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

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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?

Use replication, i.e.get several values for each level of the factor

Are the populations Normal (at least approximately)?

Testing whether all means are equal

Are there any “nuisance” factors?

How many factors of key interest are there?

Might the “nuisance” factors interact with each otherand/or the factor of interest?

NoHow many “nuisance” factors are there?

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?

Randomised block design. Possibly replication

Are the samples from populations with equal variance, which are at least approximately Normal?

Testing whether all means are equal, for each factor

Are the number of levels the same for all three factors?

Testing whether all means are equal, for each factor

How many “nuisance” factors are there?

Are there any “nuisance” factors?

Are the samples from populations with equal variance and at least approximately Normal?

Have you used replication?

Might the factors interact with each other?

For each combination of factors, does the population have the same variance and is it at least approximately Normal?

Possibly balanced incomplete blocks or partially balanced incomplete blocks

Kruskal-Wallis one-way analysis of variance

One

Two

Yes

No

Yes

No

Yes

No

Yes

No

One

Two

Yes

No

Yes

No

Yes

No

Yes

No

One

Yes

No

Yes

No

YesYes

No

YesNo

No

More advanced techniques needed (e.g. transformations or General Linear Model). Beyond the scope of this poster

Analysis beyond the scope of this poster

Latin square design

Specialised design (possibly Graeco Latin square)

Specialised design beyond the scope of this poster

Analysis beyond the scope of this poster

No suitable common testMore than two

Use a two way factorial design with randomisation and, possibly, replication

Analysis similar to that for two factors of key interest

Possibly factorial design Analysis beyond the scope of this poster

Two or more

More than two

Beyond the scope of this poster

Use a two way factorial design with randomisation and, possibly, replication

Beyond the scope of this poster Beyond the scope of this poster

Are you prepared to assume that the factors do not interact?

Testing whether all means are equal, for each factor

Testing whether all means are equal, for each factor, and whether interactions between factors exist

No simple general procedure - beyond the scope of this poster

Two-way analysis of variance(no interaction)

Two-way analysis of variance, with interaction interpreted as residual

Analysis of variance for randomised blocks

Beyond the scope of this poster, possibly Friedman's two-way analysis of variance by rank

Analysis of variance for Latin square

Two-way analysis of variance (two between

subjects factors)

One-way analysis of variance (one between subjects factor)