Computing Information Loss



Regarding calculation of information loss, in section 18-1 of Biostatistics for Biomedical Research (BBR) the following example is given:

“Some types of information may be quantified in bits. A binary variable is represented
by 0/1 in base 2, and it has 1 bit of information. This is the minimum amount of information
other than no information. Systolic blood pressure (SBP) measured accurately to the
nearest 4mmHg has 6 binary digits (bits) of information (log2(256)/4 = 6). Dichotomizing
blood pressure reduces its information content to 1 bit, resulting in enormous loss
of precision and power.”

Can anyone help explain the calculation that shows SBP values have 6 bits of information?

Thank you!


Systolic blood pressure has a biologic range of about 256mmHg which is 2^8. The measurement error is close to \pm 4 mmHg which amounts to ignoring the last 2 binary digits of the measurement, or 2 bits.


Thank you Professor Harrell!