CPE 619 The Art of Data Presentation Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama in Huntsville http://www.ece.uah.edu/~milenka http://www.ece.uah.edu/~lacasa

Overview Types of Variables Guidelines for Preparing Good Charts Common Mistakes in Preparing Charts Pictorial Games Special Charts for Computer Performance Gantt Charts Kiviat Graphs Schumacher Charts Decision Maker’s Games

Types of Variables Type of computer: Super computer, minicomputer, microcomputer Type of Workload: Scientific, engineering, educational Number of processors Response time of system

Guidelines for Preparing Good Charts 1) Require minimum effort from the reader Direct labeling vs. legend box 2) Maximize Information Words in place of symbols; cleary label the axes

Guidelines (cont’d) 3) Minimize ink 4) Use commonly accepted practices No grid lines, more details 4) Use commonly accepted practices origin at (0,0); independent variable (cause) along x axis; the dependent variable (effect) along the y axis; linear scales; increasing scales; equal divisions 5) Avoid ambiguity Show coordinate axes, scale divisions, origin; Identify individual curves and bars

Checklist for Good Graphics Are both coordinate axes shown and labeled? Are the axes labels self-explanatory and concise? Are the scales and divisions shown on both axes? Are the minimum and maximum of the ranges shown on the axes appropriate to present maximum information Is the number of curves reasonably small? Do all graphs use the same scale? Is there no curve that can be removed without reducing information? Are the curves on a line chart individually labeled? Are the cells in a bar chart individually labeled? Are all symbols on the graph accompanied by appropriate textural explanations? If the curves cross, are the line patterns different to avoid confusion? Are the units of measurement indicated? Is the horizontal scale increasing from left to right? Is the vertical scale increasing from bottom to top? Are the grid lines aiding in reading the curves? Does this whole chart add to information available to the reader? Are the scales contiguous? Is the order of bars in a bar chart systematic? If the vertical axis represents a random quantity, are confidence intervals shown? Are there no curves, symbols, or texts on the graph that can be removed without affecting the information? Is there a title for the whole chart? Is the chart title self-explanatory and concise? For bar charts with unequal class interval, is the are and width representative of the frequency and interval? Do the variable plotted on this cart give more information that other alternatives? Does the chart clearly bring out the intended message? Is the figure referenced and discussed in the text of the report?

Common Mistakes in Preparing Charts Presenting too many alternatives on a single chart Max 5 to 7 messages => Max 6 curves in a line charts, no more than 10 bars in a bar chart, max 8 components in a pie chart Presenting many y variables on a single chart

Common Mistakes in Charts (cont’d) Using symbols in place of text Placing extraneous information on the chart E.g., grid lines, granularity of the grid lines Selecting scale ranges improperly Automatic selection by programs may not be appropriate

Common Mistakes in Charts (cont’d) Using a line chart in place of column chart line => continuity MIPS 8000 8100 8200 8300 CPU Type

Pictorial Games Using non-zero origins to emphasize the difference Three quarter high-rule => height/width > 3/4 Mine is much better than yours (emphasize difference) Mine and yours are almost the same (conceal difference) Height of the highest point should be at least ¾ of the horizontal offset of the rightmost point

Pictorial Games (cont’d) Using double-whammy graph for dramatization Using related metrics

Pictorial Games (cont’d) Plotting random quantities without showing confidence intervals Means of two random variables Means are not enough. Overlapping confidence intervals usually means that the two random quantities are statistically indifferent.

Pictorial Games (cont’d) Pictograms scaled by height Wrong scaling: Area(MINE) > 4*Area(YOURS)?? Mine Performance = 2 Yours Performance = 1

Pictorial Games (cont’d) Using inappropriate cell size in histograms Normal distribution Exponential distribution 12 12 10 10 8 8 Frequency Frequency 6 6 4 4 2 2 [0,2) [2,4) [4,6) [6,8) [8,10) [10,12) [0,6) [6,12) Response Time Response Time

Pictorial Games (cont’d) Using broken scales in column charts Amplify differences 12 12 10 11 8 Resp. Time Resp. Time 10 6 4 9 2 A B C D E F A B C D E F System System

Special Charts for Computer Performance Gantt charts Kiviat Graphs Schumacher's charts

Gantt Charts Shows relative duration of a number of conditions 60 CPU 20 20 IO Channel 30 10 5 15 Network 0% 20% 40% 60% 80% 100% Utilization

Example: Data for Gantt Chart

Draft of the Gantt Chart

Final Gantt Chart

CPU in Supervisor State Kiviat Graphs Radial chart with even number of metrics HB and LB metrics alternate Ideal shape: star CPU Busy CPU in Supervisor State CPU in Problem State CPU Wait Any Channel Busy Channel only Busy CPU/Channel Overlap CPU Only Busy

Kiviat Graph for a Balanced System CPU Busy CPU in Supervisor State CPU in Problem State CPU Wait Any Channel Busy Channel only Busy CPU/Channel Overlap CPU Only Busy Problem: Inter-related metrics CPU busy = problem state + Supervisor state CPU wait = 100 – CPU busy Channel only – any channel –CPU/channel overlap CPU only = CPU busy – CPU/channel overlap

Shapes of Kiviat Graphs CPU Keel boat I/O Wedge I/O Arrow CPU bound system I/O bound system CPU- and I/O bound system

Merrill’s Figure of Merit (FoM) Performance = {x1, x2, x3, …, x2n} Odd values are HB and even values are LB x2n+1 is the same as x1 Average FOM = 50%

Example: FoM System A:

FoM Example (Cont) System B: System B has a higher figure of merit and it is better.

Figure of Merit: Known Problems All axes are considered equal Extreme values are assumed to be better Utility is not a linear function of FoM Two systems with the same FoM are not equally good System with slightly lower FoM may be better

Kiviat Graphs For Other Systems Use Kiviat graphs for networks Application Throughput Link Overhead Packets With Error Link Utilization Implicit Acknowledgements Duplicate Packets

Schumacher Charts Performance matrix are plotted in a tabular manner Values are normalized with respect to long term means and standard deviations Any observations that are beyond mean  one standard deviation need to be explained See Figure 10.25 in the book

Performance Analysis Rat Holes Workload Metrics Configuration Details

Reasons for not Accepting an Analysis This needs more analysis. You need a better understanding of the workload. It improves performance only for long IOs/packets/jobs/files, and most of the IOs/packets/jobs/files are short. It improves performance only for short IOs/packets/jobs/files, but who cares for the performance of short IOs/packets/jobs/files, its the long ones that impact the system. It needs too much memory/CPU/bandwidth and memory/CPU/bandwidth isn't free. It only saves us memory/CPU/bandwidth and memory/CPU/bandwidth is cheap. See Box 10.2 on page 162 of the book for a complete list

Examples

Summary Qualitative/quantitative, ordered/unordered, discrete/continuous variables Good charts should require minimum effort from the reader and provide maximum information with minimum ink Use no more than 5-6 curves, select ranges properly, Three-quarter high rule Gantt Charts show utilizations of various components Kiviat Graphs show HB and LB metrics alternatively on a circular graph Schumacher Charts show mean and standard deviations Workload, metrics, configuration, and details can always be challenged. Should be carefully selected.

Exercise 10.1 What type of chart (line or bar) would you use to plot: CPU usage for 12 months of the year CPU usage as a function of time in months Number of I/O's to three disk drives: A, B, and C Number of I/O's as a function of number of disk drives in a system

Exercise 10.2 List the problems with the following charts

Exercise 10.3 On a system consisting of 3 resources, called A, B, and C. The measured utilizations are shown in the following table. A zero in a column indicates that the resource is not utilized. Draw a Gantt chart showing utilization profiles.

Exercise 10.4 The measured values of the eight performance metrics listed in Example 10.2 for a system are: 70%, 10%, 60%, 20%, 80%, 30%, 50%, and 20%. Draw the Kiviat graph and compute its figure of merit.

Exercise 10.5 For a computer system of your choice, list a number of HB and LB metrics and draw a typical Kiviat graph using data values of your choice.

Ratio Games

Overview Ratio Game Examples Using an Appropriate Ratio Metric Using Relative Performance Enhancement Ratio Games with Percentages Ratio Games Guidelines Numerical Conditions for Ratio Games

Case Study 11.1: 6502 vs. 8080 1. Ratio of Totals Conclusion: 6502 is worse. It takes 4.7% more time than 8080.

6502 vs. 8080 (Cont) 3. 8080 as the base: 2. 6502 as the base: Ratio of Totals: 6502 is worse. It takes 4.7% more time than 8080. With 6502 as a base: 6502 is better. It takes 1% less time than 8080. With 8080 as a base: 6502 is worse. It takes 6% more time.

Case Study 11.2: RISC vs. CISC Conclusion: RISC-I has the largest code size. The second processor Z8002 requires 9% less code than RISC-I.

RISC vs. CISC (Cont) 11.00 13.00 8.50 10.50 8.00 Conclusion: Z8002 has the largest code size and that it takes 18% more code than RISC-I. [Peterson and Sequin 1982]

Using an Appropriate Ratio Metric Example: Throughput: A is better Response Time: A is worse Power: A is better

Using Relative Performance Enhancement Example: Two floating point accelerators Problem: Incomparable bases. Need to try both on the same machine

Ratio Games with Percentages Example: Tests on two systems 1. System B is better on both systems 2. System A is better overall. System A: System B:

Percentages (Cont) Other Misuses of Percentages: 1000% sounds more impressive than 11-time. Particularly if the performance before and after the improvement are both small Small sample sizes disguised in percentages Base = Initial. 400% reduction in prices  Base = Final

Ratio Games Guidelines If one system is better on all benchmarks, contradicting conclusions can not be drawn by any ratio game technique

Guidelines (cont) Even if one system is better than the other on all benchmarks, a better relative performance can be shown by selecting appropriate base. In the previous example, System A is 40% better than System B using raw data, 43% better using system A as a base, and 42% better using System B as a base. If a system is better on some benchmarks and worse on others, contracting conclusions can be drawn in some cases. Not in all cases. If the performance metric is an LB metric, it is better to use your system as the base If the performance metric is an HB metric, it is better to use your opponent as the base Those benchmarks that perform better on your system should be elongated and those that perform worse should be shortened

Numerical Conditions for Ratio Games Raw Data A is better than B iff With A as the Base A is better than B iff

Numerical Conditions (Cont) With B as the base A is better than B iff

Numerical Conditions (Cont) 2 B is better using all 3 Ratio of B/A response on benchmark j 1 A is better using all 3 Base B Raw Data Base A 1 1 1 2 3 Ratio of B/A response on benchmark i

Summary Ratio games arise from use of incomparable bases Ratios may be part of the metric Relative performance enhancements Percentages are ratios For HB metrics, it is better to use opponent as the base

Exercise 11.1 The following table shows execution times of three benchmarks I, J, and K on three systems A, B, and C. Use ratio game techniques to show the superiority of various systems.

Exercise 11.2 Derive conditions necessary for you to be able to use the technique of combined percentages to your advantage.

Homework Read chapter 10&11