design of experiments for germination of vigna radiata

Design of experiments for germination of vigna radiata徐任飞，金雯，马莹，包璐璐，余贞富

Agenda

• Introduction• Design of experiment• Data analysis• Data analysis after data transformation• Conclusion• Q&A

INTRODUCTION

Background and Objective

• Temperature• Humidity• Air• Moisture• Light condition• Germinating bed• Soak time• Solution strength for soak

Literature ReviewTitle Author Conclusion

三种豆科植物种子荫发特性的研究

廖建良，贺握权，许灿英，尹艳

Temperature: 15 to 20 centigradeIllumination: darkGerminating bed: on or between paper

绿豆的浸泡工艺及其对绿豆种子萌发的影响研究

吴小勇，曾庆孝，田金河，柳明鲜 Soak time: 6 to 10 days

盐胁迫对绿豆种子萌发的影响

张秀玲Solution strength for soak: neutral salt has no effect on germination, while has effect on growing of sprout. Basic salt has effect on both the two.

DESIGN OF EXPERIMENT

Design methodology

• Response variable– Germination percentage

– Where n is the number of germinated seeds– N is the total number

– Germination rate

– Where Dt is the number of days from growing– Gt is the number of seeds germinated at that day

Design methodology

• Input variable

Variable Control level

Low （ -1） High （ 1）Light condition No sunlight

Night and day

alternate

Seed soaking time 1 day 5 day

Culture medium Above napkin Soil surface

Seed soaking solution

400mmol/L NaCl Water

Design methodology

• Noise – Quality of the air

• The same experiment location and time – Quality of the seeds

• The same lot– Temperature

• The same experiment location and time

Design of the experiment

• The 24-1 fractional factorial design– Alias structure– Resolution IV design

Defining relation: I=ABCD[A]->A+BCD

[B]->B+ACD

[C]->D+ABD

[D]->C+ABC

[AB]->AB+CD

[AC]->AC+BD

[AD]->AD+BC

Design of the experiment

• Design matrix

Run

Basic designSeed

soaking solution

（ D=ABC）

Light

condition

（ A）

Seed

soaking time

（ B）

Culture

medium

（ C）1 -1 -1 -1 -1

2 1 -1 -1 1

3 -1 1 -1 1

4 1 1 -1 -1

5 -1 -1 1 1

6 1 -1 1 -1

7 -1 1 1 -1

8 1 1 1 1

Experiment implementation

– 8 groups with 30 Vigna radiatas each– Soak the vigna radiatas which need 5 days

soaking on the May, 22 at 23:20– Soak the vigna radiatas which need 1 days

soaking on the May, 26 at 23:20– Plant all of them on the May, 27 at 23:20– Water 2 or 3 times per day to keep culture

medium humid– Check the germination condition at 23:20

each day and record the data– Calculate the germination rate and

percentage

DATA ANALYSIS

Main effects

1-1

100

90

80

701-1

1-1

100

90

80

701-1

光照条件

平均值

浸种时间

培养基类别浸种溶液

发芽率主效应图数据平均值

Main effects

1-1

25

20

15

101-1

1-1

25

20

15

101-1

光照条件

平均值

浸种时间

培养基类别浸种溶液

发芽速率主效应图数据平均值

Interactions

1-1 1-1100

80

60100

80

60100

80

60

1-1

100

80

601-1

光照条件

浸种时间

培养基类别

浸种溶液

-11

条件光照

-11

时间浸种

-11

类别培养基

-11

溶液浸种

发芽率交互作用图数据平均值

1-1 1-1

24

16

824

16

824

16

8

1-1

24

16

81-1

光照条件

浸种时间

培养基类别

浸种溶液

-11

条件光照

-11

时间浸种

-11

类别培养基

-11

溶液浸种

发芽速率交互作用图数据平均值

Factor effects estimation

3020100- 10- 20- 30

99

9590

80706050403020

105

1

效应

百分比

A 光照条件B 浸种时间C 培养基类别D 浸种溶液

因子名称

不显著显著

效应类型

效应的正态图 Al pha = . 05)（响应为发芽率，

Lenth PSE = 11. 2463的

302520151050

98

95

908580

706050403020100

绝对效应

百分比


因子名称

不显著显著

效应类型

效应的半正态图 Al pha = . 05)（响应为发芽率，

Lenth PSE = 11. 2463的AB

B

C

AC

D

AD

A

403020100

项

效应

42. 33A 光照条件B 浸种时间C 培养基类别D 浸种溶液

因子名称

Pareto 效应的图 Al pha = . 05)（响应为发芽率，


Statistical testing

Model refinement

3210- 1- 2- 3- 4

99

9590

80706050403020

105

1

标准化效应

百分比

不显著显著

效应类型

光照条件

标准化效应的正态图 Al pha = . 05)（响应为发芽率，

543210

1. 0E+02

99. 98

9895

8580

50

200

绝对标准化效应

百分比

不显著显著

效应类型

光照条件

标准化效应的半正态图 Al pha = . 05)（响应为发芽率，

光照条件

43210

项

标准化效应

2. 447

Pareto 标准化效应的图 Al pha = . 05)（响应为发芽率，

Statistical testing

发芽率 =83.75-14.58*光照条件

Residual analysis

20100-10-20

99

90

50

10

1

残差

百分比

100908070

20

10

0

-10

拟合值

残差

20151050-5-10

4. 8

3. 6

2. 4

1. 2

0. 0

残差

频率

87654321

20

10

0

-10

观测值顺序

残差

正态概率图与拟合值

直方图与顺序

发芽率残差图


50- 5- 10- 15

99

9590

80706050403020

105

1

效应

百分比


因子名称

不显著显著

效应类型

A

效应的正态图 Al pha = . 05)（响应为发芽速率，


14121086420

98

95

908580

706050403020100

绝对效应

百分比


因子名称

不显著显著

效应类型

A

效应的半正态图 Al pha = . 05)（响应为发芽速率，

Lenth PSE = 1. 72125的AC

AB

C

D

AD

B

A

14121086420

项

效应

6. 48A 光照条件B 浸种时间C 培养基类别D 浸种溶液

因子名称

Pareto 效应的图 Al pha = . 05)（响应为发芽速率，


Statistical testing

Model refinement

420- 2- 4- 6- 8- 10- 12

99

9590

80706050403020

105

1

标准化效应

百分比

不显著显著

效应类型

浸种时间

光照条件

标准化效应的正态图 Al pha = . 05)（响应为发芽速率，

121086420

1. 0E+02

99. 98

9895

8580

50

200

绝对标准化效应

百分比

不显著显著

效应类型

浸种时间

光照条件

标准化效应的半正态图 Al pha = . 05)（响应为发芽速率，

浸种时间

光照条件

121086420

项

标准化效应

2. 57

Pareto 标准化效应的图 Al pha = . 05)（响应为发芽速率，

Statistical testing

发芽速率 =17.081-6.416*光照条件 -2.189*浸种时间

Residual analysis

3. 01. 50. 0-1. 5-3. 0

99

90

50

10

1

残差

百分比

25201510

1

0

-1

-2

拟合值

残差

10-1-2

3

2

1

0

残差

频率

87654321

1

0

-1

-2

观测值顺序

残差

正态概率图与拟合值

直方图与顺序

发芽速率残差图

The response surface(GP)

• Soaking time has no significant effect and darkness can maximize GP

• No interaction

The response surface(GR)

• One day soaking and darkness can maximize GR

• No interaction

Response optimization

DATA ANALYSIS AFTER DATA TRANSFORMATION

Data Transformation

• Data transformation– Bounded response variable ->

unbounded

Main effects

Interactions

Model refinement

Statistical testing

发芽率 (变换 )=3.608-2.681*光照条件 -1.614*浸种时间 +1.307*光照条件 *浸种时间

Residual analysis

Model refinement

Statistical testing

发芽速率 =17.081-6.416*光照条件 -2.189*浸种时间

Residual analysis

The response surface(transformed GP)

• One day soaking and darkness can maximize GP• Interaction effect between soaking time and light

condition.

Response optimization

Conclusion

• Light condition and seed soaking time affect germination percentage and germination rate significantly, while culture medium and seed soaking solution do not have great influence on GP and GR.

• Darkness and one day soaking time promote germination separately. Interaction effect between soaking time and light condition affects germination percentage.

• The best solution is no sunlight and one day soaking time for both maximal GP and GR.

design of experiments for germination of vigna radiata

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