Parsimonious Testing

Parsimonious testing - the simplest test is preferred

Analyse variation in response w/ one single global test

• Avoid multiple tests of same data 
• Significant results appear by chance
  • Testing at 0.05 means that you would erroneously reject H0 in 5% done
  • If 45 independent tests carried out - accept 2-3 turning up as signficant even from random data
  • Chance of getting on P<0.05 on randomly generated data from 45 tests is 0.9
• 1 global test is best as you are dealing with probability

Could follow a signficiant ANOVA with post-hoc tests e.g. Tukey's pair-wise t-tests

• These are t-tests that have been modified to allow use after the ANOVA test
• Bonferroni correction to error rate = H0 only rejected if P<0.05/45 i.e  P<0.001

Good design

• Samples minimum number of factors necessary to answer question of interest 
• Measures sufficient replicates to estimate all potential sources of variance amongst factors

Some studies have no replication accross regions = results apply only to sites tested - inferences cannot be extrapolated

Any instability could raise contact rate of badgers with cattle - raise TB incidence

Tuyttens et al - showed after a cull at one site surviving badgers had higher mobility than badgers occupying one other not-culled site

• Cannot know if mobility is due to culling without replicating treatments across several random sites
• = lack of replication can cause issues in data validity
• Having region as 'random block' allows inferences at national scale to be drawn

A random factor has levels that are randomly selected from the population of interest

Levels of a test factor are fixed by design

ANOVA needs at least one random factor which defines the error variation against which to calibrate the variation in the test variable

Experimental manipulation - cull badgers from replicate regions and compare the respsonse in TB incidence to control sites without culls

Statistical model - does the incidence of TB in cattle depend on culling badgers?

TB = Treatment + Region + Treatment:Region

10 regions picked at random across TB-susceptible SW England, each ~100km2

• Two treatment sites prepared in each region and randomly assigned to cull/no cull

Refined model - does the effect of culling depend on region?

TB = Treatment + Region + Treatment:Region + Site(Treatment:Region)

Culling influences TB

• Actually increases the incidence of TB

Conclusion - statistics saves the lives of million of badgers

Not all regions have more TB with culling - cannot test for regional differences without having any replication within Treatment:Region

With two replicates for each level of Treatment:Region - effect of culling on TB varies by region

• Multiple sites have incidences where badgers cause different effects of TB

Data from a random sample of 17 states used to test if storks are responsible for bringing babies into the world

Model - Babies = Storks + State'Storks 

Vairables are stork numbers and human birth rate

Results - stork availability explained by baby production

Due to the 'King-Kong' effect - two contries significantly contribute to r2 value 

• No valid reason for removing these two data sets - take note of them

Sometimes truth less sensational - confounding variable of land of land area which correlated indpendently

Always aim for a balance of biological understanding and statistical power

• Use biology of species to justify correlations or no correlations
• Transform data if you can biologically justify it

Always have an eye for the truth, regardless of what outcomes might want 

Test for general patterns first before exploring specifics

Statistics easily give nonsense relationships, unless you attempt to model underlying processes