Hi Minoo,

From what you describe above, it seems that the time component is intrinsic to the intervention arm. In other words, the time component cannot be separated from the exposure. On the other hand, if you have taken multiple measurements for each unit in each treatment arm, then you could compare them at the same time period.

So for example, assume you took measurements of all units every hour. That would allow you to make a comparison at the 1 hour mark across all treatments. This setup would allow you then to compare sub-lethal vs chronic for 7 measurements (hours 1-7). However, you could not compare all treatments across all time periods where there is no overlap.

So now let's assume that time is intrinsic to the exposure arm, and thus it is not an independent measure on its own. You can run a regression model with the exposure as indicator variables followed by contrasts to determine which of the exposures impacted the outcome the most.

I hope this helps

Ariel

Hi Ariel,

Thanks for your urgent comment.

Is there any possibility to compare our treatments with control group?

Which regression model should we applied? The PCA is an appropriate model for our data?

Of course you can compare to a control group, and that would be the desired approach. However you didn't mention that as one of the control groups in your study.

Which regression depends on what your outcome variable is. You have not provided any information about that either. PCA is not a method for comparing means between groups.

Yes, we had a control group as well. We determined the swimming activity of Daphnia (other behavioral responses were recorded) following mentioned treatments.

So your basic regression will include a categorical independent variable indicating assignment to one of 4 groups (or instead, you can create 3 dummy variables). If you find that the beta coefficient on this variable is statistically significant, you then perform the post-estimation test to determine which groups were statistically different than the others. This should be adjusted for multiple testing (e.g. Bonferroni, Sidak, Scheffe, etc.). 

Thanks Ariel for your nice guide. I'll run this analysis.

Please let me contact you if I found anymore issues during the further steps of analysis.

Bests

Is the time "treatment" equivalent across the ammonia treatments? In other words, for each ammonia treatment do you have data at the timepoint 0, 1 hr, 7 days, etc? Or as Ariel mentioned, are the ammonia treatments inseparable from the time treatments? I feel like ideally you would want to have the former rather than the latter, i.e.,

Acute at t0, t1, tx...

Sublethal at t0, t1, tx...

Chronic at t0, t1, tx...

Control at t0, t1, tx...

If that is akin to your design, then I think you would also want to look at a treatment-by-time interaction. This would just use a simple multiple regression model in the form of:

Outcome ~ ammonia + time + ammonia*time

But if this is not your design and you have time and treatment that cannot be considered separately, then Ariel's approach should be followed and with post-hoc tests to determine which means are different from one another. You should also adjust for multiple comparisons here, using one of the standard methods (Bonferroni, Holm, Benjamini-Hochberg, etc).

You could also consider including random effects in your analysis if appropriate. I assume that with Daphnia you wouldn't have repeated measures exactly, but perhaps replicates could be included as a random effect. 

Yes Daniel, I did not measure our parameters at different time intervals for each treatment. Therefore, we only had a simple measurement, for example we determined swimming activity only following 1h exposure to acute concentration. This measurement for acute treatment did not extend to further periods. This was similar for other treatment groups, i.e., sub-lethal for only 7h and chronic for 7d.

We did not have repeated measurement and we tested our Daphnia individually in each treatment (7 specimens for each treatment).

I have performed linear regression with dummy variable (0 and 1) and found B are significant (Output attached). Now the question is how can I perform multiple comparison (Bonferroni, Sidak, Scheffe and etc.) and which one should I used?

Another question is that when we added ammonia to water, the pH was changed. i.e., the acute treatment had a pH of 8.5, sub-lethal treatment had a pH of 8.2 and chronic had  a pH of 7.8. Therefore, we had different pH in different ammonia treatments. How do analyze the pH effect in coincident of ammonia concentrations? Should I used MANOVA here?

I also agree with what Ariel said