Transcript Robust Analysis

LOGO
Study the effects of
number characteristics
on human response
Group 10
Zhaoxueming
Sunda
JiangYiqing
WangBing
ZhangBingfeng
Guinness world record for sudoku(数独):
 Is the completing time totally determined by the IQ or response of
humans?
 Is there any potential unfair factors?
In the three sudoku games, if the color, size or
font of numbers are different, can it influence the
response of people?
At last, we determine our experiment is:
Study the effects of number characteristics
on human response
Related Articles
 2003/6《Nature Neuroscience》 Fisher
number
If the number is 1 or 2, people react quicker to the left box
If the number is 8 or 9, people react quicker to the right box

Human factors in Engineering and Design, seventh edition
In the fourth chapter, it tells about how color,
size, font and layout can influence human’s
visual perception and response.
The color psychology shows that color can affect
the emotion and the brain's reaction of human.
The conceive of our experiment
 We will use java to randomly generate 1 to N,
then remove a number. The order of the
numbers is random.
 The experimenter must write out the absent
number in the shortest time.
So, why do we choose java to do our experiment?
Reasons to use java
 We can accurately record the response time:
use timer in the java
 We can store the data automatically, reducing
the human error of copying data.
 The experiment is expandable.
 It is convenient for experimenters, just pressing
the keyboard is ok.
Fish-bone diagram
Response variable
response
variable
(units)
Reaction time
Accuracy rate
normal
operating level
& range
<5s
80% to 100%
meas. precision,
relationship of
accuracy
response variable
How known?
to
objective
use timer in the
java, accuracy up The shorter, the
to ms
better response
Accuracy=
right numbers/
total numbers
The higher, the
better response
Control variable
control variable
(units)
Size
Color
Orientation
Font
Normal level
& range
continuous
meas. precision
& setting error
How known?
close to 0
The color that java can We can use RGB:
set
R：0-255
G：0-255
B: 0-255
Horizontal \ vertical
Binary:
Horizontal \ vertical
The font that java can any font that java can
set
set
proposed settings,
based on predicted
effects
15, 25, 35
Red, yellow, black,
blue
Horizontal \ vertical
Times New Roman
/ calibri
“Held constant" variables
computer
desired
experimental
level &
allowable range
one computer
use one person’s computer
quantity of numbers
ten
Use 0 to 9
The space between numbers
fixed value
set it as fixed value
Horizontal row
Horizontal row
Held constant factor
(units)
Input style
(horizontal row
or
J,k,l,u,i,o,7,8,9,m)
how to
control (in experiment)
Nuisance factor
nuisance
factor (units)
Environment
IQ
Absent number
moods
resting conditions
strategy (e.g.,
randomization,
blocking, etc.)
Running the experiment at an
quiet environment with proper
temperature and light
conditions
blocking
randomized
预期效果
anticipated effects
Slight
Could be large
Slight
can’t run the experiment when Slight
a person’s mood is very bad
test the environment when a
Slight
person is energetic
LOGO
A 2    full factorial design
2
Descriptive analysis
 Almost all experimenters
can have a correction
ration of 100% or 97.9%.
 There are only one
whose correction ratio is
less than 90%.
Descriptive analysis
• For all the experimenters,
the average response
time is nearly normally
distributed.
• It is mostly distributed
between 3200 and
5600ms.
Descriptive analysis
The fastest three experimenters
实验者
平均时间
正确率
Yanbo
2691.104
0.9375
JiangYiQing
3071.313
1
Zhouyujie
3522.146
1
•Blocking Effects:
From the descriptive analysis, we can predict that blocking will play an important
role in the data analysis.
Analysis for response time
 There are two response variables : response time and correction ratio
 First, we do the analysis for the response time
Residual Plot of response time
Box-Cox transform
Lamda=0:
y  lny
After transformation
The residuals is normally and iid distributed.
Main effects plot for ln(response time)
Interaction plots for ln(response time)
The effect analysis
In our experiment, every experimenter is a block.
The blocking effects is important. If we construct
the linear model, it can just fit the 24
experimenters.
At first, we want to calculate the average value
of the block coefficients and contain it into the
constant. But asking Pro. Wang, we know this is
not scientific.
The purpose of model
Interpretation
Prediction
Analysis for accuracy rate
Box-cox plot
Lamda = 5
y  y^5
Main effects for (accuracy ratio)^5
Interaction effects for (accuracy ratio)^5
Robust Analysis
Why I always meet some
strange lost numbers while
playing Sudoku?
Robust Analysis
Our goal is to find the optimal
combination of different factors, so
that the influence of lost numbers
will be minimized.
 Minimize the reaction time
 Archive higher correctness rate
Robust Analysis
Taguchi Method
 Control factors:
color, size, font, arrange style
 Noise factors:
the lost number
Robust Analysis
The interaction may exist
 Fonts and the lost number
 Size and the lost number
 Color and the lost number
Robust Analysis
Fonts and the lost number
 Can you tell which number is lost?
60541973
Robust Analysis
Size of numbers
123489605
123489605
Color of numbers
723489605
132468907
Robust Analysis
Inner array
color: 4 levels
size : 3 levels
font : 2 levels
arrange style: 2 levels
Outer array
Lost numbers: 10 levels
Total experiment time:
4*3*2*2*10=480
Robust Analysis
Descriptive statistics
 We have found two brave volunteers!
 Some compare
小A
小B
Robust Analysis
Descriptive statistics
 Larger numbers may need more time
 Great differences can be found between
individuals
Robust Analysis
Taguchi Method
 We want to minimize the response
 SN ratio : smaller is better
Robust Analysis
Main Effects Plot for Means(小A)
Robust Analysis
Main Effects Plot for Means(小B)
Robust Analysis
Main Effects Plot for Means
 The most important factor :color
Robust Analysis
Main Effects Plot for SN ratios(小A)
Robust Analysis
Main Effects Plot for SN ratios (小B)
Robust Analysis
SN ratios
 We need to max the SN ratio.
Using Excel, we got some combination quite like that suggested
by the main effects plot.
 Still too few samples : we need more data for
better explanation.
LOGO
Thanks!