I am analyzing air pollution levels across 5 firms. For each firm, I have daily air pollution measurements taken over 5 days. My goal is to evaluate the variability of air pollution levels between firms and within firms across different days. However, there are additional sources of variability in my dataset due to measurement tools, which complicates my analysis.
Here is a sample table representing my data:
| Firm | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 |
|---|---|---|---|---|---|
| Firm 1 | 0.198 | 0.244 | 0.234 | 0.179 | 0.244 |
| Firm 2 | 0.188 | 0.215 | 0.161 | 0.139 | 0.210 |
| Firm 3 | 0.215 | 0.220 | 0.255 | 0.213 | 0.208 |
| Firm 4 | 0.258 | 0.223 | 0.257 | 0.167 | 0.193 |
| Firm 5 | 0.223 | 0.252 | 0.238 | 0.271 | 0.195 |
The challenges are as follows:
a) Measurements were taken using two different brands of measurement kits. Unfortunately, I do not have information on which kit was used for each measurement.
b) There is known inter-kit variability (variability between the two kits) and intra-kit variability (variability when the same kit is used repeatedly on the same sample). Both of these are documented in the literature.
Given the above context, I would like to address the following questions:
- Does the within-firm variance calculated from my data represent only day-to-day variability, or does it also include measurement errors (inter-kit and intra-kit variability)?
- Would it be misleading to interpret the calculated within-firm variance as purely day-to-day air pollution variability?
- What statistical methods can I use to separate the true day-to-day air pollution variability from the measurement errors caused by the kits?
- How can I quantify and present the proportion of variance explained by between-firm variance, within-firm variance, and the measurement errors (inter-kit and intra-kit variability)?
- Are mixed-effects models or other techniques appropriate for this type of analysis? If so, how would I incorporate known inter-kit and intra-kit variability values into the model?
ULTIMATE GOAL and QUESTION: My ultimate goal is to assess how much air pollution fluctuates from day to day within each firm and report whether this fluctuation is significant compared to other sources of variability (e.g., firm differences or measurement errors).Could you advise me on appropriate analysis methodologies and plots to effectively report on this goal, in a scientific study?
