Measurement differs from statistics in that statistics deals with the analysis and interpretation of numerical facts or data, while measurement is the vehicle that provides the data.  Therefore, measurement is fundamental.  You can have the best statistical analysis, but if the data obtained is erroneous, then your conclusions are wrong.

For example, suppose you want to determine the prevalence of tuberculosis in a specific geographic area, such as a city or village.  A sample survey is designed with proper sample size and power.  Many developing countries do not have access to the latest diagnostic and testing methods and attempt to diagnose TB by looking for stained bacilli under a microscope.  This diagnostic method is roughly equivalent to looking for a needle in a haystack and often results in false negatives.  In such a case, the statistical sampling technique used by a researcher could be correct, but the reported prevalence rate would be erroneous because of the inaccuracies associated with the diagnostic (measurement) method.