Testing differences between two experimental groups involving time series data

I am trying to apply a statistical test to data in my science fair project. I'm looking for suggestions on which test I should use. The graph is shown below the text.

I am studying the effect of a specific chemical on microbial fuel cells. I have two study groups--control and variable--that I want to compare. I would like to know if these groups respond differently to a specific stimulus. Specifically, I want to see if there is any defined response to the stimulus, such as a logarithmic increase/decrease in my outcome variable, differential voltage.

I used three different tests, each with a specific concentration of the chemical in the inoculum and an amount of water equal to the amount of the chemical inoculum added into each control fuel cell. I recorded the differential voltage of each fuel cell over a 200-ohm resistor for 72 hours (600 samples per hour). I added the water in the control fuel cells and the chemical inoculum in the variable fuel cells after 48 hours of data collection.

Here are the variables that I have:

• time
• differential voltage: dependent variable
• inoculum: water or chemical solution (independent variable)
• Concentration
• Amount

Preliminary analysis shows that my data have an extremely high variance within small amounts of time and raw data looks fuzzy on a computer screen (line graph—differential voltage on the y-axis and time on the x-axis, two sets of data—control and variable—represented as two separate lines on the graph)

I would like to consider the differential voltage responses as a variable all on its own because the type of function may be a part of the pattern. I want to find out if the effect of the chemical on each fuel cell differential voltage is different from the effect of water on each fuel cell differential voltage.

My null hypothesis is that the chemical inoculum does not affect the differential voltage of the fuel cell. The alternative hypothesis is that the chemical inoculum induces a response similar to that of the water on fuel cell differential voltages.

I would like to know which statistical test to use to find out whether:

1. responses are consistent within the two groups—control and variable
2. response magnitudes are affected by differences in concentration of the inoculum
3. differential voltages of fuel cells inoculated with the chemical respond in a way that is different from the response of fuel cells to water
4. there is any significant pattern in which the fuel cells consistently respond to the control and the variable group
5. the chemical added to the fuel cells makes the differential voltage act in any abnormal way

1) The chemical was added once at 48 hours; I think that the activity in between 64 and 68 hours is related to the spikes because the chemical was added to the fuel cells over the cathode. The cathode of each microbial fuel cell that I used in the experiment was a porous carbon pad electrode. Because typical data in biological processes is non-linear, I've been thinking that the linear decrease could be due to the increasing resistance in between microbes and the cathode wire as the chemical seeped through the pad (the wire was inside of the cathode pad). The spikes are very interesting because they appear to not be the noise. The linear decrease between 48 and 68 may be the noise because it may have been caused by the physical seeping of the chemical through the cathode, whereas I am trying to focus on the biological aspect of the data. Those spikes are very interesting to me because, if every negative data point were to be removed, then those points would very much resemble a biological process. I infer that the differential voltage increase that returns the variable back to the control between 64 and 68 is due to the increasing current being generated by microbes in the fuel cell, which indicates the microbial population, or biofilm, adapting to the chemical that was added (current is proportional to voltage because the differential voltage was measured across a 200-ohm resistor).

2) The concentration of the chemical would decrease of anything. After some time in the fuel cell, the fuel cell starts to adapt to the new stimulus (the added chemical) and starts to eat the chemical, thereby the concentration of the chemical decreases (in a non-linear way).

3) The return of the values back to those of the control at 65 hours was due to either the depletion of the chemical or the adaptation of the culture to degrade it.

Again, those were really good questions. Thank you!

Any pointers as to which specific test I should focus on would help this project so much. A few test that I have been looking at are:

-Friedman's test -Repeated measures ANOVA -Polynomial regression -Spearman correlation

But I don't know which one to focus on or if I am going in the right general direction. Which one do you think would work? Or if you have a recommendation that isn't on the list, what would that be?

• Welcome to Cross-Validated. It would be more useful for you to post a screenshot of the graph instead of the the description you included, "line graph—differential voltage on the y-axis and time on the x-axis, two sets of data—control and variable—represented as two separate lines on the graph" – Marquis de Carabas Mar 26 '16 at 21:53
• @marquisdecarabas I just added a picture of one of my graphs, thank you for the suggestion. – Hudson Mar 27 '16 at 4:28
• This looks interesting. I have only cursory knowledge of TS analysis, so I cannot comment further on the methods if you want to analyze it as TS. It looks like your control and variable groups are statistically the same up to the point where you added the chemical inoculum at 48 hrs. Do you have an explanation for the spikes at around 23 hours and 45.5 hours in the variable group? (it could just be noise). Several follow-up questions: 1.) I was not clear whether the chemical was added just once at 48 hours or if it was constantly added during the period between 48 and 72 hours, (cont.) – Marquis de Carabas Mar 27 '16 at 23:54
• as I'm trying to understand what happened between 64 and 68 hours in the variable group. I also see periodic spikes in the differential voltage for the variable group between 48 and 72 hours. 2.) How does the concentration of the chemical inoculum change over time? Does it get used up completely after several hours? Does it accumulate? 3.) Do you have an explanation for the return of the values of the variable group to the same levels as the control group at around 65 hours? Was the chemical all used up by then? – Marquis de Carabas Mar 28 '16 at 0:01