What indicates a proportional error in the results when comparing two methods?

A proportional error arises when the error in measurement increases with the concentration of the analyte. This means that as the concentration increases, the discrepancy between the values obtained from the two methods also increases, reflecting a relationship where the error is relative to the magnitude of the measurement.

Therefore, increased variance as concentration increases is indicative of a proportional error; it demonstrates that not only is there a systematic error present, but it also worsens as the concentration goes up. This variance suggests that the performance of the method is not consistent across different levels of concentration, which is a key characteristic of proportional errors.

The other choices reflect different types of errors that do not align with the concept of proportionality. A consistent difference across all concentrations implies a systematic bias rather than a proportional relationship. A constant difference regardless of concentrations suggests a fixed absolute error, and close clustering of data around zero indicates minimal error but does not address proportionality regarding concentration changes. These characteristics lead to misunderstanding of the nature of proportional errors in analytical chemistry.