Three experiments with three replicates in each; how to apply calculate SEM? - (Feb/21/2017 )

I have done the same experiment three times and in each experiment the same thing was done three times; thus I have nine data points for every sample. Should I average the three within-experiment-replicates and use those three values find a super-average and calculate an SEM or should I use all nine values to calculate an average and SEM? Obviously the average will come out the same but the SEM won't.

I think I should use the SEM calculated from the three averages because there were three experiments and the three replicates within each experiment were not really separate because they were being done together. This also reduces the value of the SEM which I think makes the data look more reliable.

I made up some data to produce an example.

Use each experiment as a sample. The within experiment replicates are not considered to be separate replicates unless you actually set them up independently (e.g. made up drug dilutions for each sample independently rather than using the same solution for all). This will give you a larger SEM as the sample size is reduced, but is more valid statistically.

Dropping it into a 2-way ANOVA will (hopefully) confirm that the Exp's are not sig. different.