Choice of ANOVA

I have a small data set based on the survivorship of plants exposed to different temperatures. There are two factors: temperature (how cold it is) and exposure time (how many hours they were exposed to these temperatures). i want to determine if there is an effect of temperature, exposure time, and the interactive effects (temp x exposure time). The data are expressed in survivorship between 0-1.0 of a sample of 15 plants per treatment. I assumed I'd use a two factor ANOVA without replication but when i do this, i Excel doesn't give me an interactive effect. also, i am not certain but i think i have to transform these data since they are only between 0 and 1.0. Any help would be appreciated and I can provide the data set.

thank you!


Active Member
you probably need to multiply your 0-1 x 15 to get number surviving out of 15. Then i think easiest way is you need to use logistic regression to do the 'two-way ANOVA', basically same idea as two way ANOVA, but the y (independant) is going to be logit( survival prob. ). i don't know if excel is going to cut it, may need R.
Thanks for the suggestion and i appreciate your time. your first suggestion is exactly how I set up the data. I will look into logistic regression and I appreciate the suggestion. I was going to transform the data since they are only between 0 and 1.0 (non integers) maybe by arc sine transformation. I'm sure I can do this in R, but I'm just trying to understand
why I can't get interactive effects in a two-way ANOVA without replication. Perhaps it's a basic misunderstanding of the test.


Active Member
Yeah i know what you mean here: I think if you don't have replication, you need to leave off the interaction term, or you have nothing left for error.

ie in 2 x 2 study with no reps you got df = 3: 1 for factor 1 + 1 for factor 2 + (2-1)*(2-1) for interaction, but oops you got nothing for error now. what you do? you drop error term: ie assume no interaction.

This is grossly different from that though, as you have proportions. your probably feeding arcsine(p) into ANOVA model? Maybe. But just use R function 'glm(..., family=binomial, weight=15', that's going to be easier, honestly i can't remeber how the formulas work out, that's what software is for.

In sas it would be proc genmod; model #survived/15 = temperature | time / link=logit;

can't go wrong the software will guide you to the right answer, and you can check it out by hand if you doubt it, or have some curiosity on the subject which you seem to.

you probably can do it with arcsine and anova, but i think you have to trick the software regarding the degrees of freedom. well maybe you can figure that out and teach me.
yup. thanks for responding again and your suggestion. I'm a biologist and I leave the formulas and deeper math to others. I just want to understand my organisms. I do understand the bit about being left with no degrees of freedom. the problem is I strongly suspect that there IS interaction and should definitely not assume no interaction. in fact, my experiment was designed with interaction in mind and just looking at the data, i'd say it definitely will be significant. I've been reading Tukey designed a test to try to go around the problem of degrees of freedom, but to be honest I don't understand it and, again, I just want to get an answer. thank you again for your suggestions!


Active Member
you should be good to go with the interaction term, the software should allow this, just include it in model,

ie in R glm( # survived ~ factor1 * factor2, will give the interaction term.

if im wrong the software will tell you, but im most likely not.