# Statistical test selection

#### Octo

##### New Member
Hi,
I produced some data during an experiment but I am not sure which statistical test I should use. I hope that you could help me with this.

Globally, I expose a defined number of cells to different drugs formulations in order to assay their toxicity (it's an MTT assay for whom is familiar with it).
So the cells are exposed to different formulations at various concentrations for 2 timepoint (24h and 48h). Consequently, I assume that my experiment count 3 predictor variables (formulation, concentration and time of exposure) and one outcome variable (the percentage of surviving cells compared to a control condition).

For the precision, they are not repeated measures and i fit a non-linear curve describing the surviving fraction at the various concentrations for each drug and exposure time.
The questions I would like to answer are:
1. Treating apart the results for 24h and 48h, is there a formulation which induces a significant toxicity among the considered interval of concentration (the aim is not to assay if one formulation is more toxic than another but to assay if a significant toxicity is detected compared to the control condition). For this part, I assume to use 2 distinct 2-way anova (one for each timepoint) combined with Dunnett's multiple comparison test to compare the surviving fraction of the different concentrations inside each formulation compared to a control condition.
2. Once I would have determined which formulations show a significant toxicity along the considered interval of concentration, I would like to know if there is a significant difference between the same formulations at the 2 timepoint. But I am not sure about the test to select, may be a multiregression analysis?

#### Karabiner

##### TS Contributor
As far as I can see, your outcome variable is not % of surviving cells, but survival yes/no?
The percentage would be an outcome variable for example in an experiment where you
treat 2x10 cell samples with a drug. The n=20 groups of cells would be the "subjects" there,
and % survival their outcome characteristic. In your description, it seems as if you have 1 sample
of cells in each condition and for each of these n cells per condition their survival yes/no
is determined. So you'd need models for binary outcomes, I suppose.

With kind regards

Karabiner

#### Octo

##### New Member
Dear Karabiner,

Please find in attachement an exemple of my data. As you can see, the outcome variable is the percentage of surviving cells. The postulate is that a more toxic drug will kill a greater fraction of cells that a less toxic one.
The outcome variable is not defined as a binary response because the number of cells involved in a test is important (My test involves 10000 cells x the number of concentration studied x the number of drugs studied x 2 endpoints x 3 technical replicates by test x 3 biological replicates).
For this reason, the fraction of survival cells is assessed by the metabolic activity of the sample, compared to a control condition (which is possible because all of my conditions are seeded with the same amount of cells)
About the exemple of my data provided:
• the first column is related to the concentration of the drug assessed.
• The columns mean are related to the mean of the metabolic activity detected among 3 technical replicates, the values are povided in %
• The columns SD and N spoke by themselves I suppose
• Here are the results for the 4h endpoint, The 48h related ones are stored in another spreadsheet. Best,
Octo

#### Karabiner

##### TS Contributor
So you have a sample size of n?3 in each condition. Your suggested analysis makes sense,
generally (I guess you meant oneway ANOVA, not 2-way, since there is no second factor
involved?), but I do not know whether it works for such a small sample size. For small
sample sizes, one would rather use Kruskal-Wallis H-test, but power would be very
low here.

For the comparison of a single drug between 2 time points, usually it would be a
dependent samples t-test. Regarding the small sample size, Wilcoxon signed rank test
would be preferable.

With kind regards

Karabiner

Dear karabiner,