field work latin square
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Field Work and Latin Square Design
Chapter 12 - Factorial Designs (covered by ason!" #nteractive e$$ects bet%een &ultiple independent variables
Chapter 1' - Field esearch
" )uasi-*+peri&ental Designs" ,rogra& *valuation" Surveys
Latin Square Design
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)uasi-*+peri&ental Designs
*+peri&ental design in natural environ&ent
Nonequivalent control-group design
%o natural groups. &easure pre and post treat&ent/placebo
Interrupted time-series designsWithin-group. &easure/treat over ti&e
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,rogra& *valuation esearch
*valuating progra&s like 0ead Start
*thical issues
ando&ied control-group designsWaitlist control group treat&ent a$ter serving as control
3onequivalent control-group design
Single group. ti&e-series designs
,retest-,osttest design %eak
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SurveysTypes:Status survey.Survey research
Instrumentsde$ine. pretest and re$ine
Questionnarie(phoneintervie% schedule!
De&ographic questions ($actual. veri$iable!Content ite&s (opinion. attitude. kno%ledge. behavior!
Sampling3onprobable unplanned,robable rando&. strati$iedCon$idence interval i&proved %ith heterogeneous
Cross sectional design
Longitudinal/panel design
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Sequence Effects4*+periences %ith earlier conditions
e$$ect responses to later conditions4,ositive and negative practice e$$ects5Carryover e$$ect5
Example*ach sub6ect plays/interprets 7 &ini-ga&es 489CD*45#nterpretation o$ * systematically confoundedby all havinge+perienced 89CD5
Within-Su!ects design*ach sub6ect given each e+peri&ental condition5Controls individual di$$erences5
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Counterbalancing
Controls sequence e$$ect by &odi$ying order that sub6ects arepresented %ith conditions5
"omplete "ounteralancing8ll possible sequences are tested an equal nu&ber o$ ti&es5
#atin SquareControls sequence e$$ect %ith $e%er sub6ects
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Latin Square Design
Sequence 1 Sequence 2 Sequence ' Sequence ;
,layer 1 8 9 C D
,layer 2 9 C D 8
,layer ' C D 8 9
,layer ; D 8 9 C
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Latin Square Designs
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Latin Square Designs
Selected Latin Squares
3 x 3 4 x 4A B C A B C DA B C DA B C DA B C D
B C A B A D CB C D AB D A CB A D C
C A B C D B AC D A BC A D BC D A B
D C A BD A B CD C B AD C B A
5 x 5 6 x 6
A B C D E A B C D E F
B A E C D B F D C A E
C D A E B C D E F B A
D E B A C D A F E C B
E C D B A E C A B F D
F E B A D C
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Definition
A Latin square is a square array of objects (letters A, B, C,! suc" t"at eac" object a##ears once and only once ineac" ro$ and eac" colu%n& E'a%#le ) ' ) Latin Square&
A B C DB C D A
C D A B
D A B C
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*n a Latin square +ou "ae t"ree factors-
.reat%ents (t! (letters A, B, C, !
/o$s (t! Colu%ns (t!
."e nu%ber of treat%ents 0 t"e nu%ber of ro$s 0 t"enu%ber of colu%s 0t&
."e ro$colu%n treat%ents are re#resented by cells in a t'tarray&
."e treat%ents are assigned to ro$colu%n co%binationsusing a Latinsquare arrange%ent
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Example
A courier co%#any is interested in decidingbet$een fie brands (D,1,F,C and /! of car for its
ne't #urc"ase of fleet cars&
."e brands are all co%#arable in #urc"ase #rice& ."e co%#any $ants to carry out a study t"at $ill enable
t"e% to co%#are t"e brands $it" res#ect to o#eratingcosts&
For t"is #ur#ose t"ey select fie driers (/o$s!& *n addition t"e study $ill be carried out oer a fie $ee2
#eriod (Colu%ns 0 $ee2s!&
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Eac" $ee2 a drier is assigned to a car usingrando%i3ation and a Latin Square Design&
."e aerage cost #er %ile is recorded at t"e end of eac"
$ee2 and is tabulated belo$-
4ee2
1 2 3 4 5
5 6&78 9&:: ;&9;
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The Model for a Latin Experiment
( ) ( )kijjikkijy ++++=
i0 5,:,, t j0 5,:,, t
yij(k)
0 t"e obseration in it"ro$ and t"ejt"colu%n
receiing t"e kt"treat%ent
0 oerall %ean
k0 t"e effect of t"e it"treat%ent
i0 t"e effect of t"e it"ro$
ij(k)0 rando% error
k0 5,:,, t
j0 t"e effect of t"ejt"colu%n
>o interaction
bet$een ro$s,
colu%ns and
treat%ents
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ALatin Squaree'#eri%ent is assu%ed to be a three
factor e'#eri%ent&
."e factors are rows, columnsand treatments&
*t is assu%ed t"at t"ere is no interactionbet$een ro$s,
colu%ns and treat%ents&
."e degrees of freedo% for t"e interactions is used to
esti%ate error&
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The Anova Tale for a Latin Square Experiment
Source S&S& d&f& ?&S& F #alue
.reat SS.r t5 ?S.r ?S.r @?SE
/o$s SS/o$ t5 ?S/o$ ?S/o$ @?SE
Cols SSCol t5 ?SCol ?SCol @?SE
Error SSE (t5!(t:! ?SE
.otal SS. t: 5
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The Anova Tale for Example
Source S&S& d&f& ?&S& F #alue
4ee2 65&5;77; ) 5:&;
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sing S1SS for a Latin Square e'#eri%ent
!o"s #ols Trts Y
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Select
Anal$%e&'(eneral Linear Model&')nivariate
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Select t"e de#endent ariable and
t"e t"ree factors /o$s, Cols, .reats
Select Model
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*dentify a %odel t"at "as only %ain effects
for /o$s, Cols, .reats
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Tests of $et%een-Su!ec ts Effects
Dependent =ariable C>S-
1?157'@a 12 175?A1 2@5@2B 5@@@212@5@7@ 1 212@5@7@ 2AA@52' 5@@@
A?5;; ; 15'A2 215BA 5@@@
7151? ; 125?7 1A5@77 5@@@
@5?@; ; 152A 2252;' 5@@@
?57A' 12 5?
2'2151;' 27
2@15@?' 2;
Source
Corrected
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