In my research project I often have to compare four experimental sets of data, say it three treatment groups and one control. However, within each group I have subdivision - different concentrations of the study compound. I want to compare how the treatments work in relation to the control group, but also to test for statistical differences between the experimental groups (let's say the three drugs). I'm using Prism 7 software and trying with t-tests and one-way ANOVAs, which I find the most suitable tests. However, they calculate the means of my sets of data and compare them, which is completely inadequate and of course I don't get statistical differences even in obvious places. I need to assess the minimal concentration at which the treatment groups show statistically significant effect over the control group, but also to calculate the difference between the experimental groups (whether one drug is better at certain concentration over the other two). Other ways to compare the groups are welcome as well. Tried also with multiple t-tests and didn't work. I'm spending hours reading on the web, but I can't find similar situation to mine - everywhere people compare the means of their datasets! I guess my values aren't completely independent, so paired, and I'm assuming a normal distribution, even though my samples' size is
If I understand your research well, I think you need to do the analysis in steps. Before the steps, I am assuming that your observations are independent (i.e. the treatments were applied to different/independent groups of subjects, not the same subjects given the different treatments at different times. In that case, first step should be simple one-way ANOVA to compare the different treatments (regardless of the concentrations. you can just use some middle concentration levels for all) with the Control group. This will help you see if any of the treatments are any different (better) than the control. If the treatments are showing promising performence over the control, then you proceed to the second step, where you analyze the data into two-way (factorial) ANOVA, where you compare the different treatments at different concentrations each. This time, you leave the control group out. This step wil clearly show you the interaction of the treatment and concentrations, which is the most important information.
The second step can also be designed analyzed in a way it includes the control groups, where these will be taken as the zero concentration of the treatments. I hope this will help.
See https://www.bing.com/search?FORM=U528DF&PC=U528&q=Montgomery+D+C+design+and+Analysis+of+experiments
I believe you may have some sort of factorial experiment as Tadesse Fikre Teferra is suggesting. Next time look at Montgomery first. Good luck. D. Booth
The main point is understanding your research and creating a link between what you have and what what you want. Here are some links that could help you.
1. https://www.scribbr.com/statistics/statistical-tests/
2. Article How to choose the right statistical test?
3. https://www.dataanalytics.org.uk/data-analytics-knowledge-base-tips-tricks-r-excel/statistics-guide/which-statistics-test/
This highly depends on the data set and the way you collected the data. In case you have several time point measurements as well (e.g. drug compound and effect after several hours), you may want to consider in this case to statistically compare the area under the curve. Besides that I agree with the answer before. Performing a one-way ANOVA first and then go into more detail.
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