I mocked up your study:
Treatment is A or B. Phase is 1 to 4. Cage is 1 to 20. Flies is the count of dead flies. Censor is set to 0 for dead. The rows for Phase = 4 are duplicated to record the number of flies still alive and Censor is set to 1 for those rows.
Note that Flies is a random number from a Weibull distribution so I could continue my reply.
The homogeneity test assumes a null hypothesis that the distribution of all the groups (Treatment in this case) are the same. The alternative hypothesis is that the distributions are not all the same. This is the test for any Treatment effect.
The Nested Models Tests are also for a Treatment effect, but they address the nature of the Treatment effect. These tests also start with the assumption of no effect. The first test compares the location parameter. The second compares the location and the scale parameter.
It seems to me that in this research there is no interest in the dynamics of the process, but are interested in comparing the types of replications by final (on the 20th day) results (ratio of dead and live in percent), i.e. want to find a statistically significant difference in the proportions of live and dead depending on replication (cages)
I wanted to introduce a so-called “Complementary Log-Log model” for binomial response data as you have (i.e., # of dead files per cage population). This model is often applied to discrete survival time data.
Please, specify for JMP 10.
I don't see "Generalized Linear Model" here. Thanks!
Please also check out this JMP blog post https://community.jmp.com/t5/JMP-Blog/Reliability-regression-with-binary-response-data-probit-analys...
Select Analyze > Fit Model. Then click the button next to Personality and select Generalized Linear Models near the bottom of the drop down menu. You should see the choice for distribution and link function appear after that
I still think that your biggest hurdle is the layout of your data table. It isn't difficult, but if you don't set up the data correctly you will have trouble with most of the procedures. Did you try the layout I suggested?
A different layout is necessary for the GLM approach...