My question is about a 2-way ANOVA for an experiment. For simplicity let's say I'm using 3 methods to stimulate cells at 3 different time points, and I want to look at a resulting output variable. Different cells were stimulated at each time point, so independence of observations is maintained. Each time point has 9 - 10 replicates. The data look like this: https://i.imgur.com/oGEagOY.png
I ran a 2-way ANOVA, and found both stimulation method and time to be significant. The multiple comparisons options in Graphpad though are confusing me. I could compare each value to each other value, but this results in irrelevant comparisons being made that decrease significance levels. The comparisons I'm interested in are:
1) The difference in mean output value between each time point. Prism calls this the main row effect.
2)The difference in mean output value between each stimulation method. Prism calls this the main column effect.
3)The difference in output values across stimulation methods within each time point (e.g. comparing day 7 method 1 vs method 2 vs method 3). Prism calls this simple effect within columns.
4)The difference in output values across time points within each stimulation (e.g. comparing stimulation method 1 day 7 vs day 10 vs day 14). Prism calls this a simple effect within rows.
My question is, can I run 4 multiple comparisons using each of these settings, and then use the p-values that are returned?
I would think certainly not, since doing them separately gives a way inflated p-value. So, I tried a similar 2-way ANOVA on both SPSS and Graphpad Prism. These data had no replicates, so I only wanted to compare the columns to each other and the rows to each other. On Prism, I ran the main row effect and main column effect multiple comparisons separately. To my surprise the Prism output matched the SPSS output. But in a 2-way ANOVA post-hoc shouldn't every row mean be compared to not only the other row means but the column means as well?
Sorry for the length. This is my first question so just let me know if I violated any rules and I'll edit accordingly.