field work latin square

8/13/2019 Field Work Latin Square

1/23

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


2/23

)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


3/23

,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


4/23

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


5/23

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


6/23

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


7/23

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


8/23

Latin Square Designs


9/23

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


10/23A Latin Square


11/23

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


12/23

*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


13/23

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!&


14/23

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;


15/23

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


16/23

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&


17/23

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


18/23

The Anova Tale for Example

Source S&S& d&f& ?&S& F #alue

4ee2 65&5;77; ) 5:&;


19/23

sing S1SS for a Latin Square e'#eri%ent

!o"s #ols Trts Y


20/23

Select

Anal$%e&'(eneral Linear Model&')nivariate


21/23

Select t"e de#endent ariable and

t"e t"ree factors /o$s, Cols, .reats

Select Model


22/23

*dentify a %odel t"at "as only %ain effects

for /o$s, Cols, .reats


23/23

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

field work latin square

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