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There are 4 experiments, each individual experiment is repeated such that there are 3 measurements to make an average -> should end up with 4 average values, one for each experiment. The aim is to measure activity from a radionuclide added to biological cells and to see whether adding a particular compound affects the uptake of the radionuclide.

The first experiment is a control, so just add the radionuclide to the cells, measure the activity, repeat with new cells until 3 measurements are made, calculate the average etc etc. The second experiment includes adding the compound to the cells, under the same environmental conditions as experiment 1 and as before to find the average value.

The 3rd experiment has different environmental conditions without the added compound to the cells, measure activity 3 times. Then for the 4th experiment, add the compound under the conditions for the 3rd experiment, then measure activity 3 times.

So, there will be 4 average values - I have to determine whether there is a statistically significant difference between the experiments. I originally thought to do a student's t-test, but I was informed that is wrong. Sadly, statistics is my weak point so I would greatly appreciate any help on the matter, which statistics test would be best? And, how do you decide where there is a cut off between a significant difference and no evidence for any difference?

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What you describe is a 2 x 2 design, the simplest form of 2-way analysis of variance (ANOVA). You have 2 environmental conditions. In each environmental condition, you have one control experiment and one experiment in which you add a compound.

An important consideration in this type of design is whether the effect of the compound differs between environmental conditions (or, equivalently, vice-versa).

You can analyze such experiments via a linear model with an interaction term. Say that env is 0 for the first environment and 1 for the second, and compound is 0 for control and 1 for addition of compound. Then the following form of model could be used in R:

outcome ~ lm(env + compound + env:compound, data = your_data)

with env:compound representing the interaction, their product.

The model will return coefficients for env (difference between env=1 and env=0 when compound=0), compound (difference between compound=1 and compound=0 when env=0). It will also return a coefficient for the interaction (the difference between what is found when both env and compound have values of 1, versus what you would have predicted based on the individual env and compound coefficients). The model will indicate the statistical significance of that interaction term.

If the interaction is significant, there is no single measure of the effects either of env or compound, and the fact of a significant interaction would be a substantive finding. The effect of env depends on the value of compound, and vice-versa. If the interaction isn't significant, you might consider a model that omits the interaction, providing separate estimates of the effects of env and compound.

Depending on the nature of what you're measuring, a simple linear model like this might not be appropriate. For example, if the outcomes involve small numbers of radiation-decay counts, you might need to use a corresponding Poisson generalized linear model. But the same principle of evaluating the interaction would still hold.

Spend some time extending your understanding of statistical principles in experimental design and analysis. Try to get some formal training. At least, use resources like this online handbook and its associated R companion to get an overview of the principles and how they might apply to your work. At a minimum, you need to understand enough to be able to communicate effectively with a statistical consultant--with whom you should consult before undertaking any complicated experimental designs.

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