© 1998, geoff kuenning vague idea “groping around” experiences hypothesis model initial...

© 1998, Geoff Kuenning

Vague idea

“groping around” experiences

Hypothesis

Model

Initialobservations

Experiment

Data, analysis, interpretation

Results & finalPresentation

Experimental Lifecycle


Common Mistakes in Graphics

• Excess information• Multiple scales• Using symbols in place of text• Poor scales• Using lines incorrectly


Multiple Scales

• Another way to meet length limits• Basically, two graphs overlaid on each other• Confuses reader (which line goes with which

scale?)• Misstates relationships

– Implies equality of magnitude that doesn’t exist

Start here


Some Especially Bad Multiple Scales

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Throughput

Response Time


Using Symbolsin Place of Text

• Graphics should be self-explanatory– Remember that the graphs often draw

the reader in• So use explanatory text, not symbols• This means no Greek letters!

– Unless your conference is in Athens...


It’s All Greek To Me...

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Explanation is Easy

Waiting Time asa Function of Offered Load

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Offered Load

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Poor Scales

• Plotting programs love non-zero origins– But people are used to zero

• Fiddle with axis ranges (and logarithms) to get your message across– But don’t lie or cheat

• Sometimes trimming off high ends makes things clearer– Brings out low-end detail


Nonzero Origins(Chosen by Microsoft)

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Proper Origins

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A Poor Axis Range

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A Logarithmic Range

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A Truncated Range

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Using Lines Incorrectly

• Don’t connect points unless interpolation is meaningful

• Don’t smooth lines that are based on samples– Exception: fitted non-linear curves


Incorrect Line Usage

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Timecp

mab

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Pictorial Games

• Non-zero origins and broken scales• Double-whammy graphs• Omitting confidence intervals• Scaling by height, not area• Poor histogram cell size


Non-Zero Originsand Broken Scales

• People expect (0,0) origins– Subconsciously

• So non-zero origins are a great way to lie• More common than not in popular press• Also very common to cheat by omitting

part of scale– “Really, Your Honor, I included (0,0)”


Non-Zero Origins

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UsThem

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The Three-Quarters Rule

• Highest point should be 3/4 of scale or more

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Double-Whammy Graphs

• Put two related measures on same graph– One is (almost) function of other

• Hits reader twice with same information– And thus overstates impact

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Units Shipped


OmittingConfidence Intervals

• Statistical data is inherently fuzzy• But means appear precise• Giving confidence intervals can make it

clear there’s no real difference– So liars and fools leave them out


Graph WithoutConfidence Intervals

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Graph WithConfidence Intervals

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Confidence Intervals

• Sample mean value is only an estimate of the true population mean

• Bounds c1 and c2 such that there is a high probability, 1-, that the population mean is in the interval (c1,c2):

Prob{ c1 < < c2} =1- where is the significance level and100(1-) is the confidence level

• Overlapping confidence intervals is interpreted as “not statistically different”


Graph WithConfidence Intervals

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Reporting Only One Run(tell-tale sign)

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Probably a fluke(It’s likely that withmultiple trials this would go away)


Scaling by HeightInstead of Area

• Clip art is popular with illustrators:

Women in the Workforce

1960 1980

Any quesses?w1980/w1960 = ?


The Troublewith Height Scaling

• Previous graph had heights of 2:1• But people perceive areas, not heights

– So areas should be what’s proportional to data• Tufte defines a lie factor: size of effect in graphic

divided by size of effect in data– Not limited to area scaling– But especially insidious there (quadratic effect)


Scaling by Area

• Here’s the same graph with 2:1 area:

Women in the Workforce

1960 1980


Histogram Cell Size

• Picking bucket size is always a problem• Prefer 5 or more observations per bucket• Choice of bucket size can affect results:

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Histogram Cell Size


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Histogram Cell Size


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Don’t Quote DataOut of Context

Traffic Deaths andEnforcement of Speed Limits

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After stricterenforcement


The Same Data in Context

Connecticut Traffic Deaths, 1951-1959

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Tell the Whole Truth

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Tell the Whole Truth

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Special-Purpose Charts

• Histograms• Scatter plots• Gantt charts• Kiviat graphs


Tukey’s Box Plot

• Shows range, median, quartiles all in one:

• Variations:

minimum maximumquartile quartilemedian


Histograms

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Scatter Plots

• Useful in statistical analysis• Also excellent for huge quantities of data

– Can show patterns otherwise invisible

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Gantt Charts

• Shows relative duration of Boolean conditions• Arranged to make lines continuous

– Each level after first follows FTTF pattern

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Gantt Charts

• Shows relative duration of Boolean conditions• Arranged to make lines continuous

– Each level after first follows FTTF pattern

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Kiviat Graphs

• Also called “star charts” or “radar plots”• Useful for looking at balance between HB and

LB metricsHB

LB


Useful Reference Works

• Edward R. Tufte, The Visual Display of Quantitative Information, Graphics Press, Cheshire, Connecticut, 1983.

• Edward R. Tufte, Envisioning Information, Graphics Press, Cheshire, Connecticut, 1990.

• Edward R. Tufte, Visual Explanations, Graphics Press, Cheshire, Connecticut, 1997.

• Darrell Huff, How to Lie With Statistics, W.W. Norton & Co., New York, 1954


Ratio Games

• Choosing a Base System• Using Ratio Metrics• Relative Performance Enhancement• Ratio Games with Percentages• Strategies for Winning a Ratio Game• Correct Analysis of Ratios


Choosing a Base System

• Run workloads on two systems• Normalize performance to chosen

system• Take average of ratios• Presto: you control what’s best

Code Size Example

Program RISC-1 Z8002 R/R Z/R

F-bit 120 180 1.0 1.5

Acker 144 302 1.0 2.1

Towers 96 240 1.0 2.5

Puzzle 2796 1398 1.0 0.5

Sum 3156 2120 4.0 6.6

Average 789 530 1.0 1.6 or .67?

Simple Example

Program 1 2 1/2 2/1

A 50 100 0.5 2.0

B 1000 500 2.0 0.5

Sum 1050 600 1.75 0.57


Using Ratio Metrics

• Pick a metric that is itself a ratio– power = throughput response time– cost / performance– improvement ratio

• Handy because division is “hidden”


Relative Performance Enhancement

• Compare systems with incomparable bases• Turn into ratios• Example: compare Ficus 1 vs. 2 replicas with UFS

vs. NFS (1 run on chosen day):

• “Proves” adding Ficus replica costs less than going from UFS to NFS

"cp" Time RatioFicus 1 vs. 2 197.4 246.6 1.25UFS vs. NFS 178.7 238.3 1.33


Ratio Games with Percentages

• Percentages are inherently ratios– But disguised– So great for ratio games

• Example: Passing tests

• A is worse, but looks better in total line!

Test A Runs A Passes A % B Runs B Passes B %1 300 60 20 32 8 252 50 2 4 500 40 8

Total 350 62 18 532 48 9


More on Percentages

• Psychological impact– 1000% sounds bigger than 10-fold (or

11-fold)– Great when both original and final

performance are lousy• E.g., salary went from $40 to $80 per week

• Small sample sizes generate big lies• Base should be initial, not final value

– E.g., price can’t drop 400%

Sequential page placement normalized to random placement for static policies -- SPEC

True Confessions

Power state policies with random placement normalized toall active memory -- SPEC

True Confessions


Strategies for Winninga Ratio Game

• Can you win?• How to win


Can You Winthe Ratio Game?

• If one system is better by all measures, a ratio game won’t work– But recall percent-passes example– And selecting the base lets you change the

magnitude of the difference• If each system wins on some measures, ratio

games might be possible (but no promises)– May have to try all bases


How to WinYour Ratio Game

• For LB metrics, use your system as the base• For HB metrics, use the other as a base• If possible, adjust lengths of benchmarks

– Elongate when your system performs best– Short when your system is worst– This gives greater weight to your strengths

© 1998, geoff kuenning vague idea “groping around” experiences hypothesis model initial...

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