Do I calculate standard error and coefficient of variation before or after subtracting background?

I have a data set of absorbances, which were used to calculate %CO2 (micrograms CO2-C per g soil per hour) in an experiment measuring respiration (CO2 output from soils).

I have to subtract the basal respiration (background) from the treatments after doing those calculations. But then do I calculate the standard error and coefficient of variation before or after that subtraction?

More details: For a given sample (9 soil samples tested total) 4 replications were done for each soil + substrate (6 different substrates and no water added), soil + water for the basal respiration, and just water as a control. So 8 treatments * 4 replicates = 32 sample tubes for each sample. The basal respiration is to be subtracted from the respective substrate amended respiration I believe. So in a 96 well plate assuming row A is substrate treated and row B is basal then A2 subtracted from A1, B2 subtracted from A2 etc.

• What is the question you are trying to answer? My intuition would say that you calculate it after subtracting the background respiration. – André.B Nov 17 '19 at 20:32
• Please say more about the details of your study. For example, for each soil sample were there corresponding measurements of basal CO2 output and for each of the various treatments? Or were some treatments only applied to some samples? How many soil samples and how many treatments? Were their any spatial or temporal correlations among the samples that were taken? What is the specific hypothesis you wish to test? Depending on your design, samples, and goals, it's possible that there could be a more powerful way to proceed than simply subtracting out individual basal respiration values. – EdM Nov 17 '19 at 20:36
• @EdM Sorry. For a given sample (9 soil samples tested total) 4 replications were done for each soil + substrate (6 different substrates), soil + water for the basal respiration, and just water as a control. So 8 treatments * 4 replicates = 32 sample tubes for each sample. The basal respirations is to be substracted from the respective substrate amended respirations I believe. So in a 96 well plate assuming row A is substrate treated and row B is basal then A2 subtracted from A1, B2 subtracted from A2 etc. – Rachel Brockamp Nov 18 '19 at 16:04
• @RachelBrockamp no need to apologize. The back-and-forth of comments is designed to get questions into more specific forms that are useful to those who would answer and to those who come upon this page in the future. Please do, however, edit your question to add that information, as comments can get lost sometimes. Also, am I correct that your interest is in differences from the basal respiration with water + soil for each of the substrates ? – EdM Nov 18 '19 at 16:47
• @EdM. Thanks, I changed the question details. Yes that is what I am interested in. The goal is to get the "substrate induced respiration" alone by subtracting basal. – Rachel Brockamp Nov 18 '19 at 17:18

If what you care about is "substrate induced respiration" you ultimately want to know the standard errors of the differences between the substrate treatments and the control soil+water treatment. Presumably you want to use those standard errors to determine statistical significance or confidence intervals for the differences of treatments from control and among each other. The question is how best to get those values in a way that most reliably allows you to perform those comparisons.

The way you are doing the differences (in a 96-well plate with rows A through H and columns 1 through 12, calculating the difference for a single replicate of each treatment from the single replicate of the control within each individual column) probably isn't the best way to use your data.

If it's reasonable to assume that the variance among replicates of observations is the same for each of the treatments and control about their corresponding mean values, you would be better off analyzing your data as a linear model. In that way you pool the information from all the observations to get a combined estimate of the variance, which is then used to estimate significance levels and confidence intervals. This helps protect you from having a control or treatment that just happens to have a randomly large or small sampling variance among replicates in your particular data set.

In the linear regression you would handle all of the substrate treatments and soil+water basal treatment as a multi-level categorical variable. If you use the soil+water basal treatment as the reference category and your software is instructed to use treatment coding, then the regression coefficients and corresponding standard errors for each substrate will give exactly what you are looking for: the difference of each substrate treatment from soil+water, and the standard error of that difference. Software typically also reports a p value for the difference of each substrate from the soil+water control when you set up the analysis this way.

If you suspect that the soil samples differ systematically in terms of baseline or substrate induced respiration, then you can also include the soil samples as predictors in the linear regression to handle baseline differences, and include interactions of soil samples with substrate treatments to handle differences in substrate induced responses. You would have a choice of whether to use fixed or random effects to model the differences among soil samples.

I know that this goes quite far beyond the question that you asked. But you seem to have a nicely designed and executed study that deserves a solid statistical analysis. Think of this as an opportunity to start to learn some fundamental principles of statistics that will serve you well throughout your career.

• Hi, thank you for taking the time to share all this information. It made me realize that the expectations for my data analysis were not as effective as they should be, i.e. your description would represent and analyze the data more effectively. I probably would have learned more if I went your route. – Rachel Brockamp Dec 12 '19 at 20:12