see - meimei.org.uk/files/pdf/mei_olympics_a4_mono.pdf · experimental design and hypothesis tests...
TRANSCRIPT
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
Seewww.winterolympics.external.bbc.co.uk/event-results-schedules/index.htmlfor results from 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
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)