Dear,
In the preparations for publishing a manuscript, we have a big argument about the proper analysis of variance to compare multiple groups for a certain staining quantification.
We have two proteins (A and B) we know that they significantly promote a third protein (C) staining when they are added as a mixture than when they are added as individual proteins due to the effect of these two protein interactions (A & B) with each other which results in a conformational change in protein B. And we know that protein C does not interact with B, but it does interact with A.
Any way, now what we want to analyze is the change in protein A and B functions in the mixture if we remove a certain post-translational modification that occurs in protein A and in protein B as well. To remove that certain post-translational modification, we need to treat the proteins with X enzyme. One issue is that we cannot heat inactivate X enzyme after incubation with either proteins. Thus, when we added the protein mixtures either both treated or one of them treated to compare to the untreated mixture, we had the enzyme there and we included the protein buffer control with the enzyme added to make sure that the effect on protein C staining comes from removing the post-translational modification, not from the remained enzyme with the added proteins to cell cultures.
Now, we have a dataset which has been arranged based on the independent variables in a way to analyze the differentiation in protein C staining (dependent) between the dataset groups. I am very convinced that we do not have in the given dataset a proper/consistent classification for any subcatagories in this dataset to analyze suitable for two-way anova. To me, the dataset are suitable for one-way anova if we consider the protein mixture as one protein (one variable) wither treated or not; otherwise, three-way anova if we consider each protein as a different variable when each is either treated or not. The images below are for the same dataset but with different variable arrangements on the datasheets.
Please, inspire me.
Thank you
I may not have completely understood the experiment, but to me it seems to be a 3-factorial experiment:
Response: stainging (intensity) of C
Factor 1: solution contains A (yes/no)
Factor 2: solution contains B (yes/no)
Factor 3: X is present (thereby modifying A and/or B) (yes/no)
You may think of this as a combination of two 2-factorial experiments (factors 1+2), one for each level of factor 3. What you described in thebeginning is the experimentin the absence of X. If C does not interact with B, the simple effect of adding B should be small, and the simple effect of adding A should be measurable. Adding both together should give an even stronger signal. This additional increase (above the sum of the two simple effects) is the interaction of the two factors. This can be analyzed in a 2-way ANOVA that analyzes just this interaction.
Considering X (present or not) adds one layer of complexity. You get the same 2-way interaction in the presence of X, too. And what you are actually interested in the the difference between these two interactions. This is analyzed as the 3-way interaction in a 3-way ANOVA.
Thank you Dr. Wilhelm.
The challenge in this to make the decision is that in the presence of both proteins, we have them either: 1) both A & B are not treated (has no enzyme added), 2) Only A is treated, but not B (still enzyme added), 3) Only A is not treat, but B(still enzyme added), 4) or both A & B (still enzyme added) are treated. However, the enzyme in the buffer control has no enzyme added or not which makes 4 factors:
Factor1: Protein A added
Factor2: Protein B added
Factor3: Either protein pre-incubated with the enzyme (treated)
Factor4: Enzyme remained in the protein mixture added to cells, or not
Which make it four-way anova and too complex
Hi Hana,
If you want to indicate the absence or presence of protein as another factor, then you need to add one more column ("protein presence") and indicate ("yes" / "no"). In this case, you will really get a four-way anova.
From my humble experience, you have very small sample sizes for the analysis. For a qualitative analysis, there is simply not enough statistical power and there is a high risk of making a type 2 error... Try to increase the sample size (to calculate the optimal value, a power analysis must be performed).
Kind regards,
Michael
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