(I have no real idea what to tag this with because I'm no statistician and I don't know what field this falls into. Feel free to add more suitable tags.)
I work for a company that produces data analysis software, and we need a decent set of data to test and demo our latest product with. We can't just fill the database with the output of a random number generator because the program's outputs would become nonsensical. One of the simplest ways to get such data is from a client; we have a large body of data from a trial we ran. Now, obviously we can't publish a client's actual data, so we need to alter it a bit, but we still need it to behave like real data.
The aim here is to take their set of data, and apply a "fuzz" to it so that it can't be recognised as specifically theirs. My memory of statistical theory is itself a little fuzzy, so I'd like to run this by you guys:
Essentially, the data we have (from the client) is itself a sample of all the data that exists (in the country, or the world). What I'd like to know is what type of operations can be applied to make the sample no longer strongly representative of the client's sample population, while still keeping it roughly representative of the world's population.
For reference, as far as we're aware the data we have generally follows rough normal (Gaussian) distributions.
The original dataset isn't widely available, but could theoretically be recognised from some regionally-specific characteristics (we don't know what those characteristics are, and it's doubtful whether anyone does to a sufficient level, but we know that variations exist from place to place). Anyways, I'm more interested in the theory of this than the practice - I want to know whether an operation makes it impossible (or at least difficult) to identify the source dataset by parameter X, whether or not anyone has or could work out parameter X in the first place.
The approach I've come up with is to separate the readings into the various types, (without giving much away, let's say a group might be "length" or "time taken to do X".) For each of those, calculate the standard deviation. Then, to each value, add a random value between the positive and negative values of (n * stddev) where n is some fraction that I can use to tune the result until the data is sufficiently "fuzzed". I didn't want to simply apply a static range (say, random between 90% and 110% of the original value) because some values vary much more or less than others - in some measurements, being 10% over the mean is barely noticeable, but in others it makes you a serious outlier.
Is this sufficient to mask the source of the original data? If not, by which statistical measures would the data still be identifiable, and how would I mask those while still keeping the resultant data vaguely realistic?
