I am completely new to both JMP and statistics and would like some help with analyzing some data (see attached file).
I work as a microbiologist and have stained bacteria from 4 different fermentations on 2 different glass slides for each fermentor. The stainings result in colored cell structures, of which I took two photos per glass slide. I now would like to know:
1) If the differences in the amounts of stained cell structures on the photos are dependent on the fermentor (A/B/C/D) or simply dependent on the glass slide.
2) If the differences in the total amount of stained structures between fermentors are significant.
How can I do this in JMP? I am very thankful for any help!
I just have to say that this common practice of performing the study and then considering the analysis is risky. It is backwards. The only way to be sure that the data coming from the study will support the analysis is to start with the analysis in mind!
The pictures are the lowest level 'experimental unit' and so do not enter directly into the analysis. They will be used to estimate the experimental error that is used in any hypothesis tests. The slides are the next level of experimental unit and enter the model as a 'random effect.' So really you have one categorical Fermentor with four levels and another (nested) categorical factor Slide with two levels. I assume that these are the only four fermentors so you want to know about fixed effects (e.g., is the response for fermentor A higher than from the others). This situation is easily handled by a 'two-way analysis of variance.'
I just looked at your data table. It seems that it was imported from a spreadsheet perhaps because the expected column properties that are created by JMP when you design the experiment with JMP are missing. Also, the sorting eliminated the possibility of checking the independence of the errors to verify the assumption of the regression model. The sorting also begs the question of how you actually ran the study: is it completely randomized or were some factors changed less often? That answer makes a huge difference in the analysis.
Here is the result of such a model:
There does not seem to be a significant difference between the fermentors or the slides. I attached the modified data table and saved script for the Fit Model dialog and the Fit Least Squares platform.
Adding to @markbailey's excellent advice, here are some things to think about:
1. How much of a change in the response variable (Colored Structures) is of practical significance? What is the smallest increment of change you care about or would be of scientific interest?
2. The pictures may be considered components of the measurement system. What is done with the pictures? How is the response quantified from the pictures?
3. Here is a variability plot for the data set:
As you can see there is a good deal of variability within slides 4 and 8 (is this measurement error?). This will ultimately have a large affect on any quantitative analysis. This will also likely make it difficult to detect Fermentor-to-fermentor variability.
Thank you so much @statman for your input!
I am not sure how much of a change in the response variable is of practical significance. I would prefer to see larger differences between fermentors than what I obtained :). Thank you for the nice plot! It makes it more clear that I will probably not be able to see any differences from this experiment.
Thank you so much @markbailey for your help! You really made me look at my data in a different way. The counting of the colored structures from the pictures was performed manually, but the pictures were coded by my colleague to avoid any bias. The staining, resulting in the different slides, was performed on two slides at the same time from one fermentate. Then the staining of two more slides was performed, but for another fermentate and so on. Yes, the data was imported from an Excel sheet.
I will look into what you've written here, and also read up a little more on statistics. Thanks again for the help!