Any Test comparing differences among differences in %?

[Victor Tarrago]

Dear colleagues,

I would like to ask a question to the list hoping that somebody could help
me.

We interviewed buyers of a certain product. Amongst other things we asked
them what brands and what brand activities they remember having seen in the
point of sale (Multi response).

The table below summarizes the remembered brand activities broken down
into “bought the brand” and “Did not buy the brand”.

Let’s take “Brand Activity A” as example: 281+176 respondents remember
having seen the brand activity of which 176 (31.4%) bought the brand and
281 (20.8%) did not buy it.

That corresponds to 31.4% of buyers and 20.8% of not buyers remembering the
activity.

The last column of the table states the difference between these two
percentages (31,4% - 20,8% = 10,7%)

The second table shows the same calculations but just taking into account
the brand activities of brand “X”.

What I am looking for is a way to compare the differences in percentages
between the two tables (Differences in column percentages).

For example: Is the effect (assuming a causal model) of brand activity A
the same for brand X as for the total market? Is the difference in the
total market (10.7%) significantly higher than for brand X (3.8%)? Is there
any statistical test to do that? Are the differences significant?

Thank you very much in advance for your comments!

Table 1. ANY BRAND (Total sample, including Brand "X")
   Has purchased
   No Column Yes Column Dif.
% visibility  1353 % 560 % % Columns
Brand Activity A 281 20,8 176 31,4 10,7
Brand Activity B 131 9,7 88 15,7 6,0
Brand Activity C 147 10,9 69 12,3 1,5
Brand Activity D 214 15,8 160 28,6 12,8
Brand Activity E 357 26,4 167 29,8 3,4
...   19 1,4 19 3,4 2,0
...   143 10,6 75 13,4 2,8


Table 2. BRAND "X"
   Has purchased
   No Column Yes Column Dif.
% visibility  324 % 214 % % Columns
Brand Activity A 92 28,4 69 32,2 3,8
Brand Activity B 41 12,7 41 19,2 6,5
Brand Activity C 40 12,3 26 12,1 -0,2
Brand Activity D 53 16,4 52 24,3 7,9
Brand Activity E 92 28,4 62 29,0 0,6
...   6 1,9 6 2,8 1,0
...   37 11,4 30 14,0 2,6

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