Split Plot Design(ppt).ppt

split plot design

1. Split Plot Design
Infactorialexperimentscertainfactorsmayrequirelargerplots
thanforothers.Fore.g.,experimentsonirrigation,tillageetc
requirelargerareas.
Ontheotherhandexperimentsonfertilizers,weedicidesetc.,may
notrequirelargerarea.
Toaccommodatefactorswhichrequiredifferentsizesof
experimentalplotsinthesameexperimentsplit-plotdesignhas
beenevolved.

2. Inthisdesignlargerplotsaretakenforthefactorwhichrequires
largerplots.
Eachofthelargerplotsissplitintosmallerplots.To
accommodatetheotherfactors.Thedifferenttreatments
areallottedatrandomtotheirrespectiveplots.Such
arrangementiscalledsplit-plotdesign.
Factor–A–largerarea–3levels
Factor–B–smallerarea–3levels

3. Example 1:
a
1 a
0 a
2
a
1b
1 a
0b
0 a
2b
1
a
1b
2 a
0b
1 a
2b
0
a
1b
0 a
0b
2 a
2b
2
a
1b
1a
2b
0a
0b
0
a
1b
0a
2b
1a
0b
1

4. InsplitplotdesignthelargerplotsarecalledMainplots.Smaller
plotswithineachofthislargerplotarecalledassubplots.
ThefactorlevelsallottedtotheMainplotsormainplot
treatmentsandthefactorlevelsallottedtothesubplotsare
calledassubplottreatments.
Advantages:
Thisdesignprovidesincreasedprecisionintheestimatesof
subplottreatmentsandinteractioneffectcomparedtoFRBD
with2factors.
Thisdesignhelpsinsavinginexperimentalmaterial.Inmany
casesitwouldbeenoughtohavewiderbordersbetweenmain
plotsonly.Thisresultsinthesavingofexperimentalareaand
resourcesdevotedtotheprovisionofborderrows.

5. Disadvantages
Themajordisadvantageofsplitplotdesignisthattheeffects
ofmainplottreatmentsareestimatedwithlessprecisionthan
theyareinfactorialRBD.
Theanalysisbecomesmorecomplexwhenmissingdata
occurs.
Thedifferenceintheprecisionoftheestimatesofmainplot
treatment&subplottreatmentisduetothesizesofmainplots
&subplots.Sincethemainplotsarelargerinsizethanthe
subplot,theheterogeneitywillbemorewithinmainplotthan
withinsubplot.

6. Hencetheexperimentalerrorformainplotwillbemorethanthat
forsubplottreatments.Splitplotshouldthereforeweusedonly
aftercarefulconsiderationoftherelativeimportanceofthe
factorstobeexamine.Itshouldnotbeusedwhenallthe
factorsaretobecomparedwithequalprecision.
Layoutandanalysis:
First,themainplottreatmentandsubplottreatmentare
decidedbasedontherequiredprecision.
Thefactorforwhichgreaterprecisionisrequiredisassigned
tosubplots.Thereplicationisthendividedintonumberof
mainplotsequaltomainplottreatments.

7. Eachmainplotisdividedintosubplotdependingonthenumber
ofsubplottreatments.Themainplottreatmentsareallottedat
randomtothemainplotsasinthecaseofRBD.
Withineachmainplotthesubplottreatmentsareallocatedatrandomas
inthecaseofRBD.Thesameprocedureisfollowedforallthe
replications.
RepI RepII RepIII
a
3a
1a
2
b
2b
3b
1
b
3b
2b
1
b
1b
2b
3

8. ANOVA Model:
Y
ij=µ+r
i+t
j+e
ij----------RBD
Y
ijk=µ+r
i+A
j+b
k
+AB
jk+e
ijk---------FRBD(twofactors)
Splitplotdesign
Y
ijk=µ+r
i+M
j+e(a)
ij+S
k+MS
jk+e(b)
ijk

9. Sources df SS Mss F
Rep r-1 Rss RmsRms/ E(a)ms
Main plot m-1 Mss Mms Mms/ E(a) ms
Error (a) (r-1) (m-1) E(a)ssE(a)ms
Subplot s-1 Sss Sms Sms/ E(b)ms
Main X Sub (m-1) (s-1) M x Sss M x Sms M x Sms/ E (b) ms
Error (b) m(r-1) (s-1) E(b)ss E(b)ms
Total rms-1 Tss
Note: Error (b) df = Total df -all df