Winter Lawn

8/10/2019 Winter Lawn

1/26

IEE 572

DESIGNOFENGINEERINGEXPERIMENTS

Final Project Report

How to Plant a Successful Winter Lawn

Prepared by:

Gus Barajas,

Chris Birely

Jennifer Smith

Instructor: Dr. D.C. Montgomery

Arizona State University


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Tempe, Arizona

Fall 2000

2


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Problem Statement

For the new homeowner, it is not clear on what the best method of growing a successful winter

lawn is. When entering the local Home Depot, there are many choices of grass seed and fertilizer. Also

the watering plan used on a newly planted winter lawn varies by whom you tal to. A lac of a clear

process maes it difficult for the new homeowner to decide what is necessary to grow a winter lawn

successfully. !hree ma"or factors that are #said$ to be significant in growing a winter lawn include% the

grass seed used, the type of fertilizer used and the watering techni&ue that is applied. An e'periment

will be performed to determine the best combination of these factors to use in the planting a winter lawn

!he e'periment will also be used to determine if any or all of these factors are significant in the success

of the winter lawn.

Choice of Factors, Levels and Range

!he e'periment will be a ( level factorial. )ach factor will be tested at 2 levels. !he e'periment

will be replicated three times giving a total of 2* runs. !he e'perimenters felt that a power of ++.- at

2 standard deviations was sufficient for the e'periment. !he power was calculated by using Design

)'pert /!able 01.

Power at 5 % alpha level for effect of

Term Stdrr!! "#F Ri$S&ared '() Std* +ev* ' Std* +ev* ) Std* +ev*

loc 0 3.23A 3.23 0.33 3.3333 20.0 - (.( - ++. -

3.23 0.33 3.3333 20.0 - (.( - ++. -

A 3.23 0.33 3.3333 20.0 - (.( - ++. -

A4 3.23 0.33 3.3333 20.0 - (.( - ++. -4 3.23 0.33 3.3333 20.0 - (.( - ++. -

A4 3.23 0.33 3.3333 20.0 - (.( - ++. -!!asis Std* +ev* - '*.

Table 1: Power at 5% alpha

)ach run will be a 0$ by 0$ plot of land utilizing a specified combination of factor levels determined by

Design )'pert. .

0


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!he factors include type of fertilizer, type of grass seed and watering techni&ue. For fertilizer

the team will use an average fertilizer /lower cost and nitrogen content1 and higher &uality fertilizer

/higher cost and higher nitrogen content1. !he grass seed will be varied in terms of seed type% annua

rye and perennial rye. !he perennial rye is said to grow a greener and lusher lawn but has a higher cost

Finally, watering techni&ue will consist of 2 different watering schedules. !he first watering techni&ue

will utilize a sprinler for a duration of 2 minutes, (' a day, until germination /503 days1. !hen the

sprinler time will be ad"usted to a duration of 2 minutes, 2' a day for a wee. !he second watering

techni&ue will utilize a sprinler for a duration of minutes, (' a day, until germination /503 days1.

!hen the sprinler time will be ad"usted to a duration of minutes, 2' a day for a wee. !he factors and

levels are summarized in the !able 2.

Factor +escription Levels

!ype of Fertilizer $6cotts 6tarter 23257

/8ltra 9igoro (02*!ype of 6eed $Annual

:;erennialWatering !echni&ue $!echni&ue 0 /less water1

/!echni&ue 2 /more water1Table 2: Factor Summary

6ome of the uncontrollable factors and nuisance variables include climate, elevation differences,

soil differences and nature. 4limate includes rainfall, temperature and sun e'posure. !hese are factors

that are out of control of the e'perimenters.


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same mi'ture or nutrients throughout and that cannot be avoided. Finally, nature is completely

uncontrollable. =ature includes the climate already mentioned, but also bird interference and insect

interaction. ne measurement

will be done at each of the four corners of the plot, one inch diagonally from the corner of the plot. !he

fifth measurement will be done at the geometric center of the plot.

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Choice of 0perimental +esign

>ur e'periment will be designed using a section of one our team member$s lawn. !he plot we

will be using is appro'imately 273 s&uare feet /03 feet by 27 feet1. !he design used is a 2( factorial

design with ( replicates.

Figure 1: Lawn Plot

Table 3: Random assignments of experimental trials

ecause of our plentiful size lawn lot, we are separating each plot into 0$ by 0$ segments. !his will

allow us to cover the seed and fertilizer evenly and we will be able to segregate each of the plots to

avoid mi'ture of seed and fertilizer combinations. !he method of watering will cause the watering

techni&ue factor to be cofounded. !his will cause the plots to be evenly separated by watering

*

Plot 1 (-,+,-) Plot 5 (+,-,-) Plot 9 (+,-,-) Plot 13 (+,-,+) Plot 17 (-,+,+) Plot 21 (-,-,+)

Plot 2 (-,-,-) Plot 6 (+,-,-) Plot 10(-,-,-) Plot 14 (+,+,+) Plot 18 (+,-,+) Plot 22(+,-,+)

Plot 3 (-,-,-) Plot 7 (-,+,-) Plot 11(+,+,-) Plot 15 (-,-,+) Plot 19 (-,+,+) Plot 23(+,+,+)

Plot 4 (+,+,-) Plot 8 (+,+,-) Plot 12 (-,+,-) Plot 16 (+,+,+) Plot 20 (-,+,+) Plot 24 (-,-,+)

Factor 1 Factor 2 Factor 3

Std Run Block !F"rt#l#$"r B!%ra&& '()" *!+at"r#n, Plan

7 1 Block 1 -1 1 -1

2 2 Block 1 -1 -1 -1

3 3 Block 1 -1 -1 -1

10 4 Block 1 1 1 -1

6 5 Block 1 1 -1 -15 6 Block 1 1 -1 -1

8 7 Block 1 -1 1 -1

12 8 Block 1 1 1 -1

4 9 Block 1 1 -1 -1

1 10 Block 1 -1 -1 -1

11 11 Block 1 1 1 -1

9 12 Block 1 -1 1 -1

18 13 Block 2 1 -1 1

23 14 Block 2 1 1 1

15 15 Block 2 -1 -1 1

22 16 Block 2 1 1 1

19 17 Block 2 -1 1 1

16 18 Block 2 1 -1 1

21 19 Block 2 -1 1 1

20 20 Block 2 -1 1 1

14 21 Block 2 -1 -1 1

17 22 Block 2 1 -1 1

24 23 Block 2 1 1 1

13 24 Block 2 -1 -1 1


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techni&ue /Figure 01. !he remaining plot locations will be randomly located with the help of Design

)'pert.

8tilizing our Design )'pert software, we will be able to input our Fertilizer, 6eed, and Water

parameters to determine our )'perimental design. With our e'perimental ob"ective in mind, planting

our winter lawn, we now have an e'perimental procedure to carefully perform our e'periment.

Performing the 0periment

When setting up the e'periment, the team segregated the area into two sections. >ne section

would be used for watering schedule 0 and the second for watering schedule 2. !he soil was tilled and

mi'ed up to prevent inconsistency in the soil mi'ture. !hen, plots of land were sectioned into 0$

s&uares. >nce all the plots were sectioned off, the team systematically laid down the fertilizer and seed

An 0BC cup of fertilizer was used on each plot and spread evenly. !hen 0 cup of seed was used for each

plot and again spread evenly. After laying down the fertilizer and seed, the team covered both with 0

cup of topsoil to prevent the seed from getting washed away or eaten by the birds. )ach section was

watered according to their respective watering schedules. A picture of the e'periment on day zero is

provided in Figure 2.

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Figure 2: Picture of Experiment on Day ero

>ne problem that the team ran into is that the weather did not cooperate with the e'periment.

During the e'periment, there were days when the watering could not be completed due to the soil being

saturated with water from the rainstorms. ucily grass was able to grow and the plots were still in tact

after all the rain. !he rainy days may invalidate any results with respect to the watering response.

!he team too the final measurements one wee after germination. A picture of the e'periment

on the day of the measurement taing is provided on Figure (.

Figure !: Picture of Experiment on Day of "ea#urement Ta$ing


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Five replicates were taen off of each plot for each of the responses. !here was one measurement taen

at 0? from each of the corners and at the center of the plot. !he measurements were taen in the same

order for all samples. !he order of the measurements is in Figure *.

Figure : "ea#urement &r'er

!he average of the five measurements are what we entered into Design )'pert to analyze the results.

Statistical 1nal2sis of the +ata

8sing A=>9A in Design )'pert the significant factors for the density response include /type

of seed1, 4 /watering techni&ue1 and the 4 interaction. !hese were determined using the Half =ormal

;lot shown in Figure 7.

5

1

5

4 3

2


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.S/%-.P.R' Plot"nt R"&on&"

! F"rt#l#$"rB! %ra&& '"*! +at"r#n, Plan

al oral )lot

al

oralroa#l#

t

."ct

000 1478 2957 4435 5913

0

20

40

60

70

80

85

90

95

97

99

B

*

B*

Figure 5: (alf )ormal Plot for the 'en#ity re#pon#e

C


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8pon looing at the =ormal plot of the residuals in Figure , we concluded that it was necessary to

perform a transformation because the plot e'hibited some curvature.

.S/%-.P.R' Plot"nt R"&on&"

Stud"nt#$"d R"dual&

o

ralroa#l#t

oral )lot o r"dual&

-227 -107 013 132 252

1

5

10

20

30

50

70

80

90

95

99

Figure *: )ormal plot of re#i'ual# for 'en#ity re#pon#e with no tran#formation+

+


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We choose to use the natural log transformation. With this transformation, the significant factors include

/type of seed1 and 4 /watering techni&ue1. !he half normal plot is shown in Figure 5.

.S/%-.P.R' Plot

"nt R"&on&"

! F"rt#l#$"r

B! %ra&& '"

*! +at"r#n, Plan

al oral )lot

aloralroa#l#t

."ct

000

036

073

109

145

0

20

40

60

70

80

85

90

95

97

99

B

*

Figure ,: (alf )ormal plot for the tran#forme' 'en#ity re#pon#e+

!he A=>9A show in Figure C confirms that and are significant that 3.37 level of significance.

Response3 Response ' Transform3 4at&ral log Constant3 .

14"1 for Selected Factorial 6odel

1nal2sis of variance table 7Partial s&m of s&ares8

S&m of 6ean FSo&rce S&ares +F S&are "al&e Prob 9 F

Eodel 0*.2( 2 5.02 5C.2+ 3.3330 significant

- 12+* 1 12+* 1!.+11 / 0+0001 1+5. 1 1+5. 1,+, 0+000

Gesidual 0.+0 20 3.3+0

ac$ of Fit 0+2 5 0+035 0+.1 0+.31 not #ignificant

Pure Error 1+. 1* 0+0.!

4or !otal 0.0* 2(

!he Eodel Fvalue of 5C.2+ implies the model is significant. !here is onlya 3.30- chance that a Eodel F9alue this large could occur due to noise.

Figure 3: 4)&4 for the tran#forme' 'en#ity re#pon#e

!he regression e&uation is as follows%

03


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n /density response1 (.73+(+ : 3.527C* @!ype of 6eed : 3.2750+@ Watering ;lan

!he normal probability plot of the residuals indicates that the normality assumption is not violated.


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.S/%-.P.R'"nt R"&on&"

Pr"d#ct"d

Stud"nt#$"dR"dual&

R"dual& & Pr"d#ct"d

-300

-150

000

150

300

253

302

351

400

449

.S/%-.P.R'

"nt R"&on&"

Stud"nt

#$"dR"

R"dual& & Run

000

150

300

02


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.S/%-.P.R'"nt R"&on&"

F"rt#l#$"r

Stud"nt#$"dR"dual&

R"dual& & F"rt#l#$"r

-300

-150

000

150

300

-1

0

1

Figure .: 6e#i'ual plot# for tran#forme' 'en#ity re#pon#e

!he >ne Factor ;lot /Figure 031 indicates that using ;erennial Gye grass at the high level will result in a

higher density of grass as will the higher watering plan.

.S/%-.P.R' Plot

"nt R"&on&"

: B! %ra&& '"

ctual Factor&

! F"rt#l#$"r : 016

*! +at"r#n, Plan : 000

-100

-050

000

050

100

1887

2716

3545

4374

5203

B! %ra&& '"

;n(R"&on&"1)


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!he same sorts of techni&ues were used in analyzing the grass length response. For the grass

length response there was no need to do a transformation. y looing at the Half =ormal ;lot and

confirming with the A=>9A table, the significant factor is /type of seed1 at the 3.37 level of

significance. !he Half =ormal ;lot and the A=>9A table are shown in Figure 00.

.S/%-.P.R'%ra&& ;"n,t= R"&on&"

! F"rt#l#$"r

B! %ra&& '"

*! +at"r#n, Plan

al oral )lot

alor

al)roa#l#t(

."ct

000 025 051 076 101

0

20

40

60

70

80

85

90

95

97

99

B

Response3 Response )



S&m of 6ean F

So&rce S&ares +F S&are "al&e Prob 9 F

Eodel .0C 0 .0C 0*(.+C 3.3330 significant - *+13 1 *+13 1!+.3 0+0001

Gesidual 3.+* 22 3.3*(

ac$ of Fit 0+2 * 0+00 0+3. 0+5221 not #ignificant

Pure Error 0+,1 1* 0+0 4or !otal 5.02 2(

!he Eodel Fvalue of 0*(.+C implies the model is significant. !here is only

a 3.30- chance that a Eodel F9alue this large could occur due to noise.

Figure 11 (alf )ormal Plot an' 4)&4 for gra## length re#pon#e

0*


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!he regression e&uation for calculating grass length is as follows%

Irass enth 0.7CC7* 3.7352+ @ !ype of 6eed

!he residual plots do not show any violation of assumptions. y looing at the >ne Factor ;lot /Figure

021 for the grass length response, the response indicates that the length of grass is higher when using the

Annual Irass seed.

.S/%-.P.R'

%ra&& ;"n,t= R"&on&"

: B! %ra&& '"

ctual Factor&! F"rt#l#$"r : -084

*! +at"r#n, Plan : 100

-100

-050

000

050

100

0875

126875

16625

205625

245

B! %ra&& '()"

R"&)on&"2


18/26

.S/%-.P.R'%r""nn"&& R"&on&"

! F"rt#l#$"r

B! %ra&& '"

*! +at"r#n, Plan

al oral )lot

aloralroa#l#t

."ct

000 012 023 035 047

0

20

40

60

70

80

85

90

95

97

99

B

Response3 Response :



S&m of Eean F

So&rce S&are +F S&are "al&e Prob 9 F

Eodel 0.(0 0 0.(0 5.03 3.30*0 significant- 1+!1 1 1+!1 ,+10 0+011

Gesidual *.37 22 3.0Cac$ of Fit 0+.! * 0+15 0+,. 0+53. not #ignificant

Pure Error !+12 1* 0+1.

4or !otal 7.(7 2(

!he Eodel Fvalue of 5.03 implies the model is significant. !here is only

a 0.*0- chance that a Eodel F9alue this large could occur due to noise.

Figure 1!: (alf )ormal Plot an' 4)&4 for greenne## re#pon#e

!he regression e&uation for the greenness response is as follows%

Ireeness *.*05 : 3.2(((( @ !ype of 6eed

0


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!he residual plots do not show any violation of assumptions. y looing at the >ne Factor ;lot /Figure

0*1 for the grass length response, the response indicates that the level of greeness is higher when using

the ;erennial Irass seed.

.S/%-.P.R'

%r""nn"&& R"&on&"

: B! %ra&& '"

ctual Factor&

! F"rt#l#$"r : -008

*! +at"r#n, Plan : 100

-100 -050 000 050 100

32

365

41

455

5

B! %ra&& '()"

R"&)on&"

3


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grass seed. )ach individual lawn owner would need to decide which he or she prefers% greener more

dense grass or longer grass. 4ommon sense would say that the owner would want a greener and more

dense lawn that doesn$t have to be mowed that fre&uently. However, this type of lawn would be at a

higher cost. y performing this e'periment we were able to conclude that the type of fertilizer does not

affect the density, greenness or length of the grass. For a future lawn e'periment, it would be necessary

to compare the result of a plot with fertilizer against one that did not use fertilizer at all. ut, before

that is completed we at least now it does not matter what type of fertilizer is used. !herefore, a

homeowner can use a lower cost fertilizer. !he watering techni&ue is only important when it comes to

density. !his portion of the e'periment would be interesting to redo because the results may come out

differently when you tae away all the rain that occurred during the middle of the e'periment. !he

rainfall caused the plots to flood that may have moved the seed within the plot.


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+T1#L+ +1T1 S

S&mmar2 0periment Plot

+ata

0+


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Plot 1 # of blades height (in) color Plot 5 # of blades height (in) color

6 0875 4 17 1 3>4 4

70 1 4 9 2 1>2 4

8 1125 4 28 2 1>2 5

40 1375 4 23 1 3>4 5

42 125 4 19 2 5

average 332 1125 4 average 192 21 46


18 2 1>4 5 4 1 3>4 4

9 2 1>2 5 0 0 0

23 2 1>2 5 8 1 3>4 4

7 2 1>4 5 18 2 3>4 5

5 2 4 3 1 1>2 4

average 124 23 48 average 66 155 34


10 2 3 33 1 1>4 4

19 2 3 41 1 1>4 5

7 2 3 39 1 1>4 4

11 2 1>8 4 34 1 1>4 4

22 2 1>2 3 59 1 5

average 138 2125 32 average 412 12 44


41 075 5 44 1 4 23 1 1>4 4 6 0625 4

57 1 1>2 5 53 1 4

61 1 1>2 5 48 1 4

77 1 5 102 0875 5



23


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5 1 7>8 4 9 1 3>4 4

8 2 4 33 2 1>2 5

11 2 4 22 1 1>2 5

25 2 1>4 4 19 2 5

18 1 7>8 4 21 2 5



9 2 4 104 1 1>8 5

17 1 1>4 4 70 3>4 4

33 2 1>2 5 65 1 1>8 4

23 2 4 82 7>8 5

19 1 1>2 5 53 0625 5

average 202 185 44 average 748 09 46

Plot 11 # of blades height (in) color Plot 15 # of blades height (in) color 82 1 4 11 1 1>2 4

35 1 3>8 4 12 2 1>2 4

125 1 5 3 1 7>8 3

47 1 1>4 5 47 2 5

38 1>2 5 16 2 5

average 654 1025 46 average 178 1975 42


61 075 4 39 100 5

83 0875 5 144 7>8 5 60 1 1>4 5 76 1 1>8 5

91 075 4 110 1 1>4 5

28 075 5 87 075 5



136 1 1>4 5 27 2 1>2 4

20


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63 7>8 5 19 2 1>8 4

35 1 5 13 2 1>8 3

69 7>8 5 21 2 1>4 5

78 1 1>4 5 23 2 1>8 5

average 762 105 5 average 206 2225 42


9 1 3>4 4 13 2 1>2 4

14 2 1>4 4 17 2 3>4 4

49 2 3>8 4 24 2 1>2 4

14 2 1>4 4 14 2 4

7 2 1>4 4 13 2 1>2 4

average 186 2175 4 average 162 245 4


197 1 1>2 5 23 0875 4 160 1 1>2 5 98 1 1>4 4

138 1 1>4 5 107 1 1>2 5

205 1 5 89 1 1>4 5

209 1 1>8 5 102 1 3>8 5

average 1818 1275 5 average 838 125 46


65 1 1>4 5 28 2 1>2 5

108 075 5 21 2 1>2 5

94 1 1>4 5 16 2 1>2 4 110 1 1>8 5 43 2 3>4 5

115 1 1>2 5 11 2 4

average 984 1175 5 average 238 245 46

+T1#L+ +1T1 S


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=1ppendi0 >

?reen Response Templates

2(


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Documents

Winter Lawn