I would like to ask for help in choosing the correct statistical test for analyzing experimental data on small samples (4 repeats)
THE EXPERIMENT: the experiment simulates development of a deposit on a sample. It allows for evaluation of different deposit sources and factors affecting its growth. Each combination of source & factor is a treatment. The main response is the deposit extent recorded 4 times over the experiment duration.
THE DESIGN OF EXPERIMENT:
- 18 treatments
- 4 repeats for each treatment
- All the setups are tested at the same time (18 treatments x 4 = 72 setups), under the same, controlled conditions
- the test goes for 4 weeks and responses are collected 4 times for every single setup
I choose 4 repeats, because the reference setups show high repeatability, and because of practical limitations. However, for a few of the treated setups I have identified single outliers, based on visual data analysis. So for some setups I have only 3 repeats available.
THE DATA ANALYSIS: The main aim is to compare the final deposit extent and its growth trend (e.g. inhibited after 1 week vs still developing). I was considering the following approaches:
- DOE in SAS JMP (regression on dummy categorical variables), but it always asks for randomization, while all my setups are run at the same time
- ANOVA, but I was advised to use it only for much larger sample sizes (>30)
- Recent idea: compare data visually based on graph with 95% confidence intervals using a Student's t distribution (CONFIDENCE.T function in Excel)