10-28-2014 03:19 PM
I have multiple groups - each one different from the others. All groups are exposed to one chemical. For each group, I have derived a number that denotes the number of milligrams per liter of the chemical that takes to be toxic to that group. The number has a 95% confidence interval, and is the aggregate of multiple testing replicates.
Group A is the "standard" - the wild type. The other groups have been altered genetically in specific ways (to see whether a given gene is involved in the toxicity).
Here are sample numbers (95% CI in parentheses):
Group A = 13,607 (10,302 - 20,338)
Group B = 12,222 (8,251 - 27,120)
Group C = 16,912 (11,232 - 28,327)
How can I run a procedure that will tell me whether Group B is statistically different from Group A? That Group C is statistically different from Group A?
I guess I mean one-way ANOVA. Could you suggest what code I would run? I am using SAS 9.3.
10-28-2014 05:36 PM
Do you have the raw data available, ie each result from the replicate? It's more accurate to perform analysis on that data.
In general, if your confidence intervals overlap then the results are not statistically different.
10-29-2014 03:40 PM
And given that these strongly overlap, I would suspect that they are not different. However, without some knowledge of how the CI's were constructed, I don't want to venture too far out on this one.
10-30-2014 03:19 PM
If you have the raw numbers, that should work, if there are no real complicating factors.
However, I suspect there is a lot more behind the scene here--I think there is some inverse regression. I also wonder how a toxic dose is defined--lethal to all in the group, LD50 (by probit regression), NOEL by lowest level tested, etc. The toxicology world has a lot of stuff going on, and without knowing which method was used, I worry that without taking this into account, we get something unexpected.
Still, those confidence bounds are huge in comparison to the mean, and are not symmetric around the mean, so I think there is more here than meets the eye.