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I have 5 flasks.

Flask 1 has only water (50 ml).

Flask 2 has salt water (50 ml) at a certain concentration (say 10%). I call it dilution factor 1x.

For flask 3, I create a 2x dilution solution by mixing 10% salt solution with water in 1:1 ratio.

For flask 4, I create a 4x dilution by mixing 10% salt solution with water in 1:3 ratio.

For flask 5, I create a 8x dilution by mixing 10% salt solution with water in 1:7 ratio.

I add bacteria in each flask and calculate bacterial growth* after a day. I want to know if there is a significant difference in bacterial growth between the different flasks (i.e. dilution factors). Can I use one-way ANOVA for this, and then use Tukey's test to do pairwise comparisons? My only concern is whether the variable I am testing here (dilution factor) be considered categorical (a requirement for ANOVA) and if the different levels of this variable can be thought to be independent of each other (another requirement?). All experiments were done in triplicates.

*bacterial growth is quantified by measuring the absorbance of the bacterial solution at a wavelength, which is a function of how many bacteria are in the solution.

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    $\begingroup$ As such, you can certainly use these discrete levels of concentration as factor levels in ANOVA, but with only one flask per factor level you have no more degrees of freedom to work with. $\endgroup$
    – Galen
    Jul 29 at 16:39
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    $\begingroup$ You may find that terms like "treatment" or "group" or "condition" are clearer for readers on this site. The term "flask" sounds like you are considering an individual flask, rather than a collection of flasks that were identically prepared (up to an equivalence relation). $\endgroup$
    – Galen
    Jul 29 at 16:44
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    $\begingroup$ You have the concentration (salt molarity) of each type of flask, right? It might make more sense to model the data continuously, rather the discretizing the concentrations. $\endgroup$
    – Dave
    Jul 29 at 16:53
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    $\begingroup$ Another question with respect to ANOVA is whether the OD600 outcome values (or whichever wavelength you use for absorbance) have close to constant variance, over the range of observations seen in the 5 circumstances. $\endgroup$
    – EdM
    Jul 29 at 16:58
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    $\begingroup$ It would be regression, perhaps with some nonlinearity like splines. The small sample size concerns me for such an approach, however. // When you get into the details of ANOVA, it turns out that ANOVA is a particular kind of regression. $\endgroup$
    – Dave
    Jul 29 at 19:56

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