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Study the effects of number characteristics

on human responseGroup 10

ZhaoxuemingSundaJiangYiqingWangBingZhangBingfeng

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

responsevariable(units)

normaloperating level

& range

meas. precision,accuracy

How known?

relationship ofresponse variable

toobjective

Reaction time <5s

use timer in the java, accuracy up to ms

The shorter, the better response

Accuracy rate 80% to 100%

Accuracy= right numbers/ total numbers

The higher, the better response

Control variable

control variable (units)

Normal level & range

meas. precision & setting error How known?

proposed settings, based on predicted

effects Size

continuous

close to 0

15, 25, 35

Color

The color that java can set

We can use RGB:R ： 0-255

G ： 0-255B: 0-255

Red, yellow, black, blue

Orientation

Horizontal \ vertical Binary: Horizontal \ vertical

Horizontal \ vertical

Font The font that java can set

any font that java can set

Times New Roman/ calibri

“Held constant" variables

Held constant factor (units)

desired experimental

level & allowable range

how to control (in experiment)

computer 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

Input style(horizontal row orJ,k,l,u,i,o,7,8,9,m)

Horizontal row

Horizontal row

Nuisance factor

nuisance factor (units)

strategy (e.g.,randomization,blocking, etc.)

预期效果

anticipated effects

Environment Running the experiment at an quiet environment with proper temperature and light conditions

Slight

IQ blocking Could be large

Absent number randomized Slight

moods can’t run the experiment when a person’s mood is very bad

Slight

resting conditions test the environment when a person is energetic

Slight

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A full factorial design 22

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 0.9375JiangYiQing 3071.313 1

Zhouyujie 3522.146 1

From the descriptive analysis, we can predict that blocking will play an important role in the data analysis.

•Blocking Effects:

Analysis for response time

Residual Plot of response time

There are two response variables : response time and correction ratio First, we do the analysis for the 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.

Interpretation

The purpose of model

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 numbers123489605 123489605

Color of numbers723489605 132468907

Robust Analysis

Inner array color: 4 levels size : 3 levels font : 2 levels arrange style: 2 levels

Outer arrayLost numbers: 10 levels

Total experiment time: 4*3*2*2*10=480

Robust Analysis

Descriptive statistics We have found two brave volunteers! Some compare

0 2 4 6 8 10 120

500

1000

1500

2000

2500

3000

3500

4000

4500

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.

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Thanks!