I would like to compare four slopes (which are in fact are reaction rates) I got from linear fits through five data points for each fit. The fitting results for the slopes are as follows:
1: 0.08885 ± 0.00991
2: 0.08744 ± 0.0118
3: 0.10288 ± 0.00669
4: 0.0926 ± 0.01285

My hypothesis is that they are all not significantly different from each other (or in other words that they represent the same reaction rate within an experimental error) and I would like to prove that with a statistical test. But I have no idea which test is appropriate here. If there is somebody with some knowledge on statistics out there, help is very much appreciated. Thanks a lot for your help in advance.

So....
1) You need to test for equivalence (not superiority)- what is your equivalence boundary
2) A sample size of four is almost certainly too small- lack of an effect will just be due to lack of power.

Ok. Thanks. I had a look into equivalence testing (TOST). The point is, I don't have a defined equivalence boundary. I could arbitrarily pick one, but that's probably not the best choice. Is there sth like a t-test which tells me if the difference between two points is significant or not?

I think you are missing the point- you want to show equivalence, so will need to set an equivalence boundary (arbitrary is possibly OK, as long as others agree that they are reasonable).

You still haven't addressed the lack of power issue!

My opinion is that statistics aid an argument but cant compensate for bad experimental design. Understanding the theory first is better than trying to use statistics to determine a conclusion especially with equivalence in what I assume is chemistry/biology.

Do you have 4 sets of experiments measuring the same reaction or different reactions? If you are using four different methods you need to understand how the methods would affect the result (ie are you actually keeping everything the same). If it is different reactions they are different reactions and looking at theory is better than using statistics. It could coincidence that they are the same or they have a similar rate limiting step(or mechanism) but you need the theory first.

More details would be helpful but I would really recommend looking at the underlying theory to see if equivalence is possible or is it just coincidence.

It is always the same reaction in the same medium at a polymer brush-substrate interface varying properties of the polymer. There is not much of an underlying theory yet that's what i try to develop. I have different sets of experiments varying different properties of the polymer (here i picked one set for illustration) and I want to know if this property has an effect on the reaction rate.

For now i simply cannot produce more data points. If i could measure this quantity directly, I could perform a number of measurements for each condition and perform a t-test to compare two points. This would tell me if the difference between those two is significant or not. I was wondering if there is a similar test for quantities derived from linear regression (as it is the case here).

iiwanovic, that makes more sense now.

I wouldn't try to prove equivalence but do analysis of variance (ANOVA). It is where you are comparing how different variables affect the overall result. Ie take all your data with all the variables and analyze them together to get an overall equation. It means you can possibly look at interactions between the variables and thus determine the more important variables. It lets you use your entire data set at the same time and you can compare anything as long as it has the same output (ie yield or conversion).

I don't really understand the underlying theory so not going to try and explain it but I use DesignExpert to do all my multi-variable analysis. There are a few other software options like MiniTab or SPSS that do similar or you can try ANOVA from scratch.

Hope that helps