are these split plot designs?

Hi,

I have two similar experimental designs, which people in my lab are
analysing using different ANOVA designs. I thought I was clear on
split-plots but now I'm confused can anyone clarify?

ONE:
I have 4 ferrets identifying the location of sound sources in a behavioural
task. i.e. a speaker makes a noise and the animal must approach the speaker
from which it believes the sound to have orginated. Responses are treated
as "correct" or "incorrect" in this analysis.

Each animal does 4 consecutive "Runs." Runs work as follows: the animal
makes 300 localisation responses to sounds of one fixed duration. Sounds
are presented at one of 5 sound intensities. These are chosen at random
from trial to trial. Once it has completed 300 trials, it goes down to a
shorter sound duration. There are 5 durations. I want to know if the animal
is performing better on the right or the left, so I break down the
percentage of correct responses by left or right (Hemifield).

I have been analysing this as a split plot design with "Ferret" as a random
effect. So my design is (where "/" indicates that the subsequent term is
nested within the previous term): Ferret/Run/Duration/Intensity/Hemifield

My logic for doing this is that, say, Intensity is not independent of
Duration because performance at a given intensity depends upon the
Duration. Although all intensities are carried out at all durations.
The resulting ANOVA table therefore has multiple error strata to take this
into account. Does this look correct to people? If so, am I right in adding
"Hemifield" as the last nesting level or should it be further up (before
duration)? That one confuses me but the rest seems ok to my mind. In R I
am doing:

aov(response~(run*duration*intensity*hemifield)+
Error(ferret/run/duration/intensity/hemifield))

I've had this verified at a stats consultation and the design has been used
in a previous Thesis and it makes sense to me (ish). Only said previous
Thesis has not been consistent with the nesting level at which Hemifield
was added so something looks fishy.

TWO:
A similar study from out lab has has not used a nested design and I'm
wondering why. They have the following

- 6 ferrets divided into 2 Groups (a between-subjects factor).
- Each animal then does 2 Conditions. Each condition is done at two
durations (on separate occasions). These are within-subjects factors and
each animal does both conditions and both durations, so they are crossed.
- Performance at the task is measured as the proportion of correct responses
at 12 different speakers. So rather than breaking down the responses as
left and right they put in the data from all 12 speakers. They have these
12 speaker measurements for all levels of the other factors.

They do an ANOVA where Ferret is treated as a random effect. So there are
two error strata:
1. Between-subjects: Group and Ferret.
2. Within-subjects: Duration, Condition, Speaker

The within-subjects factors *are not* nested in their ANOVA. Now according
to the thinking above, shouldn't Duration be nested within Condition
because performance at a given duration might depend upon the Condition?
But that sounds wrong, because you could equally nest Condition in
Duration. So maybe no nesting is needed. But I don't understand why.


Are both these approaches right, or is one wrong???

Thanks,
Rob


--
remove FERRET for reply
www.robertcampbell.co.uk
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