Blocking Flashcards
what is statistical power
the probability of the
occurance
Factorial design
consider the effect of two or more explanatory variables on a response variable of interest
very efficient in terms of the number of experimental units –
however we should note that factorial design impact on the degrees of freedom.
advantages of blocking
remove the effects of
* space
* time
* sex
* individual characters that can be ranked
continous characters that effect among individual variation can be used as covariates to remove effects and imprive signal to noise ratio
what biological questions dont involve hypothesis testing
exploratory analyses
parameter estimation
prediction
null hypotheis
Formal statement about the ‘true value’ of a statistic or parameter
Indicates no difference between parameters
used as more straight-forward to refute with data
‘two-way factorial’ design. What does this mean?
a model that involves two factors. Each of these two factors can take any number of levels, for example sex can take levels “male”, “female”, or “non-binary”, or country, which has somewhere around 195 levels.
n-way factorial designs
describe a study that has n factors. For example, we could look at a three-way factorial design to investigate the effects of a vaccine, which includes sex, vaccination, and say ethnic background as the explanatory factors.
‘fully-factorial’, or ‘crossed design’
every possible combination of the n factor levels is represented in the data. If I’m interested in education level and ethnic background, for example, I will have data from all ethnic backgrounds who have achieved all levels of education.
fractional factorial design
design where not all combinations of the factor levels are represented.
This may arise simply as a consequence of the data collected,
can also be useful in cases where a carefully chosen subset of factor combinations is represented in the data.
This may be a compromise made due to, for example, costs of running the experiment, but such an approach requires thoughtful design to avoid incorrect inference.
Some important things to consider when deciding whether a factorial design is the right type of design
Factors levels should be non-ambiguous
An experimental unit should only fit into one level of each factor
Groups sizes should be equal
Unequal groups can lead to inference errors, especially if the factors can be confounded
Modern statistical software can still calculate, but will warn of potentially ‘unbalanced effects’
Having too many factors can be hard to interpret
>3 factors, interactions are hard to interpret
potential advangates and disadvanges in one-at-a-time design
+ Design is simple
(to the point of being overly simplistic!)
− Twice as many experimental units (£££)
− Potential for uncontrolled noise/error
(Different conditions during A vs B? Faulty vaccine vial? …)
− Cannot actually compare the efficacy of vaccination males vs. females! (the interaction effect)
advantages and disadvanges of factorial design
+ Need fewer experimental units
(can be very small, if effect is large)
+ Uncontrolled noise/error is consistent
+ Can investigate multiple factors at once
+ Can study interaction effects between factors
− Increased complexity
− Not very robust against unequal group sizes
(though some modern statistical approaches can cope)
how to analysis factorial design data
Two-way ANOVA with interaction
lets us estimate both the main effects of the model, that is Sex and Vaccination, and it also lets us directly estimate the interaction effect between these two factors.
(more statistical power than t-tests)
what are blocks in blocking
Blocks are commonly apportioned over space or time
e.g. sections of a field, multiple days of the week
Blocks are a type of factor that we usually don’t care about scientifically, but need to account for statistically
complete randomised block
all factor combinations appear in all blocks the same number of times.
