I am testing the ability of bacteriophage to combat biofilms.
I have one interval dependent variable and two independent categorical variables (one being treatment time)
The dependant ratio/interval variable is the amount of biofilm (measured by absorbance). The independent categorical variable is condition i.e I have a treatment group and an untreated control group.
I am measuring absorbance (effect of treatment) at different time periods post treatment (after application of phage) such that time becomes a predictor for amount of biofilm as well.
I would like to know not only if the overall (global) effect of treatment is significant compared to control, but also to gain insight into the significance of changes at each time period?
If I use a Two Way Anova I cannot do post hoc tests on the effect of condition (treatment or control) because there are only two levels. In addition analysing treatment time independently of condition with post hocs is also meaningless to me?
Should I do a separate ANOVA for each time interval?
Hello. To your question:
" If I use a Two Way Anova I cannot do post hoc tests on the effect of condition (treatment or control) because there are only two levels."
If a factor (treatment in your case) has only 2 levels, it has no sense to do the Post Hoc Tests - they only say, which pairs of factor levels differ. And if your ANOVA result for that factor is, that it has an influence on the measured variable (absorbance), then it also means, that the 2 levels of treatment significantly differ.
So there is no need to do Post Hoc Tests for factors with only 2 levels, no software does it.
Hi Marc-Michel,
Doing separate ANOVAs increase the alpha's error, so don't.
Here, if I understood well your plan, you have different times of measure (how many?) with an independent variable (i.e., treatment vs control). Therefore, you have a mixed ANOVAs with repeated measures.
Then, you can perform a posthoc test (e.g., a Tukey test) for the the following set of variables: Time (if you have more than two time of measurement; e.g., Time 1, Time 2, Time 3, ...Time X); and Condition (Treatment vs control) x Time.
As Veronica said, there is no need to check with a posthoc test if treatment vs control differ significantly because you have the answer with the ANOVA (you can just check the means to see which one is higher than the other). However, with a posthoc test, you will be able to see if Time 1, 2, 3 differ significantly by comparing them in pairs (e.g., Time 1-Time 2; Time 1-Time 3; Time 2-Time 3). Also, you can have detailed differences if you cross Time and Condition (Treatment vs control).
You can also introduce another independent variable: gender (if it encounters your interest).
Hope that helps,
Best regards
If you said how many time points there are I missed. Here is an example of one way to do your analysis that assumes 3 time points. You can modify the code as needed. Y1, Y2 and Y3 are the variables in the data file that record the 3 DV at the 3 time points.
GLM Y1 Y2 Y3 BY Group
/WSFACTOR=Time 3
/PLOT=PROFILE(Group*Time)
/EMMEANS=TABLES(Group)
/EMMEANS=TABLES(Time)
/EMMEANS=TABLES(Group*Time) COMPARE(Group)
/EMMEANS=TABLES(Group*Time) COMPARE(Time)
/WSDESIGN=Treatment
/DESIGN=Order.
The COMPARE keyword on the EMMEANS sub-command will give you the simple main effects of the variable in brackets at each level the other variable involved in the interaction. You may need only one of those EMMEANS lines. You may also have to switch the order of the variables in the PROFILE plot to get the graph looking the way you want.
HTH.
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