I am comparing 2 different methods of sample delivery and I have challenges in interpreting the table of results results of analysis provided in the analysis of deviance table. What does these values mean?
DF Deviance Resid. DF Resid. Dev Pr(>Chi)
Methods 1 4.751 160 460.98 P=0.029
Sample 8 123.224 152 337.76 P
The table in the output is similar in spirit to the anova table from a two-way analysis of variance (anova) or factorial anova. The statistics reported aren't exactly the same, but will be pretty much parallel in interpretation. I would recommend finding an design of experiments or analysis of experiments book that covers a two-way analysis of variance. That should get you most of the way there.
Technically the deviance is -2 x log likelihood and can be used to see how much it departs from the null model. See section 4.3.3 The Deviance Table in this document https://data.princeton.edu/wws509/notes/c4.pdf
for a fuller explanation for interpretation.
To interpret the model you'd want to use the parameter estimates which are on a log count scale - this is just the tests of significants. You have a main effect of method, sample and an interaction of count by sample so your counts depend on the method and differ between samples and the effect of method varies between samples. The best approach here is probably to visualise the interaction on the model scale and probably also the count scale.
For example:
http://www.strengejacke.de/sjPlot/articles/plot_model_estimates.html
for coefficients
http://www.strengejacke.de/sjPlot/articles/plot_interactions.html
for the interaction.
Other plotting packages are available in R, but sjPlot is pretty flexible.
Thom
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