See
www.w interolympics.
external.bbc.co.uk/
event-results-sched
ules/in dex.html
for results fro m the
Winter Olympics
This reference flowchart is one of a series of three, designed by Stella Dudzic.
The series includes: Hypothesis tests for one sample, Hypothesis tests for two samples, and
Experimental Design and Hypothesis tests for several samples: ANOVA (Analysis of Variance)
The series is also available as a set of three full colour posters in A2 size for wall display.
To view the colour posters and to place an order please visit the MEI website at
www.mei.org.uk
No
Use replication,
i.e.
get several
values for each
level of the
factor
Yes
Are the
samples from
populations
with equal
variance?
Are the
populations
Normal
(at least
approximately)?
No
Are there
any
“nuisance”
factors?
More advanced techniques needed (e.g. transformations or
General Linear Model). Beyond the scope of this poster
Yes
One
One
Might the
“nuisance”
factors
interact with
each other
and/or the
factor of
interest?
How many
factors of
key interest
are there?
No
No
How many
“nuisance”
factors are
there?
Two
Use each level
of the
“nuisance”
factor
as a block
Is it possible to
include each
level of the
factor of
interest in
each block?
Are the
number of
levels the
same for all
three factors?
No
More
than
two
Specialised design
(possibly Graeco
Latin square)
Yes
How many
“nuisance”
factors are
there?
One
Two or
more
No
Latin
square
design
Yes
Randomised
block design.
Possibly
replication
Yes
Are there
any
“nuisance”
factors?
Beyond the scope of this poster
No
Yes
Use a two way
factorial design
with randomisation
and, possibly,
replication
Are the samples
from populations
with equal variance
and at least
approximately
Normal?
Beyond the scope of this poster
This reference flowchart is one of a series of three, designed by Stella Dudzic.
The series includes: Hypothesis tests for one sample, Hypothesis tests for two samples, and
Experimental Design and Hypothesis tests for several samples: ANOVA (Analysis of Variance)
The series is also available as a set of three full colour posters in A2 size for wall display.
To view the colour posters and to place an order please visit the MEI website at
www.mei.org.uk
Are the samples
from populations
with equal
variance, which
are at least
approximately
Normal?
Testing whether
all means are
equal, for each
factor
Yes
For each combination of factors,
does the population have the
same variance and is it at least
approximately Normal?
Specialised design beyond the scope of this poster
Analysis of variance
for randomised blocks
Beyond the scope of this poster, possibly
Friedman's two-way analysis of variance by rank
No
Possibly balanced incomplete
blocks or partially balanced
incomplete blocks
Analysis beyond the scope of this poster
Yes
Testing whether all
means are equal, for
each factor
No
Analysis of variance
for Latin square
No suitable common test
Analysis beyond the scope of this poster
Use a two way factorial
design with randomisation
and, possibly, replication
Analysis similar to that for
two factors of key interest
Possibly factorial
design
No
Two
One-way analysis of variance
(one between subjects factor)
Kruskal-Wallis one-way analysis of variance
No
Yes
More
than
two
Testing
whether all
means are equal
Yes
Have you
use d
replication?
Yes
No
Might the factors
interact with
each other?
Are you prepared
to assume that
the factors do
not interact?
Yes
Analysis beyond the scope of this poster
Testing whether all means
are equal, for each factor
Testing whether all means
are equal, for each factor,
and whether interactions
between factors exist
Yes
Two-way analysis of variance
(no interaction)
Two-way analysis of
variance (two between
subjects factors)
Two-way analysis of variance, with interaction
interpreted as residual
No
Beyond the scope of this poster
No
No simple general procedure - beyond the scope of this poster