Lab K

An exercise in experimental design and implementation

Between-subjects design Within-subjects design- each person in the lab would

be assigned to one of the four ‘treatments’ using random allocation (eg. rolling a fair die and ignoring two of the faces, generating random numbers in minitab and ignoring all but digits 1, 2, 3 and 4, etc.)

- Randomisation is used so that there are no systematic differences between the people allocated to different treatments – i.e. it attempts to control for potential confounding variables

- each person in the lab would be asked to perform the experiment under each of the conditions, i.e. four times

- randomization would be used to assign participants to a particular order of the treatments, thereby counterbalancing the design to minimize the potential order-effects acting as a confounding factor

Between-subjects design Within-subjects designAdvantages and disadvantages+ only requires each participant to do

the experiment once, thereby saving time

+ potential order effects (eg. fatigue, practice, crossover effects) are avoided and do not need to be controlled for in the design

+ the subsequent analysis is straight forward, as there are four independent groups to compare

+ the randomization is relatively straight forward

- would require a larger number of participants to get adequate numbers in each treatment group

Advantages and disadvantages- requires each participant to do the

experiment four times, thereby needing a lot of time

- introduces potential order effects (eg. fatigue, practice, crossover effects) which the design should carefully consider in order to minimize the potential effects (i.e. lag between experiments)

- the subsequent analysis is complex, involving the analysis of repeated measures

+ more powerful to detect treatment differences, since effects of individuals are controlled

+ would require a relatively small number of participants to get reliable results for each treatment level

Suggested design and why

Given our limited numbers in the lab group, we would favour the within-subjects design, notwithstanding the additional work involved in the randomization and the analysis.

To make a Latin square…

1. Create a random order of the levels, (e.g. BACD for a four-level IV)

2. Sequentially number the levels in this random order starting with 1. (e.g. B=1, A=2, C=3 and D=4)

3. To create the first order in the Latin square, put the last number/level in the 3rd position, (e.g. 1, 2, 4, 3). If we had more than four levels, N say, then every subsequent unevenly numbered position (e.g. 5, 7, and so on) would have one less than the previous unevenly numbered position as shown in the following table.

Ordernumber

1 2 3 4 5 6 7 8 9 10

Level 1 2 N 3 N-1 4 N-2 5 N-3 6

Labeling of the treatment levels in the random order

1 = C 2 = D 3 = B 4 = A

Latin Square of labels Latin square of treatments

1 2 4 3 Order 1 C D A B

2 3 1 4 Order 2 D B C A

3 4 2 1 Order 3 B A D C

4 1 3 2 Order 4 A C B D

Random allocation to orders1 4 11 2 21 4 31 2

2 1 12 1 22 1 32 3

3 2 13 4 23 3 33 1

4 2 14 2 24 3 34 2

5 3 15 3 25 2 35 1

6 3 16 2 26 4 36 2

7 2 17 4 27 1 37 3

8 4 18 3 28 1 38 1

9 1 19 4 29 4 39 1

10 3 20 1 30 1 40 1

Series 1

baboon

peanut

locust

carpet

glider

fleece

almond

cymbal

jackal

bikini

chisel

pepper

budgie

sandal

coyote

Series 2

badger

raisin

maggot

cooker

rocket

jacket

banana

fiddle

jaguar

blazer

hammer

potato

canary

sarong

donkey

Series 3

beaver

tomato

slater

fridge

sledge

jumper

cherry

guitar

lizard

blouse

roller

radish

condor

shorts

ferret

Series 4

cougar

walnut

spider

heater

sleigh

mitten

orange

violin

monkey

braces

shovel

sprout

cuckoo

slacks

gerbil

Series 1

baboon

peanut

locust

carpet

glider

fleece

almond

cymbal

jackal

bikini

chisel

pepper

budgie

sandal

coyote

Series 2

badger

raisin

maggot

cooker

rocket

jacket

banana

fiddle

jaguar

blazer

hammer

potato

canary

sarong

donkey

Series 3

beaver

tomato

slater

fridge

sledge

jumper

cherry

guitar

lizard

blouse

roller

radish

condor

shorts

ferret

Series 4

cougar

walnut

spider

heater

sleigh

mitten

orange

violin

monkey

braces

shovel

sprout

cuckoo

slacks

gerbil