# What is statistical Bias?

I am asking this question in context to section 4.1 in this paper: security control methods for statistical Database (http://www.utdallas.edu/~muratk/courses/privacy08f_files/stat_database_sec.pdf)

As I am not statistician or Mathematician so I had hard time understanding it. If someone could explain what is statistical bias or the bias problem in section 4.1 of this paper, that would be great :).

Thanks! :)

• Bias in statistics comes up in several ways. The bias of an estimator is the difference between its expected value and the thing it estimates. However, bias in the sense the term is being used in the paper - is defined in the paper, 2nd paragraph of p522, but it seems somewhat specialized to the application. You'd need to clarify in what way that definition was inadequate. Jul 23, 2014 at 11:00

Biasedness is a property of a statistical method you're using to discover the 'true value' of a parameter (normally the relationship between two variables). If the method is 'biased', then it will not estimate the true value, except by luck. Typically, this property gets worse as you get more data: as your sample size grows to infinity, you become certain about the wrong number!

A common example would be if you're looking at the relationship between years of education and income. The typical estimate of the relationship between these two variables will be biased. This is because those with more years of education will tend to have better social groups, more supportive families, and other things that help one earn more independently of their education.

Consistency, a related property, is when your method gets better at predicting the true value as the sample size increases. Some methods may be biased but consistent, so that in small samples they tend to be wrong, but as the sample size grows, they zoom in on the true value.

So I just skimmed the paper... but the idea is to perturb the data returned from a query to stop a snooper discovering personal information by making very specific 'summary' queries.

eg (my example- I just skimmed the paper) maybe you have an age variable and just add zero mean gaussian random noise to each person in the database. Then in any sizeable group (in your database query, eg 40-50 year old smokers ) the average age stays ~ the same (as the unperturbed statistic for the group, say =48). it is unbiased meaning that if you do multiple queries for the average age of your group (adding new noise each time to your data), then the average over each query for the average age using the perturbed data will converge to the average age for the unperturbed data ( as you average over more and more queries).

Now if you ask for the variance in age of the group then this will be biased by adding noise to the age variable - since the very addition of noise makes the perturbed age data more variable than the original group's (imagine you only had 1 person in the group). No amount of averaging of the variance across different queries will reduce the variance to that of the original groups variance.

In terms biasness in estimators I always like to have this image in mind http://www.bing.com/images/search?q=statistical+bias+estimator&FORM=HDRSC2#view=detail&id=1A42A3038835264F8655F4AC54D928BAD6D6A359&selectedIndex=5