Experimental design

Experimental design

Dr Richard GoodeySEMS

4/5/2012 Researcher’s Development Day

What is an experiment?

• A test– To find out something about a process– More specifically, usually a series of tests

• Something we do all the time in our everyday lives

• In this context, most relevant to physical and social sciences

• In these fields, most PhD candidates and researchers do some sort of experiment


A simple example

• What is the effect of temperature on the rate of reaction between limestone and acid?

• 2HCl + CaCO3 -> CaCl2 + H2O + CO2

• So this should be simple?• Add limestone to acid, measure the volume of

gas produced in one minute (e.g.)


Results

• Have we answered the question?4/5/2012 Researcher’s Development Day

10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120

Temperature (°C)

Vol o

f car

bon

diox

ide

(cc)

General model


Process

x1 x2 xn

z1 z2 zn

Input Output

Uncontrollable factors

Controllable factors

Our simple experiment………?

• Temperature control• Concentration of acid• Volume of acid• Mass of limestone• Size of limestone particles• Mechanism for measuring gas volume and time• Purity of reagents• Atmospheric pressure


Basic principles

• Replication– Not to be confused with repeated measurement

• Randomisation– Design against unknown nuisance factors

• Blocking– Eliminate or reduce known nuisance factors


Guidelines for design

• Recognise and state the problem• Choose factors, range and levels• Select response variable• Design experiment• Perform experiment• Analyse data• Conclude and recommend


Things to note

• Keep the design and analysis as simple as possible

• Practical vs statistical significance• Experiments are iterative and repetitive


Experiment with a single factor

• Recognise and state the problem

• Choose factors, range and levels

• Select response variable

• What is the strength of fibres used to make shirts?

• Influenced by weight percent of cotton in fibre. Range between 10 and 40 percent. Levels 15, 20, 25, 30 and 35%

• Tensile strength


Design experiment• Utilise replication and randomisation• Replication = 5 samples per level, total

number of tests therefore 25• Randomisation:


Cotton weight %

Experimental run number

15 1 2 3 4 5

20 6 7 8 9 10

25 11 12 13 14 15

30 16 17 18 19 20

35 21 22 23 24 25

• Use a process to put those in random order

• Minimises unknown nuisance factors


Test sequence Run number Cotton weight %

1 8 20

2 18 30

…… …… ……

25 3 15

Perform the experiment, collect data

• Now we need to perform some data analysis to assess significance etc


10 15 20 25 30 35 400

5

10

15

20

25

30

Cotton weight %

Tens

ile st

reng

th (p

si)

Summary

• Performing an experiment is maybe not so straightforward as it seems?

• Careful planning will minimise:– Inaccuracy– Time wasted

• Some level of statistical analysis will be required to prove or disprove your hypothesis


Technology

Experimental design