Hi Everyone
I have calculated the effect of a drug on the inactivation of a protein at different temperatures using unpaired experiments. The drug has a significant effect (p
You have use only three Levels of temperature. You need to use more Levels to get strongest results and conclusions. You can draw a curve between temperature and drug response which will give you the peak of drug response and the temperature Corresponding to it. Statistically, you can use ANOVA and then complete the test by using Duncan multiple range test or tukey which will give you the Best treatment conditions.
I second Abdulmuhsin S. Shihab : you show data for only very few temperatures (but with many replicated for ach temperature). If you want to identify the optimum temperature, you should use an experimental design where you have as many different temperatures as possible. It's only important to have a decent total number of independent measurements; there is no need to have several measurements for the same temperature.
If your question is simply if the effect at 25°C is the largest, the simplest solution imo is to do two 2x2-ANOVAs where you test the interaction: one for the temperatures 12°C and 25°C, and the other for the temperatures 25°C and 37°C. The signs if the interaction effects must be positive in the first case and negative in the second. The two p-values should be corrected for multiple testing (multiply by two, or judge the statistical significance by alpha/2). If the signs are both correct and statistically significant, than you have shown that your data are incompatible with hypotheses that the effect at 25°C would not be the largest of the three temperatures.
With the data you have, probably you want to keep the 2-way anova design with interaction, and then use the lsmeans or emmeans procedure appropriate for that model that your software provides to determine if groups (e.g. levels of the Temperature x Treatment interaction) are significantly different.
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