• Use different colors, or different hues of a

color, to visually represent differences in your data

• In MS Excel, use Home / Conditional Formatting / Color Scales

• In the rules, type in the limits you want to establish for each color or hue. Make sure they are consistent throughout all your data

(c) 2016 / Raul Soto 59

Heat Maps - example

• Mammalian cell culture: human fibroblasts and mesenchymal stem cells

• Grown in 2D matrix, different concentrations of fibronectin or collagen for 8 days

• Used live/dead fluorescent stain, and measured fluorescence per well to ascertain cell growth under each condition

(c) 2016 / Raul Soto 60

Color scale: green = higher fluorescence; yellow = lower fluorescence 61

Color scale: green = higher fluorescence; yellow = lower fluorescence 62

Run Chart: Trends

• Plot a variable vs time

• An easy way to summarize graphically an univariate data set

• Shifts in location and scale are usually evident

• Outliers can be detected


Observation

C1

30282624222018161412108642

53

52

51

50

49

48

47

46

Run Chart of C1

63

Limitations of Run Charts• In Run charts people frequently see things (special causes of variations) that aren’t

there:

• “obvious” cycles• trends• outliers• process instability

• If we misinterpret normal variation as a Special Cause, we end up overadjusting the process

• If we misinterpret a special cause of variation as normal, we fail to take action

(c) 2016 / Raul Soto 64

Control Charts / SPC: Trends and Control

• Control limits • drawn at 3 sigma levels from the mean• If nothing changes in our process we expect to

see all observations between 45.01 and 54.25

• Special Cause Variation: • Control charts use eight statistical rules to

detect special cause variation (trends, outliers, etc.)


Sample

Sam

ple

Mea

n

30272421181512963

54

53

52

51

50

49

48

47

46

45

__X=49.63

+3SL=54.25

-3SL=45.01

+2SL=52.71

-2SL=46.55

+1SL=51.17

-1SL=48.09

6

Xbar Chart of C1

65

Main Types of Control Charts(Shewhart)

• Variable data• Xbar – R : mean and range of each sample• Xbar – s : mean and standard deviation of each sample• I – MR : individual values observations vs time

• Attributes• np : actual number of defectives• p : proportion of defectives• c : actual number of defects • u : defects per unit

• Defects : a single unit can have multiple flaws• Defectives : a single unit itself is either good or bad

(c) 2016 / Raul Soto 66

Pareto Chart: Rank Importance

• Display Categorical Inputs vs Categorical Outputs

• Pareto Principle : 80% of events due to 20% of the categories

• Help to focus efforts on areas where they will have the most impact

(c) 2016 / Raul Soto 67

Which chart type should I pick?To Display Use thisProportions Pie Charts

Change in Proportions: Proportions vs timeProportions vs categorical variable

Stacked Bar ChartsStacked Area Charts

Trends Line Charts

Comparisons Bar ChartsColumn Charts

Multivariable Relationships Bubble ChartsRadar Charts

Relationships X-Y => see NEXT PAGE

(c) 2016 / Raul Soto 68


To Display Use thisY (continuous) vs frequency Histograms

Box plots

Y (continuous) vs time Run chartsControl charts

Y (continuous) vsX (categorical)

Bar charts Column charts

Y (continuous) vsX (continuous)

Scatter plots

Y (categorical) vsX (categorical)

Pareto Charts

Which XY chart type should I pick?

69

References• Duquia, Rodrigo Pereira, Bastos, João Luiz, Bonamigo, Renan Rangel, González-Chica, David Alejandro, & Martínez-Mesa,

Jeovany. (2014). Presenting data in tables and charts. Anais Brasileiros de Dermatologia, 89(2), 280-285. https://dx.doi.org/10.1590/abd1806-4841.20143388

• NIST/SEMATECH e-Handbook of Statistical Methodshttp://www.itl.nist.gov/div898/handbook

• Exploratory Data Analysis. NIST Engineering Statistics Handbookhttp://www.itl.nist.gov/div898/handbook/eda/eda_d.htm

• Few, Stephen. Information Dashboard Design: The Effective Visual Communication of Data. Beijing: O'Reilly, 2006. Print.http://www.amazon.com/Information-Dashboard-Design-Effective-Communication/dp/0596100167

• Jaedicke, Katrin. Applied Statistics: How to Present your Data Analysis in Graphs. Newcastle University.http://fms-itskills.ncl.ac.uk/pgres/stats/docs/14_presenting_data_in_graphs.pdf

(c) 2016 / Raul Soto 70

References• Kelly, Dave, Jaap A Jasperse, I Westbrooke, and New Zealand. Designing Science Graphs For Data Analysis And

Presentation: The Bad, The Good And The Better. Wellington, N.Z.: Dept. of Conservation, 2005.http://www.doc.govt.nz/Documents/science-and-technical/docts32entire.pdf

• Misleading graphs. http://gator.gatewayk12.org/~smcgrail/myweb/powerpoint/misleading_graphs/here_are_some_examples_of_mislea.htm

• Misleading graphs: Real Life Exampleshttp://www.statisticshowto.com/misleading-graphs/

• Smeltzer, Philip. Presenting Health Care in Visual Displays. https://www.optum.com/content/dam/optum/resources/whitePapers/112912-OH-data-visibility-WP.pdf

• Sharma, Himanshu. How to select best Excel Charts for Data Analysis & Reporting. https://www.optimizesmart.com/how-to-select-best-excel-charts-for-your-data-analysis-reporting/

(c) 2016 / Raul Soto 71