Sidak correction For variables A (product research) and B (product purchase), I am proposing to do three levels of analysis as follows:


*

*Test 1: Overall: 
The goal here is to see if there is a relationship between A and B. My data is at the interval level and the scatter plot shows a linear relationship, so I am doing bivariate correlation using Pearson's r.

*Test 2 (Demographic difference in the relationship between A and B):
The goal here is to see if gender, age and income level affect the relationship between A and B. I am finding this out using GLM (ANCOVA), so I am running 3 separate tests (i.e. on gender, age and income).

*Test 3 (Equality of the correlation coefficients):
I know this is controversial and perhaps meaningless but I am curious! My goal here (if I do this test) is to see how A and B correlate for different demographic characteristics (i.e. it could be higher for males, or for people under the age of 18 years). There are eight controls - two for gender; three for age (e.g. less than 18 years, 18 to 45 years and Over 45 years) and five for income level. I am doing three equality of correlation tests again.
Given the above, I am performing seven tests on the same data.
Question: Should I do do Sidak correction based on all seven tests or do separate corrections (i.e. one for Test 2 and one for Test 3 - unsure how to handle the correction for Test 1)? 
 A: This reply begins by addressing the remarks in "Test 3" concerning the meaning of comparing correlation coefficients, then it applies the results to the question itself.
We need a simple example that is easy to understand and interpret.  To introduce it, the following graphics document the heights (in centimeters) and weights (in kilograms) at matriculation of all 600 students currently attending a former all-women's college which recently became coeducational.  A minority (20%) of students are male.  Values for males are shown in blue and values for females in pink.  First, the frequency histogram of heights:

Now the frequencies of weights:

You can see these are realistic values (although a bit on the small side--perhaps some precociously young students have been admitted; there is no football team).  How about their correlation?  We use a scatterplot:

This is a beautiful example of the classic football-shaped point cloud; there are no problems with nonlinearity, heteroscedasticity, outliers, or limited data (there are 125 males and 475 females).  If anything is suitable for correlation analysis, this is it.  So let's do it:
Correlation coefficients
Males:   0.51
Females: 0.78

Tests will find these to be strongly significantly different from each other (as well as different from 0).  What do you suppose it means?  In this case, absolutely nothing.  It's time to reveal where these data really came from.  An iid sample of 600 (height, weight) values from a bivariate normal distribution with correlation coefficient 0.8 was generated by computer.  Each of those 600 cases was randomly assigned to be either "male" or "female."  The probability of assignment increased with height, resulting in the 125 "males" having greater heights on average and, due to the correlation with weights, they also have greater weights than average.
In effect we are carving the bivariate cloud into two overlapping regions.  One of them is the upper right tip (the males), emphasized in this version of the preceding plot:

It should be visually obvious that the tip of such a cloud will tend to be diffuse: its correlation coefficient is less than that of the cloud itself.  (It's not hard to generate examples where the cloud has high absolute correlation but its tips have almost zero correlation.)  The reason stems from the limited range of the subpopulation (males) compared to the overall range of the population (in terms of either height or weight).
That explains the difference in correlation coefficients.  It's purely a mathematical phenomenon related to the fact that males and females have different average heights (and weights), that's all.  It does not imply there is any gender-related difference between the height-weight relationships: obviously, in this case, there is no such difference, because no difference was used to create the data.
For this reason, merely testing correlation coefficients for differences among subpopulations in a sample is practically useless.  Instead, look to exploratory graphics (like these here) to get a sense of what's going on and use regression modeling to quantify relationships.
Now we have an answer to the main question (as well as to the four dozen or so questions that preceded it): making the corrections is pointless.  Analyze the data in a different way.
A: *

*There is no rule of thumb on how to decide which hypothesis should be bundled together into one "family", nor which measure of error to control for (FWE, FDR,...). Also- are you actually interested in inference on all of your variables or do you just want to control for possible effect? If you are not interested in inference on some variables, just leave them in the regression and don't count them as a "hypothesis".

*Sidack is appropriate when the test statistics are independent. This does not seem to be your case.

*For the tests you have mentioned I suggest fitting one linear model, with one dependent variable and all your predictors and interactions of interest. The tests you want will now be linear contrasts on the model's coefficients. Now use the multcompt R package to define these contrasts. The glht function will give you multiplicity control by using the exact joint distribution of the test statistics. If you do not have access to R and then consider using the Holm correction which does not assume independence between the test statistics. 

A: The first test needs no correction - it's one test.
The second test (a GLM with several IVs) also needs no correction if you are including all three demographics in one GLM. If N is reasonably large, this is what I recommend. 
The third test is silly, as @whuber and I have been telling you, and as he just demonstrated beautifully.
