Dear statistics experts,
I have trouble to find a sensible statistical approach to back up some very obvious (at least to my eyes) interpretation of a dataset (see descriptive plot below).
I measure a response to two different stimulus (Stimulus 1 and 2) at 3 different intensities (weak medium high), in 2 different populations (population 1 and 2).
What I see and would like to support with a statistical test, is that overall the response exhibit a dynamic range along the intensity range, but more importantly, that this range is very steep for stimulus 1 in the population 2 but, not in population 1.
In terms of design, I have
- a continuous dependent variable (my response).
- two categorical variables with two levels each (stimulus and population)
- one ordinal variable with 3 levels (stimulus strength)
Samples are not independent, as response to each stimulus/strength pair is assessed on the same subjects in the two populations.
I thought of using a mixed effect ANOVA with subject as a random variable to account for the repeated measure.
First problem : How to measure the departure from the homoscedasticity assumption ? A Levene's test reject the null hypothesis of equality of variance between groups. Anova is said to be robust to violations of its assomptions, but is there a way of judging the severity of this violation, especially given my unbalanced design?
Second, would my biological statements be reinforced if I was to find a significant 3-way interaction population x stimulus x strength ? I have two concerns :
Does a 3-way interaction p-value have any meaning on such a design and especially given my first point (disparity in variance) ?
even if this effect was real, is it allowed (not to say feasible), to conclude anything biologically relevant from a three-way significant interaction, which essentially mean, (correct me if I am wrong), that at least one of the two-way interaction between a pair of factors is influenced by the third one ? Specifically here, I would like to test if the stimulus x strength interaction is influenced by the population factor. Should I then test for significance of this two-way interaction beforehand ?
My meditations have carried me far beyond what my very basic understanding of statistics allow me to comprehend.
Thanks in advance for your input,