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What would be the best way of determining the statistical significance of the differences in concentration between trials of a dataset such as this one:

+-------+---------------+
| Trial | Concentration |
+-------+---------------+
|     1 | 2.41          |
|     2 | 8.43          |
|     3 | 3.48          |
|     4 | 6.22          |
|     5 | 4.66          |
|     6 | 3.58          |
+-------+---------------+

Would it be a t-test?

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  • $\begingroup$ Do you repeat each trial only once? $\endgroup$
    – user12719
    Feb 5, 2013 at 19:03
  • $\begingroup$ There are 3 repeats for each trial, from which an average concentration is determined in the table above. $\endgroup$
    – Ben
    Feb 5, 2013 at 19:04
  • $\begingroup$ Do you still have the original data on the repeats, or is there a reason that the variances of the distributions must be a function of the mean? $\endgroup$ Feb 5, 2013 at 19:23
  • $\begingroup$ What are the different trials? Does one subject undergo each trial 3 times, so you have N = 6? Or are there more than one subject per trial? Or is N = 1 and he/she/it undergoes 18 trials (3 repeats of each of 6). $\endgroup$
    – Peter Flom
    Feb 5, 2013 at 19:38
  • $\begingroup$ The different trials are slight variations of the same theme. There are three identical repeats of each trial. The trials are entirely independent from one another in that the outcome of one will not affect the outcome of another in any way. $\endgroup$
    – Ben
    Feb 5, 2013 at 20:09

1 Answer 1

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I'd suggest that you use the whole data set, i.e. not average. This would potentially allow you to estimate the variance at each trial. Let's assume that 3 repeats per trial allow you a sufficient model fit (or you are able to record more repeats). You would run an ANOVA if the trials constitute separate categories, e.g. different experimental conditions. You could run a linear regression model if there is a relationship between following trials. You don't want to run multiple t-tests to compare every possible combination, e.g. Trial 1 vs Trial 2, Trial 1 vs Trial 3, etc without correcting for multiple comparisons.

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  • $\begingroup$ So given that each trial is under slightly different conditions, ANOVA should be ran on the data (including the concentrations from each of the three repeats?) $\endgroup$
    – Ben
    Feb 5, 2013 at 19:24
  • $\begingroup$ It sounds like different trials could be modeled as different categories, in which case you would chose an ANOVA. Depending on your answer to Peter Flom, you would run a repeated measures ANOVA if the same subject gets tested multiple times. $\endgroup$
    – user12719
    Feb 5, 2013 at 19:48

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