show high correlations, as they stem from the same chemical process(es). these correlations depend on space (i.e., location) and time (i.e., period). therefore, a pollutant distribution is not necessarily representative for every location and every period. if a low-cost measurement instrument is calibrated with field data in a multivariate manner, more precisely by collocation next to a reference instrument, the relationships between the different compounds are incorporated into the calibration model. by relocation of the measurement instrument, erroneous results can be produced. a twenty-first century example is the covid-19 pandemic, where variations in sampling bias in covid-19 testing have been shown to account for wide variations in both case fatality rates and the age distribution of cases across countries. statistical corrections for a biased sample if entire segments of the population are excluded from a sample, then there are no adjustments that can produce estimates that are representative of the entire population. but if some groups are underrepresented and the degree of underrepresentation can be quantified, then sample weights can correct the bias. however, the success of the correction is limited to the selection model chosen. if certain variables are missing the methods used to correct the bias could be inaccurate. for example, a hypothetical population might include 10 million men and 10 million women. suppose that a biased sample of 100 patients included 20 men and 80 women. a researcher could correct for this imbalance by attaching a weight of 2.5 for each male and 0.625 for each female. this would adjust any estimates to achieve the same expected value as a sample that included exactly 50 men and 50 women, unless men and women differed in their likelihood of taking part in the survey.