I have a two-factor experiment. We investigated the effect of the drug on the level of erythrocytes after surgery. One of the factors is the presence of the operation, the second is the presence of the drug, the third is the interaction of these factors. I have difficulty in interpreting the received data. We have one time point. Example: we obtained the influence of the operation factor (P
It depends on the way the effects of the two factors (drug and operation) are coded.
For instance, the default coding scheme in R is "contrast coding", where one level is chosen as the "reference" level (numerically coded by 0, and the other level is coded by 1). You would typically choose "no" (operation) as the reference level for the factor "operation" and "no" (drug) as the reference level for the factor "drug".
It then depends further on if your model includes an intercept term. The default in R is again that the model does include an intercept term. Therefore, you get the folloring coefficients with the following meanings:
a) the intercept (=mean response for non-operated untreated)
b) the drug effect (=mean difference drug yes vs. no for non-operated)
c) the operation effect (=mean difference operation yes vs. no for untreated)
d) the interaction (= mean difference between the drug effect for operated vs. the drug effect in non-operated; what is the same as the mean difference between the operation-effect for treated vs. the operation effect in untreated).
If you want other contrast (e.g. the operation effect in treated or the drug effect in operated), you can either re-code the levels appropriately or use a function to make these comparisons based on the fitted model. A trick (in R, again) is to combine both factors into a single factor with 4 levels and use multcomp::glht() to get all desired contrasts between any of these 4 groups.
Hello Irina Adler. The significance of the interaction term tells you that the effects of the focal variable at the two levels of the "moderator" (or effect modifier) differ significantly. In other words, the difference in differences is significant. In this situation, it doesn't make much sense to look at the main effect for the focal variable, because it averages two heterogeneous (simple main) effects. Sometimes, people go on to examine each simple main effect, testing for a difference from 0. I have no idea how to do that via Statistica. I've searched for documentation for it online without much success. I found a YouTube video showing how to do2x2 ANOVA including interaction plots, but it had nothing on tests of the simple main effects. Do you have access to any other software?
HTH.
Hi Irina Adler. what software did you use in the analysis? and could you please attach the result
Jochen Wilhelm Thanks for the answer. Do you mean coefficients when using post hoc test or identify the type I errors? I thought that to calculate identify the type I errors statistical program calculates the Fisher criterion, formula: F (for factor A) = MSA/MSW. F (for factor B) = MSB/MSW.
I wrote the code in statistics and in minitabs. Each of the 2 factors in different columns, drug factor and surgery factor marked as 1 and in groups where these factors were absent marked as 0. I don't know how to write this code for two-way ANOVA differently.
No, the F statistics are not the coefficients. I thought if you want to interpret the effects, you would want to know by how much the response differs between the groups. This "how much" is given by the coefficients of the linear model that is behind your ANOVA.
https://en.wikipedia.org/wiki/General_linear_model
I don't know minitab.
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