Graphs, Tables and Captions My biased take on how to view your data - - PowerPoint PPT Presentation

Graphs, Tables and Captions

My biased take on how to view your data

Aaron Schulman Featuring graphs from many talented artists

Saturday, January 7, 12

Why do we graph?

• To grasp lots of observations
• To find patterns in observations
• To see the distribution of observations
• To determine the relationship between
• bservations (be careful with correlation)
• To find bugs in the experiment
• To show others our observations

Saturday, January 7, 12

A graph

500 1000 1500 2000 2500 2 4 6 8 10 power (mW) time (s)

axis labels (and units) X

• i

n d e p e n d e n t Y

• d

e p e n d e n t data

Saturday, January 7, 12

A graph

500 1000 1500 2000 2500 2 4 6 8 10 power (mW) time (s)

axis labels (and units) X

• i

n d e p e n d e n t Y

• d

e p e n d e n t data

Saturday, January 7, 12

A graph

500 1000 1500 2000 2500 2 4 6 8 10 power (mW) time (s)

axis labels (and units) X

• i

n d e p e n d e n t Y

• d

e p e n d e n t data

Saturday, January 7, 12

A graph

500 1000 1500 2000 2500 2 4 6 8 10 power (mW) time (s)

axis labels (and units) X

• i

n d e p e n d e n t Y

• d

e p e n d e n t data

Saturday, January 7, 12

jitter the the a with

10 20 30

Backbone routers in POP

10 20 30

POP outdegree

y = 1.091x + 0.696

• Fig. 11. POP outdegree vs backbone routers in the POP. A small random jitter

was added to the data points to expose their density. Circles represent the median of at least ten nearby values: fewer medians are present for the few large POPs. The solid line traces a linear regression fit, with R2 = 0.70. This is an aggregate graph over nine ISPs, excluding Level3 due to its logical mesh topology that gives POPs very high outdegree.

• E. Router Degree Distribution

0.2 0.4 0.6 0.8 1 5 10 15 20 Fraction to BitTorrent’s download time Torrent ID, sorted by PropShare completion time PropShare BitTyrant

Figure 6: Runs on live swarms

Always view the raw data first

Scatter plot

Credit: Neil Spring (left) Dave Levin (right)

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Bar graph

0.1 0.2 0.3 0.4 0.5 0.6 0.7 130 227 306 Percentage of Nodes Network Size Percentage (Average Battery) of Leaders, Bridges, and Clients Leader Bridge Client .746 .545 .388 .690 .578 .395 .736 .592 .389

Figure 5: Percentage of leaders, bridges, and clients in different topologies. The value on top of each bar denotes the average remaining battery for each case.

Credit: Seungjoon Lee

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20 40 60

POP size (routers)

0.0 0.2 0.4 0.6 0.8 1.0

P ( POP size < x)

Fraction of POPs Fraction of Routers

• Fig. 9. The cumulative distribution of POP sizes (solid), and the distribution of

routers in POPs of different sizes (dotted). The mean POP size is 7.4 routers, and the median is 3 routers.

Distributions

CDF Box and whisker

50 100 150 count 0.5 1 1.5 2

• 120
• 110
• 100
• 90
• 80
• 70
• 60
• 50
• 40
• 30

throughput (Mbit/s) signal strength (dBm)

Credit: Neil Spring

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Standard deviation and confidence interval

• 0.04
• 0.02

0.02 0.04 0.06 0.08 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

• Rel. error of miss. packet estimate
• Frac. non-beacon packets removed

Know your data

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3D and heatmap

• 3D is not your

friend

• Use a heatmap

1 10 100 1000 10000 IETF 2005 chan. 11 ple 10 20 30 40 50 Load (change in sequence number) 0.2 0.4 0.6 0.8 1 Score

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Multiple axis and shared axis

2 4 6 8 10 12 14 16 18 0.5 1 1.5 Current(mA) Time(ms) LED1(G) On Mean (3.05 mA) 0.5 1 1.5 2 4 6 8 10 12 14 16 18 Time(ms) All LEDs On Mean (6.30 mA)

0.7 0.8 0.9 1 60 120 180 240 300 fraction of naive energy forced delay (s) 120 240 360 480 600 prediction window (s)

• ptimal

first widest

Credit: Prabal Dutta (bottom)

Saturday, January 7, 12

Watch out for grayscale

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 throughput (Mbit/s) signal

• 50
• 60
• 70
• 80
• 90
• 100
• 110
• 120

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 signal

• 50
• 60
• 70
• 80
• 90
• 100
• 110
• 120

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Captions

• Hypothesis or conclusion from the figure
• Description the experiment
• Description of the data points
• Point out interesting ones
• Give statistics
• Explain outliers

Saturday, January 7, 12

Credit: Lawrence Brakmo

Saturday, January 7, 12

Saturday, January 7, 12

preemption Packet wireless card device driver device driver wireless card interrupt Ignored buffer full Socket packets dropped Redundant kernel app Access Point Monitor Out−of−range Interference

...

Causes timing delays Causes missed packets

Saturday, January 7, 12

Demo

Saturday, January 7, 12

Graphing tools

• Gnuplot - does everything, horrible defaults
• matplotlib - python
• Matlab, R - statistics, not flexible?
• Jgraph - nice defaults, obscure
• Excel - simple, horrible defaults, plot and data

are one, not easy to script

Saturday, January 7, 12

Why make a table

• If you only have a few data points
• If the interesting data is obvious
• If you want to present a visual comparison

Saturday, January 7, 12

Tables

No extra bits Maintain Compatible Incremental Partial Packet Technique Protocol for correct packets link latency with 802.11 deployment Recovery Maranello X X X X X Checksum Seda [6] N/A X X FRJ [11] X X FEC ZipTx [14] X X PHY layer PPR [12] X X N/A X hints SOFT [27] X X N/A MRD [20] X X X Diversity SPaC [4] X N/A N/A X PRO [16] X X X X Table 1: Desired behavior and functionality of wireless error recovery protocols

Parameter Value Hardware iPhone 3GS [1] Software SignalScope Pro [2] Function Signal Generator Output Headphones Type Tone Frequency 20 Hz to 24 kHz (5 kHz nom) Amplitude 0.00 dB Pan 0.000% Volume Maximum Table 1: Experiment parameters for determining the available power from the iPhone 3GS headset port.

Saturday, January 7, 12

Deadlines & camera ready

• Easiest to edit smallest to distribute
• Script + data files EPS,PS PDF
• You will have to make changes after submission
• PDF Embedded fonts

Saturday, January 7, 12