No
Use replication,
i.e.
get several
values for each
level of the
factor
Yes
Are the
samples from
populations
with equal
variance?
Are there
any
“nuisance”
factors?
Testing
whether all
means are equal
Yes
No
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
an d/or the
factor of
interest?
How many
factors of
key interest
are there?
No
No
How many
“nuisance”
factors are
there?
Two
More
than
two
Use each level
of the
“nuisance”
factor as a
block
Is it possible to
inclu de each
level of the
factor of
interest in
each block?
Are the
number of
levels the
same for all
three factors?
Yes
No
No
Latin
square
design
Randomised
block design.
Possibly
replication
Are the samples
fro m populations
with equal
variance, which
are at least
approximately
Nor mal?
Testing whether
all means are
equal, for each
factor
Yes
Possibly balanced incomplete
blocks or partially balanced
incomplete blocks
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
Yes
How many
“nuisance”
factors are
there?
Two or
more
Analysis beyond the scope of this poster
Yes
Testing whether all
means are equal, for
each factor
No
More
than
two
Are there
any
“nuisance”
factors?
Beyond the scope of this poster
This poster 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)
To view the other two posters and to place orders for these and for extra sets of all three
posters, please visit the MEI website at www.mei.org.uk
The set of three posters is also available in a simplified format (on CD) to print in A4 size for
student folders or for use on a whiteboard.
Included on the CD are test statistics for one and two samples, and worked examples for
analysis of variance (ANOVA).
Yes
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?
Use a two way factorial
design with randomisation
and, possibly, replication
Beyond the scope of this poster
No suitable common test
Analysis similar to that for
two factors of key interest
Possibly factorial
design
Have yo u
used
replication?
Yes
No
No
Analysis of variance
for Latin square
Analysis beyond the scope of this poster
No
Two
Analysis of variance
for randomised blocks
Beyond the scope of this poster, possibly
Friedman's two-way analysis of variance by rank
No
Specialised design
(possibly Graeco
Latin square)
One
One-way analysis of variance
(one between subjects factor)
Kruskal-Wallis one-way analysis of variance
No
Yes
See
www.winterolympics
.external.bbc.co.uk/
event-results-sched
ules/index.html
for results fro m the
Winter Olympics
Are the
populations
Normal
(at least
approximately)?
Might the factors
interact with
each other ?
Are you prepared
to assume that
the factors do
not interact?
Beyond the scope of this poster
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
No
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 simple general procedure - beyond the scope of this poster
Yes
Test on
mean/
me dian
Do you
have a
large
sample?
No
Yes
Do you
know the
variance?
Are the data
from a Normal
distribution?
No
Single
variable
Test on
variance
See
www.lotter y.co.uk/st
atistics/
for data
Symmetrical Distribution
Other
For Normal population
This poster 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)
To view the other two posters and to place orders for these and for extra sets of all three
posters, please visit the MEI website at www.mei.org.uk
The set of three posters is also available in a simplified format (on CD) to print in A4 size for
student folders or for use on a whiteboard.
Included on the CD are test statistics for one and two samples, and worked examples for
analysis of variance (ANOVA).
Wilcoxon single
sample test
Sign test
test for variance
Binomial test or Normal approximation
Go odness
of fit test
test or Kolmogorov-Smirnov (see fig 3)
Number pairs
fig 1
test
Yes
Are the data
fro m a bivariate
Normal distribution?
(see fig 2)
fig 2
No
fig 3
1
female
right
handed
32
28
left
handed
7
5
Contingency table
Poisson test
Test of
proportion
Are the
variables
categories
or numbers?
Male
Estimate variance as s²
and use t test
Poisson
What
distribution
are the
data from?
cumulative probability
38 has co me up
213 times to en d
March 2010 but
20 has only co me
up 148 times
Yo u co uld u
se a
go o dness o
f fit
test to che
ck if
there is ev
idence
that the lo
tter y
is not fair
Normal test
No
Categories in a contingency table (see fig 1)
Bivariate
data
Estimate variance as s²
and use Normal test
Yes
Do you
know the
variance?
Yes
No
Are the
data single
variable or
bivariate?
Normal test
0.75
observed
D
0.5
EXPECTED
0.25
0
x
With a large set of data, the scatter diagram for a
bivariate Normal distribution is approximately elliptical
Test statistic for
Kolmogorov-Smirnov test
Pearson’s product
moment correlation test
Spearman’s rank
correlation test or Kendall’s
rank correlation test
Test on
difference of
means/medians
Yes
Do yo u know
the variance
of the
differences?
No
Do you know
the variance
of the
differences?
Do you
have large
samples?
Matched
(paired)
samples
Yes
Are the
differences
Normally
distribute d?
To do a test
on paired samples, first find the
differences between paired data
values and then proceed as for
a single sample test
Are your
samples
matched?
Unpaired
samples
No
Do yo u
have large
samples?
Yes
Are the data
from Normal
distributions?
No
A survey of TV watching habits is conducted with the following results
Women
Men
Sample size
50
60
Number of hours of TV watched per week
Sample mean
11.2
9.6
Sample variance
135.2
66.9
Does this provide evidence that
there is a difference in the
mean number of hours of TV
watched by men and women?
This poster 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)
To view the other two posters and to place orders for these and for extra sets of all three
posters, please visit the MEI website at www.mei.org.uk
The set of three posters is also available in a simplified format (on CD) to print in A4 size for
student folders or for use on a whiteboard.
Included on the CD are test statistics for one and two samples, and worked examples for
analysis of variance (ANOVA).
Test on
difference
of variances
Are the
differences
symmetrically
distribute d?
Do you
know
the
variances?
Yes
No
Normal test
No
Estimate variance of differences
using s² and use Normal test
Yes
Normal test
No
Estimate variance of differences
using s² and use t test
Yes
Testing whether
they are from
the same
distribution
Test on difference
of means/medians
Yes
Do you
know
the
variances?
Are the data
from distribut
ions
w ith the sam
e
shape?
Wilcoxon paired
sample test
No
Sign test
Kolmogorov-Smirnov 2-sample test
Yes
Normal test
No
Estimate variances using
s²,s² and use Normal test
Yes
Yes
No
Yes
No
Are the
variances
equal?
No
Normal test
t test with pooled
estimate of variance
No suitable simple test
Wilcoxon rank sum test
or Mann Whitney U test
No suitable simple test
F test